FACTORIZATION METHOD
(1). Factorise the following expression 2x2 + x – 15 S.S.C.E NOV 1989 NO
(A)(2x + 5)(x – 3) (B)(2x – 5)(x + 3) (C)(2x – 5)(x – 3) (D)(2x – 3)(x + 5)
Solution:-Using CASIO fx-991MS calculator
make x = any number of your choice from 1,2,3,-------------------100 or any
i.e make x = 1,2,3,4,----------------------------------------100 or 10000......contd
Using CASIO fx-991MS calculator make x = 9
[ON] [9] [SHIFT] [STO] [x] (X=9)
Note:-Please use the key [AC] during calculcations after you press the key [ON] on any question given.
[AC] [2] [ALPHA] [X] [X2] [+] [ALPHA] [X] [-] [1] [5] [=] (156)
If option A,B,C,D gives 156 it is correct but if it doesnt give 156 it is wrong
Checking option (A)(2x + 5)(x – 3)
Using CASIO fx-991MS calculator since X=9
[AC] [(] [2] [ALPHA] [X] [+] [5] [)] [(] [ALPHA] [X] [-] [3] [)] [=] (138)
Option “A” is wrong because it did not give 156
Checking option (B)(2x – 5)(x + 3)
[AC] [(] [2] [ALPHA] [X] [-] [5] [)] [(] [ALPHA] [X] [+] [3] [)] [=] (156)
Option “B” is correct because it gives 156
Checking option (C)(2x – 5)(x – 3)
[AC] [(] [2] [ALPHA] [X] [-] [5] [)] [(] [ALPHA] [X] [-] [3] [)] [=] (78)
Option “C” is wrong because it did not give 156
Checking option (D)(2x – 3)(x + 5)
[AC] [(] [2] [ALPHA] [X] [-] [3] [)] [(] [ALPHA] [X] [+] [5] [)] [=] (210)
Option “D” is wrong because it did not give 156
(2). Construct a quadratic equation whose root are - ½ and 2
(A)3x2 – 3x + 2 = 0 (B)3x2 + 3x – 2 = 0 (C)2x2 + 3x – 2 = 0 (D)2x2 – 3x + 2 = 0
Solution:-Using CASIO fx-991MS calculator, make x = -1/2 and x = 2, To produce the correct answer first make x = - ½
Checking option(A)3x2 – 3x + 2 = 0
[ON] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = -1/2)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [3] [ALPHA] [X] [x2] [-] [3] [ALPHA] [X] [+] [2] [=] (4.75)
Option (A) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (B)3x2 + 3x – 2 = 0
make one of the factors x = - ½
[AC] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [3] [ALPHA] [X] [x2] [+] [3] [ALPHA] [X] [-] [2] [=] (-2.75)
Option (B) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (C)2x2 + 3x – 2 = 0
make one of the factors x = - ½
[AC] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [2] [ALPHA] [X] [x2] [+] [3] [ALPHA] [X] [-] [2] [=] (-3)
Option (C) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (D)2x2 – 3x + 2 = 0
make one of the factors x= - ½
[AC] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [2] [ALPHA] [X] [x2] [-] [3] [ALPHA] [X] [+] [2] [=] (0)
one of the root is correct because it gives zero. Since it gives zero calculate the other root go to the next factor x = 2 make the other root x=2
[AC] [2] [STO] [X] (x=2)
[AC] [2] [ALPHA] [X] [X2] [-] [3] [ALPHA] [X] [-] [2] [=](0)
if the roots -1/2 and 2 is equal to 2x2-3x+2 option E is correct The correct option is option “(D)” because it is equal to zero
Solution:-Using CASIO fx-991MS calculator, make x = -1/2 and x = 2, To produce the correct answer first make x = - ½
Checking option(A)3x2 – 3x + 2 = 0
[ON] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = -1/2)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [3] [ALPHA] [X] [x2] [-] [3] [ALPHA] [X] [+] [2] [=] (4.75)
Option (A) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (B)3x2 + 3x – 2 = 0
make one of the factors x = - ½
[AC] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [3] [ALPHA] [X] [x2] [+] [3] [ALPHA] [X] [-] [2] [=] (-2.75)
Option (B) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (C)2x2 + 3x – 2 = 0
make one of the factors x = - ½
[AC] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [2] [ALPHA] [X] [x2] [+] [3] [ALPHA] [X] [-] [2] [=] (-3)
Option (C) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (D)2x2 – 3x + 2 = 0
make one of the factors x= - ½
[AC] [(-)] [1] [ab/c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [2] [ALPHA] [X] [x2] [-] [3] [ALPHA] [X] [+] [2] [=] (0)
one of the root is correct because it gives zero. Since it gives zero calculate the other root go to the next factor x = 2 make the other root x=2
[AC] [2] [STO] [X] (x=2)
[AC] [2] [ALPHA] [X] [X2] [-] [3] [ALPHA] [X] [-] [2] [=](0)
if the roots -1/2 and 2 is equal to 2x2-3x+2 option E is correct The correct option is option “(D)” because it is equal to zero
OR
(2). Construct a quadratic equation whose root are - ½ and 2
(A)3x2 – 3x + 2 = 0 (B)3x2 + 3x – 2 = 0 (C)2x2 + 3x – 2 = 0 (D)2x2 – 3x + 2 = 0
Solution:-Using CASIO fx-991MS calculator
Checking option (A) 3x2 – 3x + 2 = 0
Solving the equation 3x2 – 3x + 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = -3, c = 2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [(-)] [3] [=] [2] [=] (X1 = 0.5) press [ab/c] ( ½ ) press [=] or [↓] (X2 = 0.5) press [MODE] [1]
Option “A” is wrong because it didn’t give the roots as - ½ and 2. Go to the next option
Checking option (B) 3x2 + 3x – 2 = 0
Solving the equation 3x2 + 3x – 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = 3, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [3] [=] [(-)] [2] [=] (X1 = 0.457427107) press [=] or [↓] (X2 = 0.5) press [MODE] [1]
Option “B” is wrong because it didn’t give the roots as - ½ and 2. Go to the next option
Checking option (C) 2x2 + 3x – 2 = 0
Solving the equation 3x2 + 3x – 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = 3, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [2] [=] [3] [=] [(-)] [2] [=] (X1 = 0.5) press [ab/c] (½) [=] or [↓] (X2 = -2) press [MODE] [1]
Option “C” is correct because it give the roots as - ½ and 2. The correct option is “c”
(3). Factorise the expression 2y2 + xy – 3x2
(A) 2y(y + x) – 3x2 (B) (2y – x)(2y + x) (C) (3x – 2y)(x – y ) (D)(x – y)(2y + 3X)
Solution:-Using CASIO fx-991MS calculator
Make x and y = any number of your choice, i.e. x=1,2,3,4,5................................100 and y=1,2,3,4,5................................100 or more, make x=10, y=20
Using CASIO fx-991MS calculator
[ON] [1] [0] [SHIFT] [STO] [X] (x=10)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [2] [0] [SHIFT] [STO] [Y] (Y=20)
Question 2y2 + xy – 3x2
[AC] [2] [ALPHA] [Y] [x2] [+] [ALPHA] [X] [ALPHA] [Y] [-] [3] [ALPHA] [X] [x2] [=] (700)
if any of the options gives 700 it is correct but if it doesn't give 700 it is wrong
Checking option(A) 2y(y + x) – 3x2
Since you have make x=10, y=20 calculate the option Using CASIO fx-991MS calculator
[AC] [2] [ALPHA] [Y] [(] [ALPHA] [Y] [+] [ALPHA] [X] [)] [-][3] [ALPHA] [X] [X2] [=] (900)
Option (A) is wrong because it did not give 700
Checking option(B)(2y – x )(2y + x)
[AC] [(] [2] [ALPHA] [Y] [-] [ALPHA] [X] [)] [(] [2] [ALPHA] [Y] [+] [ALPHA] [X] [)] [=] (1500)
Option (B) is wrong because it did not give 700
Checking option(C) (3x – 2y)(x – y)
[AC] [(] [3] [ALPHA] [X] [-] [2] [ALPHA] [Y] [)] [(] [ALPHA] [X] [-] [ALPHA] [Y] [)] [=] (100)
Option(C) is wrong because it did not give 700
Checking option(D) (x – y )(2y + 3x)
[AC] [(] [ALPHA] [X] [-] [ALPHA] [Y] [)] [(] [2] [ALPHA] [Y] [+] [3] [ALPHA] [X] [)] [=](700)
The correct answer is option (E)
(A)3x2 – 3x + 2 = 0 (B)3x2 + 3x – 2 = 0 (C)2x2 + 3x – 2 = 0 (D)2x2 – 3x + 2 = 0
Solution:-Using CASIO fx-991MS calculator
Checking option (A) 3x2 – 3x + 2 = 0
Solving the equation 3x2 – 3x + 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = -3, c = 2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [(-)] [3] [=] [2] [=] (X1 = 0.5) press [ab/c] ( ½ ) press [=] or [↓] (X2 = 0.5) press [MODE] [1]
Option “A” is wrong because it didn’t give the roots as - ½ and 2. Go to the next option
Checking option (B) 3x2 + 3x – 2 = 0
Solving the equation 3x2 + 3x – 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = 3, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [3] [=] [(-)] [2] [=] (X1 = 0.457427107) press [=] or [↓] (X2 = 0.5) press [MODE] [1]
Option “B” is wrong because it didn’t give the roots as - ½ and 2. Go to the next option
Checking option (C) 2x2 + 3x – 2 = 0
Solving the equation 3x2 + 3x – 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = 3, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [2] [=] [3] [=] [(-)] [2] [=] (X1 = 0.5) press [ab/c] (½) [=] or [↓] (X2 = -2) press [MODE] [1]
Option “C” is correct because it give the roots as - ½ and 2. The correct option is “c”
(3). Factorise the expression 2y2 + xy – 3x2
(A) 2y(y + x) – 3x2 (B) (2y – x)(2y + x) (C) (3x – 2y)(x – y ) (D)(x – y)(2y + 3X)
Solution:-Using CASIO fx-991MS calculator
Make x and y = any number of your choice, i.e. x=1,2,3,4,5................................100 and y=1,2,3,4,5................................100 or more, make x=10, y=20
Using CASIO fx-991MS calculator
[ON] [1] [0] [SHIFT] [STO] [X] (x=10)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [2] [0] [SHIFT] [STO] [Y] (Y=20)
Question 2y2 + xy – 3x2
[AC] [2] [ALPHA] [Y] [x2] [+] [ALPHA] [X] [ALPHA] [Y] [-] [3] [ALPHA] [X] [x2] [=] (700)
if any of the options gives 700 it is correct but if it doesn't give 700 it is wrong
Checking option(A) 2y(y + x) – 3x2
Since you have make x=10, y=20 calculate the option Using CASIO fx-991MS calculator
[AC] [2] [ALPHA] [Y] [(] [ALPHA] [Y] [+] [ALPHA] [X] [)] [-][3] [ALPHA] [X] [X2] [=] (900)
Option (A) is wrong because it did not give 700
Checking option(B)(2y – x )(2y + x)
[AC] [(] [2] [ALPHA] [Y] [-] [ALPHA] [X] [)] [(] [2] [ALPHA] [Y] [+] [ALPHA] [X] [)] [=] (1500)
Option (B) is wrong because it did not give 700
Checking option(C) (3x – 2y)(x – y)
[AC] [(] [3] [ALPHA] [X] [-] [2] [ALPHA] [Y] [)] [(] [ALPHA] [X] [-] [ALPHA] [Y] [)] [=] (100)
Option(C) is wrong because it did not give 700
Checking option(D) (x – y )(2y + 3x)
[AC] [(] [ALPHA] [X] [-] [ALPHA] [Y] [)] [(] [2] [ALPHA] [Y] [+] [3] [ALPHA] [X] [)] [=](700)
The correct answer is option (E)
Unforgiveness is a sin, if you don’t forgive; your trespasses (sins) will not be forgiven
Reason. In Mathew 6:14-15- if ye forgive men their trespasses your heavenly father will also forgive your trespasses but if ye forgive not men their trespasses neither will your father forgive your trespasses
Also in Mark 11:25-26- And when ye stand praying forgive if you have ought against any that your father also which is in heaven will forgive your trespasses. But if ye do not forgive, neither will your father which is in heaven forgive your trespasses.
For your heavenly father to forgive your trespasses. You must forgive those that trespass against you including your enemies. In Matthew 5:44-Love your enemies, bless them that curse you, do good to them that hate you, pray for them which despitefully use you and persecute you. As a Christian/Believer of JESUS CHRIST you must forgive your enemies including those that commit evil against you because if you don’t forgive them you are in darkness. In 1 John 2:9-11 – He that saith he is in the light and hateth his brother is in darkness even until now. He that loveth his brother abideth in the light and there is none occasion of stumbling in him. But he that hateth his brother is in darkness and walketh in darkness and knoweth not wither because that darkness has blinded his eyes. A believer will say I am in the light by being a deacon, choir, usher, pastor, evangelist, But know that Christians/believers who is indulge in unforgiveness will not inherit the kingdom of God and they will spend their eternity in hell (the fire that never shall be quenched). Mark 9:43
Know that if you don’t forgive today, your prayers will not be answered. But if you are touched by the word of GOD on unforgiveness and you have make a decision in your heart to forgive whomsoever wronged you, offend you, please make this confession
LORD JESUS, as I come to you, have mercy upon me, as I forgive those that offend me today. Forgive me my trespasses; receive me into your kingdom, IN JESUS NAME AMEN.
NOW: that you have confess this prayer of unforgiveness you are free to confess the next prayer below if you are not
Born-again
if you have not born-again or given your life to Jesus Christ say this prayer “Lord JESUS, as I come to you today, Have mercy upon me, Forgive me all my sins, wash me with your precious blood, save my soul, as I receive you today as my lord and personal savior, write my name in the book of life, IN JESUS NAME AMEN.
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