Answer to Q1:
x = 3 or x = -1
Explanation:
We have given an equation.
x²-2x-3 = 0
We have to solve above equation by factoring.
Splitting the middle term of above equation so that the sum of two term should be -2 and product be -3.
x²-3x+x-3 = 0
x(x-3)+1(x-3) = 0
(x-3)(x+1) = 0
Zero Product Property :
If ab = 0 then a = 0 or b = 0
Applying Zero Product Property,we have
x-3= 0 or x+1 = 0
x = 3 or x = -1 which is the solution of x²-2x-3 = 0
Answer to Q2:
x = 1/2 or x = 3
Explanation:
We have given an equation.
2x²-5x-3 =0
We have to solve above equation by factoring.
Splitting the middle term of above equation so that the sum of two term should be -5 and product be -6.
2x²-6x+1x-3 = 0
2x(x-3)-1(x-3) = 0
(2x-1)(x-3) = 0
Applying Zero Product Property,we have
2x-1 = 0 or x-3 = 0
2x = 1 or x = 3
x = 1/2 or x = 3 which is solution of given equation.
Answer to Q3:
x = 4 or x = 3
Explanation:
We have given an equation.
x²-7x = -12
x²-7x+12 = 0
We have to solve above equation by factoring.
Splitting the middle term of above equation so that the sum of two term should be -7 and product be 12.
x²-4x-3x+12 = 0
x(x-4)-3(x-4) = 0
(x-4)(x-3) = 0
Applying Zero Product Property,we have
x-4 = 0 or x-3 = 0
x = 4 or x = 3 which is solution of given equation.
Answer to Q4:
x = -2/3 or x = 6
Explanation:
We have given an equation.
3x² = 16x+12
3x²-16x-12 = 0
We have to solve above equation by factoring.
Splitting the middle term of above equation so that the sum of two term should be -16 and product be -36.
3x²-18x+2x-12 = 0
3x(x-6)+2(x-6) = 0
(3x+2)(x-6) = 0
Applying Zero Product Property,we have
3x+2 = 0 or x-6 =0
3x = -2 or x = 6
x = -2/3 or x = 6 which is solution of given equation.
Answer to Q5:
x = 6 or x = -4
Explanation:
We have given an equation.
x²-2x-24 = 0
We have to solve above equation by factoring.
Splitting the middle term of above equation so that the sum of two term should be -2 and product be -24, we have
x²-6x+4x-24 = 0
x(x-6)+4(x-6) = 0
(x-6)(x+4) = 0
Applying Zero Product Property,we have
x-6 = 0 or x+4 = 0
x = 6 or x = -4 which is solution of given equation.
Answer to Q6:
x = 4/3 or x = -1
Explanation:
We have given an equation.
3x² = x+4
3x²-x-4 = 0
We have to solve above equation by factoring.
Splitting the middle term of above equation so that the sum of two term should be -1 and product be -12, we have
3x²-4x+3x-4 = 0
x(3x-4)+1(3x-4) =0
(3x-4)(x+1) = 0
Applying Zero Product Property,we have
3x-4 =0 or x+1 =0
3x = 4 or x = -1
x = 4/3 or x = -1 which is solution of given equation.