Question

Three polynomials are factored below but some coefficients and constants are missing. all of the missing values of a, b, c and d are integers. 1. x^2 +2x-8=(ax+b)(cx+d) 2. 2x^3+2x^2-24x=2x(ax+b)(cx+d) 3. 6x^2-15x-9=(ax+b)(cx+d) Fill in the table with the missing values of a,b,c and d.

Answer 1

Answer:

1) d = 4

2) b = -3. c = 1

3) a = 3 and d = 1

Step-by-step explanation:

To get the missing values in the table, we will factorize the given expression and compare the factored expression with the expression containing the missing constants.

1) For the expression x²+2x-8, on factorizing we have;

x²+2x-8

= (x²+4x)-(2x-8)

Factoring out the common terms from both parenthesis;

= x(x+4)-2(x+4)

= (1x+4)(1x-2)

=  (1x-2)(1x+4)

Comparing the resulting expression with (ax+b)(cx+d)

a = 1, b = -2, c = 1 and d = 4

2) For the expression 2x³+2x²-24x

Factoring out the common term we will have;

= 2x(x²+x-12)

= 2x(x²-3x+4x-12)

= 2x{x(x-3)+4(x-3)}

= 2x{(x+4)(x-3)}

=  2x(1x-3)(1x+4)

Comparing the resulting expression with 2x(ax+b)(cx+d)

a = 1, b = -3. c = 1 and d = 4

3) For the expression 6x²-15x-9 we will have;

On simplifying,

= 6x²+3x-18x-9

= 3x(2x+1)-9(2x+1)

= (3x-9)(2x+1)

Comparing the resulting expression with (ax+b)(cx+d)

a = 3, b = -9, c = 2 and d = 1