Question

Brian needs to find the value of a number, a, so that when (x^2+3x) is added to the binomial (3x^2+ax), the sum simplifies to 4x^2+12x. What is the value of a?

Answer 1

a = 9

Explanation:

First we need to add (x^2+3x) to (3x^2+ax),

(x^2+3x)+(3x^2+ax)

Expand

= x^2+3x+3x^2+ax

Collect the like terms

= x^2+3x^2+3x+ax

= 4x^2 + 3x + ax

= 4x^2+(3+a)x

Equate the solution to 4x^2+12x

4x^2+(3+a)x = 4x^2+12x

Comparing the like terms on both sides

(3+a)x =12x

3 + a = 12

a = 12 - 3

a = 9

Hence the value of a is 9