Question

What is the factored form of the expression?

28x^2+81x+56

a. (4x+7)(7x-8)
b. (4x-7)(7x+8)
c. (4x-7)(7x-8)
d. (4x+7)(7x+8)

Answer 1

Answer: The answer is (d)
`(4x+7)(7x+8).`

Step-by-step explanation: Given equation to be factored is

`28x^2+81x+56.`

The given expression is quadratic, so we can factor it into two linear factors, by using the following factorisation rule.

`x^2+(a+b)x+ab=(x+a)(x+b).`

So, the given equation can be factorised using the above rule. The factorisation is as follows.

`28x^2+81x+56\\\\=28x^2+49x+32x+56\\\\=7x(4x+7)+8(4x+7)\\\\=(4x+7)(7x+8).`

Thus, the correct option is (d).