Question

What is the factored form of the expression?

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).