Question

Factor completely: 8x5 + 28x4 + 12x3

Answer 1

Answer: The answer is $4x^3(x+3)(2x+1).$

Step-by-step explanation: Given expression is

$8x^5+28x^4+12x^3.$

To factorise the given expression, first we need to take common the powers of 'x' which are common to all the three terms. Then, we need to factorise the remaining expression using the formula

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

Let us start as follows

$8x^5+28x^4+12x^3\\\\=4x^3(2x^3+7x+3)\\\\=4x^3(2x^3+6x+x+3)\\\\=4x^3\{2x(x+3)+1(x+3)\}\\\\=4x^3(x+3)(2x+1).$

Thus, the required factorised expression is

$4x^3(x+3)(2x+1).$