Question

Express the product of 2x squared plus 6x -8 and x+3 in standard form

Answer 1

ANSWER

The standard form is:

$2 {x}^{3} + 12 {x}^{2} + 10x - 24$

EXPLANATION

The given product is

$(2 {x}^{2} + 6x - 8)(x + 3)$

We expand using the distributive property to get:

$x(2 {x}^{2} + 6x - 8) + 3(2 {x}^{2} + 6x - 8)$

Expand the parenthesis;

$2 {x}^{3} + 6 {x}^{2} - 8x + 6 {x}^{2} + 18x - 24$

This simplifies to

$2 {x}^{3} + 12 {x}^{2} + 10x -24$

Standard form is when the polynomial is arranged in decreasing powers of x.