Questionlest Yourself! practice tool
Express the product of $2 x^{2}+6 x-8$ and $x+3$ in standard form. $\square$

Studdy Solution

STEP 1

1. We are given a polynomial expression to expand and express in standard form.
2. Standard form for a polynomial is written as $ax^n + bx^{n-1} + \ldots + zx^0$ , where the terms are ordered by descending powers of $x$ .

STEP 2

1. Distribute each term in the first polynomial $2x^2 + 6x - 8$ across each term in the second polynomial $x + 3$ .
2. Combine like terms to simplify the expression.
3. Arrange the terms in descending order of the powers of $x$ .

STEP 3

Distribute each term in $2x^2 + 6x - 8$ across $x + 3$ .
$(2x^2 + 6x - 8)(x + 3) = 2x^2 \cdot x + 2x^2 \cdot 3 + 6x \cdot x + 6x \cdot 3 - 8 \cdot x - 8 \cdot 3$
This results in:
$2x^3 + 6x^2 + 6x^2 + 18x - 8x - 24$

STEP 4

Combine like terms:
$2x^3 + (6x^2 + 6x^2) + (18x - 8x) - 24$
$2x^3 + 12x^2 + 10x - 24$

STEP 5

The expression is already in standard form, with terms ordered by descending powers of $x$ :
$2x^3 + 12x^2 + 10x - 24$
The product of $2x^2 + 6x - 8$ and $x + 3$ expressed in standard form is:
$\boxed{2x^3 + 12x^2 + 10x - 24}$

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