Question Find the standard form of $g(x) = (5x + 14)(4x + 8)$ .

Studdy Solution

STEP 1

Assumptions
1. The function $g(x)$ is given as the product of two binomials: $(5x + 14)$ and $(4x + 8)$ .
2. We need to expand the product to write $g(x)$ in standard form, which is $ax^2 + bx + c$ where $a$ , $b$ , and $c$ are constants.

STEP 2

To write $g(x)$ in standard form, we will use the distributive property (also known as the FOIL method for binomials) to expand the product of the two binomials.
$g(x) = (5x + 14)(4x + 8)$

STEP 3

Apply the distributive property to multiply each term in the first binomial by each term in the second binomial.
$g(x) = 5x \cdot 4x + 5x \cdot 8 + 14 \cdot 4x + 14 \cdot 8$

STEP 4

Perform the multiplication for each term.
$g(x) = 20x^2 + 40x + 56x + 112$

STEP 5

Combine like terms ( $40x$ and $56x$ are like terms).
$g(x) = 20x^2 + (40x + 56x) + 112$

STEP 6

Add the coefficients of the like terms.
$g(x) = 20x^2 + 96x + 112$

STEP 7

The function $g(x)$ is now written in standard form.
$g(x) = 20x^2 + 96x + 112$
The correct answer is A $g(x)=20 x^{2}+96 x+112$ .

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