Question

given that $f(x) = x^2 + 11x + 28$ and $g(x) = x + 4$, find $(f - g)(x)$ and express the result as a polynomial in simplest form.

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attempt 1 out of 2

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Explanation:

Step1: Recall the definition of (f - g)(x)

The difference of two functions \( (f - g)(x) \) is defined as \( f(x)-g(x) \). So we substitute the given functions \( f(x)=x^{2}+11x + 28 \) and \( g(x)=x + 4 \) into this formula.

$$ (f - g)(x)=f(x)-g(x)=(x^{2}+11x + 28)-(x + 4) $$

Step2: Distribute the negative sign

Distribute the negative sign to each term in \( g(x) \):

$$ (x^{2}+11x + 28)-(x + 4)=x^{2}+11x + 28 - x-4 $$

Step3: Combine like terms

Combine the like terms (the \( x \)-terms and the constant terms):

• For the \( x \)-terms: \( 11x-x = 10x \)
• For the constant terms: \( 28 - 4=24 \)

So we have \( x^{2}+10x + 24 \)

Answer:

\( x^{2}+10x + 24 \)