Question

6 g(x)=(x + 4)(x - 5) dilate the function by x + 3.

Explanation:

Step1: Expand the original function

First, expand \(g(x)=(x + 4)(x - 5)\) using FOIL method. \(g(x)=x^{2}-5x+4x - 20=x^{2}-x - 20\).

Step2: Dilate the function

To dilate the function \(y = g(x)\) by \(x + 3\), we multiply \(g(x)\) by \(x + 3\). So \((x + 3)(x^{2}-x - 20)\).

Step3: Multiply the polynomials

Use the distributive property: \(x(x^{2}-x - 20)+3(x^{2}-x - 20)=x^{3}-x^{2}-20x+3x^{2}-3x - 60\).

Step4: Combine like - terms

Combine the \(x^{2}\) terms and the \(x\) terms: \(x^{3}+(-1 + 3)x^{2}+(-20-3)x - 60=x^{3}+2x^{2}-23x - 60\).

Answer:

\(x^{3}+2x^{2}-23x - 60\)