Question

1. given (f(x)=x + 2) and (g(x)=x^{2}-3x + 5). express (f(x)^{2}-g(x)) as a polynomial in standard form.

(f(x)^{2}-g(x)
(x + 2)^{2}-(x^{2}-3x + 5)
(x + 2)+(x + 2)-(x^{2}-3x + 5))

Explanation:

Step1: Expand \([f(x)]^2\)

We know \(f(x)=x + 2\), so \([f(x)]^2=(x + 2)^2=x^{2}+4x + 4\) using the formula \((a + b)^2=a^{2}+2ab + b^{2}\) where \(a=x\) and \(b = 2\).

Step2: Subtract \(g(x)\)

We have \(g(x)=x^{2}-3x + 5\). Then \([f(x)]^2-g(x)=(x^{2}+4x + 4)-(x^{2}-3x + 5)\).

Step3: Remove parentheses and combine like - terms

\((x^{2}+4x + 4)-(x^{2}-3x + 5)=x^{2}+4x + 4-x^{2}+3x-5=(x^{2}-x^{2})+(4x+3x)+(4 - 5)=7x-1\)

Answer:

\(7x-1\)