Question

1. multiply. (5x + 2)(x² - 3x + 6)

a) 5x³ - 17x²+24x +12
c) 5x³ - 13x² + 24x +12
b) 5x³ + 17x² - 24x +12
d) 5x³ +13x² - 24x - 12

1. multiply the expression: (x + 5)²

a) x² + 25
b) x² + 5x + 25
c) x² - 10x + 25
d) x² + 10x + 25

1. identify the type of polynomial shown 5x² + 7x - 2

a) trinomial
b) polynomial with more than 3 terms
c) binomial
d) monomial

1. factor the following polynomial 14x²+7x

a) 7x(2x+1)
b) 2x(2+7x)
c) x(14x+7)
d) 14(x²+7)

1. factor x² + 14x + 33

a) (x + 33)(x + 1)
b) (x - 11)(x - 3)
c) (x + 30)(x + 3)
d) (x + 11)(x + 3)

1. factor completely: x² - 36

a) (x + 6)(x - 6)
b) (x + 9)(x - 4)
c) (x - 6)(x - 6)
d) (x - 9)(x + 4)

1. what is the first step when factoring polynomials?

a) write the answer
b) make a triangle
c) find the gcf
d) list all the terms

1. factor completely: 3x² + 18x +15

a) (x + 5)(x + 1)
b) none of the above
c) 3(x² + 6x + 5)
d) 3(x + 5)(x + 1)

Explanation:

15.

Step1: Distribute 5x and 2

\[

$$\begin{align*} (5x + 2)(x^{2}-3x + 6)&=5x(x^{2}-3x + 6)+2(x^{2}-3x + 6)\\ \end{align*}$$

\]

Step2: Multiply each term

\[

$$\begin{align*} 5x(x^{2}-3x + 6)&=5x\cdot x^{2}-5x\cdot3x + 5x\cdot6=5x^{3}-15x^{2}+30x\\ 2(x^{2}-3x + 6)&=2x^{2}-6x + 12 \end{align*}$$

\]

Step3: Combine like - terms

\[

$$\begin{align*} (5x^{3}-15x^{2}+30x)+(2x^{2}-6x + 12)&=5x^{3}+(-15x^{2}+2x^{2})+(30x-6x)+12\\ &=5x^{3}-13x^{2}+24x + 12 \end{align*}$$

\]

Step1: Use the formula \((a + b)^{2}=a^{2}+2ab + b^{2}\)

Here \(a = x\) and \(b = 5\), so \((x + 5)^{2}=x^{2}+2\cdot x\cdot5+5^{2}\)

Step2: Simplify the expression

\(x^{2}+10x + 25\)

A polynomial with three terms is called a trinomial. The polynomial \(5x^{2}+7x - 2\) has three non - zero terms \(5x^{2}\), \(7x\) and \(-2\).

Answer:

C. \(5x^{3}-13x^{2}+24x + 12\)

16.