Question

1 multiple choice 1 point multiply: (5x^2 - 7x - 9)(2x + 1) 10x^3 - 9x^2 - 25x - 9 10x^3 + 9x^2 - 25x + 9 10x^3 + 9x^2 + 25x + 9 10x^3 - 9x^2 + 25x - 9 2 multiple choice 1 point simplify: (3a^2b - 6ab^2) - (5 + 7ab^2 - 3a^2b) 3ab^2 - 5 6a^2b - 13ab^2 - 5 6a^2b + ab^2 - 5 ab^2 - 5 3 multiple choice 1 point factor: 3x^2 - 13x - 10 (3x - 5)(x - 2) (3x + 10)(x + 1) (3x + 2)(x - 5) (3x - 5)(x + 2)

Explanation:

Step1: Multiply polynomials in question 1

\[

$$\begin{align*} &(5x^{2}-7x - 9)(2x + 1)\\ =&5x^{2}\times(2x+1)-7x\times(2x + 1)-9\times(2x + 1)\\ =&10x^{3}+5x^{2}-14x^{2}-7x-18x - 9\\ =&10x^{3}-9x^{2}-25x - 9 \end{align*}$$

\]

Step2: Simplify polynomials in question 2

\[

$$\begin{align*} &(3a^{2}b-6ab^{2})-(5 + 7ab^{2}-3a^{2}b)\\ =&3a^{2}b-6ab^{2}-5-7ab^{2}+3a^{2}b\\ =&(3a^{2}b + 3a^{2}b)+(-6ab^{2}-7ab^{2})-5\\ =&6a^{2}b-13ab^{2}-5 \end{align*}$$

\]

Step3: Factor polynomial in question 3

For \(3x^{2}-13x - 10\), we need to find two numbers \(m\) and \(n\) such that \(m\times n=3\times(- 10)=-30\) and \(m + n=-13\). The numbers are \(-15\) and \(2\).
\[

$$\begin{align*} 3x^{2}-13x - 10&=3x^{2}-15x+2x - 10\\ &=3x(x - 5)+2(x - 5)\\ &=(3x + 2)(x - 5) \end{align*}$$

\]

Answer:

1. \(10x^{3}-9x^{2}-25x - 9\)
2. \(6a^{2}b-13ab^{2}-5\)
3. \((3x + 2)(x - 5)\)