Question

7 multiple choice 1 point factor: $2x^{2}+13x - 15$ $(2x + 3)(x - 5)$ $(2x + 5)(x - 3)$ $(2x - 1)(x - 15)$ $(2x + 15)(x - 1)$ 8 multiple choice 1 point simplify: $(2xy^{2}+9x^{2}y)-(6xy^{2}+7xy)$ $9x^{2}y-7xy - 4xy^{2}$ $-4xy^{2}+16xy$ $9x^{2}y-7xy + 8xy^{2}$ $9x^{2}y+7xy - 4xy^{2}$ 9 multiple choice 1 point the expression $3x(2x^{2}-5x + 7)$ can also be written as $6x^{3}-15x^{2}+21x$ $5x^{2}-2x + 10$ $6x^{2}-15x + 21$ $5x^{3}-2x^{2}+10x$

Explanation:

Step1: Factor $2x^{2}+13x - 15$

We need two numbers that multiply to $2\times(- 15)=-30$ and add up to $13$. The numbers are $15$ and $-2$. Then we rewrite the middle - term: $2x^{2}+15x-2x - 15=x(2x + 15)-1(2x + 15)=(2x + 15)(x - 1)$.

Step2: Simplify $(2xy^{2}+9x^{2}y)-(6xy^{2}+7xy)$

Distribute the negative sign: $2xy^{2}+9x^{2}y-6xy^{2}-7xy$. Combine like - terms: $(2xy^{2}-6xy^{2})+9x^{2}y-7xy=-4xy^{2}+9x^{2}y-7xy$.

Step3: Expand $3x(2x^{2}-5x + 7)$

Use the distributive property: $3x\times2x^{2}-3x\times5x + 3x\times7=6x^{3}-15x^{2}+21x$.

Answer:

1. D. $(2x + 15)(x - 1)$
2. A. $9x^{2}y-7xy - 4xy^{2}$
3. A. $6x^{3}-15x^{2}+21x$