Question

find the product of $(x - 2)$ and $(3x^2 - 4x - 5)$. select the two terms that would complete the following answer. $3x^2$ ____ ____ $+10$| $- 10x^2$ | $- 4x^2$ | $+ 3x^2$ | $+ 10x^2$ || --- | --- | --- | --- || $- 13x$ | $- 4x$ | $- 3x$ | $+ 3x$ |

Explanation:

Step1: Expand using distributive property

$$(x - 2)(3x^2 - 4x - 5) = x(3x^2 - 4x - 5) - 2(3x^2 - 4x - 5)$$

Step2: Distribute each term

$$= 3x^3 - 4x^2 - 5x - 6x^2 + 8x + 10$$

Step3: Combine like $x^2$ terms

$$-4x^2 -6x^2 = -10x^2$$

Step4: Combine like $x$ terms

$$-5x + 8x = 3x$$

Step5: Assemble simplified polynomial

$$= 3x^3 -10x^2 + 3x + 10$$

Answer:

The missing terms are $\boldsymbol{-10x^2}$ and $\boldsymbol{+3x}$