Question

The product of a + 3 and –2a2 + 15a + 6 is –2a3 + xa2 + 51a + 18. What is the value of x?

Answer 1

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Answer 2

Answer:

The value of x is 9

Step-by-step explanation:

$\text{Given that the product of }a+3\text{ and }-2a^2+15a+6\text{ is }-2a^3+xa^2+51a+18$

we have to find the value of x.

The product is

$(a+3)(-2a^2+15a+6)=-2a^3+xa^2+51a+18....(1)$

First we have to find the product then equate

$(a+3)(-2a^2+15a+6)$

Opening brackets

$a(-2a^2+15a+6)+3(-2a^2+15a+6)$

By distributive property

$=-2a^3+15a^2+6a-6a^2+45a+18$

Combining like terms

$=(-2a^3)+(15a^2-6a^2)+(6a+45a)+18$

$=-2a^3+9a^2+51a+18$

Equation (1) becomes

$-2a^3+9a^2+51a+18=-2a^3+xa^2+51a+18$

Comparing both sides, we get

x=9

Hence, the value of x is 9