Find the value of B, Please. (-5x^3+2x+3)/(x+2) = A+(B)/(x+2) A. -13 B. 39 C. -21 D. -33

Question

Find the value of B, Please.


`(-5x^3+2x+3)/(x+2) = A+(B)/(x+2)`

A. -13
B. 39
C. -21
D. -33

Answer 1

B. 39

Explanation:

Divide the polynomials using long division:

`\large \begin{array}{r}-5x^2+10x-18\phantom{)}\\x+2{\overline{\smash{\big)}\,-5x^3\;\;\;\;\;\;\;\;\;\;\;+2x+3\phantom{)}}}\\{-~\phantom{(}\underline{(-5x^3-10x^2)\phantom{-b)))))))}}\\10x^2+2x+3\phantom{)}\\-~\phantom{()}\underline{(10x^2+20x)\phantom{)))}}\\-18x+3\phantom{)}\\-~\phantom{()}\underline{(-18x-36)\phantom{}}\\39\phantom{)}\\\end{array}`

The solution is the quotient plus the remainder divided by the divisor.

Solution

`-5x^2+10x-18+(39)/(x+2)`

Answer 2

• B) 39

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We need to find the remainder when -5x³ + 2x + 3 is divided by x + 2.

According to the remainder theorem, the remainder is the value of the polynomial when x = - 2:

• -5(-2)³ + 2(-2) + 3 =
• - 5(-8) - 4 + 3 =
• 40 - 1 =
• 39

The matching choice is B.