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7 votes
What polynomial has quotient x2 + 6x – 4 when divided by x + 3?​

1 Answer

11 votes

Answer:


(x^(3) + 9\, x^(2) + 14\, x - 12).

Explanation:

Let
p(x) denote the polynomial in question.

The question states that dividing
p(x) by
(x + 3) gives the quotient
(x^(2) + 6\, x - 4) (with no remainder.) In other words:


\displaystyle (p(x))/(x + 3) = x^(2) + 6\, x - 4.

Multiply both sides by
(x + 3) to find an expression for the polynomial in question,
p(x):


p(x) = (x^(2) + 6\, x - 4)\, (x + 3).

Expand this expression to obtain:


\begin{aligned}p(x) &= (x^(2) + 6\, x - 4) \, (x + 3) \\ &= x\, (x^(2) + 6\, x - 4) \\ & \quad + 3\, (x^(2) + 6\, x - 4) \\ &= x^(3) + 6\, x^(2) - 4\, x \\ &\quad + 3\, x^(2) + 18\, x - 12 \\ &= x^(3) + 9\, x^(2) + 14\, x - 12\end{aligned}.

User Maxim Kim
by
7.0k points
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