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german
3 years ago
7

when a polynomial x^3-ax^2-2x+2a+6 leaves a remainder (a+2) when divided by (x-a), find the value of a.​

Mathematics
1 answer:
Tatiana [17]3 years ago
7 0

Answer:

a = 4

Step-by-step explanation:

We are given that the polynomial:

\displaystyle x^3 - ax^2 - 2x + 2a + 6

Has the remainder (<em>a</em> + 2) when divided by (<em>x</em> - <em>a</em>), and we want to determine the value of <em>a</em>.

Recall that from the Polynomial Remainder Theorem, when dividing a polynomial P(x) by a binomial (<em>x</em> - <em>a</em>), the remainder will be given by P(a).

Since the remainder is (<em>a</em> + 2) when divided by (<em>x</em> - <em>a</em>), P(a) must equal (<em>a</em> + 2):

\displaystyle P(a) = a+2

Substitute:

\displaystyle (a)^3 - a(a)^2 -2(a) + 2a + 6 = a + 2

Simplify and solve for <em>a: </em>

<em />\displaystyle \begin{aligned} a^3 - a^3 - 2a + 2a + 6 &= a + 2 \\ \\ 6 &= a+2 \\ \\ a &= 4\end{aligned}<em />

<em />

In conclusion, the value of <em>a</em> is 4.

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