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vovikov84 [41]
2 years ago
14

Find the remainder when f(x)=x3−4x2−6x−3 f ( x ) = x 3 − 4 x 2 − 6 x − 3 is divided by x+1

Mathematics
1 answer:
loris [4]2 years ago
5 0

Answer:

The remainder is -2.

Step-by-step explanation:

According to the Polynomial Remainder Theorem, if we divide a polynomial P(x) by a binomial (<em>x</em> - <em>a</em>), then the remainder of the operation will be given by P(a).

Our polynomial is:

P(x) = x^3-4x^2-6x-3

And we want to find the remainder when it's divided by the binomial:

x+1

We can rewrite our divisor as (<em>x</em> - (-1)). Hence, <em>a</em> = -1.

Then by the PRT, the remainder will be:

\displaystyle\begin{aligned}  R &= P(-1)\\ &=(-1)^3-4(-1)^2-6(-1)-3 \\ &= (-1)-4(1)+(6)-3 \\ &= -2 \end{aligned}

The remainder is -2.

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