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stepladder [879]
3 years ago
5

Can someone please help me with this?

Mathematics
1 answer:
madreJ [45]3 years ago
6 0

Answer:

2.664 * 10^{7}

Step-by-step explanation:

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The binomial x-2 is a factor of the polynomial below. f(x)=x3+x2+nx+10 What is the value of n?
Nutka1998 [239]
<h3>Answer: n = -11</h3>

=========================================================

Explanation:

Since x-2 is a factor of f(x), this means f(2) = 0.

More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.

So if we plugged x = 2 into f(x), we'd get

f(x) = x^3+x^2+nx+10

f(2) = 2^3+2^2+n(2)+10

f(2) = 8+4+2n+10

f(2) = 2n+22

Set this equal to 0 and solve for n

2n+22 = 0

2n = -22

n = -22/2

n = -11 is the answer

Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10

Plug x = 2 into that updated f(x) function to find....

f(x) = x^3+x^2-11x+10

f(2) = 2^3+2^2-11(2)+10

f(2) = 8+4-22+10

f(2) = 0

Which confirms our answer.

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3 years ago
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