Fundamental Theorem of Algebra

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Answer explanation

The Fundamental Theorem of Algebra states that a polynomial of degree n has a total of n real and complex solutions.

Answer explanation

If we divide the quadratic by one of the binomials in this question, we should get no remainder. That is what makes it a factor.

• It can't be done.

Answer explanation

The Factor Theorem states if (x-a) is a factor of f(x), then f(a)=0.

Likewise, if f(a)=0, then (x-a) is a factor of f(x).

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Tags

CCSS.HSN.CN.C.9

Answer explanation

If f(a)=0, then x-a is a factor.

We are considering if (x+2) is a factor. For the factor theorem we need to substitute x=-2 and confirm the answer is 0.

Answer explanation

Complex solutions to a polynomial are always in conjugate pairs. Remember the +/- in the quadratic formula?

If a+bi is a root, then a-bi is also a root. Just change the +/- between the real and imaginary terms of the complex number to get its conjugate.

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Answer explanation

Complex roots are always in conjugate pairs. If 3-7i is a root, then 3+7i is also a root. Therefore, we are given 4 roots. The lowest degree for P(x) is 4

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