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.

Tags

CCSS.HSN.CN.C.9

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).

Tags

CCSS.HSA.APR.B.2

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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.

Tags

CCSS.HSA.APR.B.2

Tags

CCSS.HSA.APR.B.2

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.

Tags

CCSS.HSN.CN.A.3

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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

• We need more information.

Tags

CCSS.HSA.APR.B.3