Question

Use the factor theorem to determine whether v + 5 is a factor of v 4 + 16v 3 + 8v 2 - 725. No yes.

Answer 1

By factor theorem (v+5) is not a factor of the given polynomial f(v).

What does factor theorem mean?

When thoroughly factoring the polynomials, mathematicians apply the factor theorem. The polynomial's zeros and factors are connected by this theorem.

                   The factor theorem states that if a is any real number and f(x) is a polynomial of degree n 1 then (x-a) is a factor of f(x) if f(a)=0.

The factor theorem states that

f(x) has a factor (x-k) if and only if f(k) = 0

We are given the following information.

F(v) = v 4 + 16v 3 + 8v 2 - 725

        We have to check whether (v+5) is a factor of given polynomial.

( v + 5 ) = ( v - ( - 5 )

 f( -5 ) = $( -5 )^{4} + 16( -5)^{3} + 8( -5)^{2} - 725$

          = - 1900

 f(-5) ≠ 0

Learn more about factor theorem

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