Given that (x - 2) is a factor of this polynomial, use the Factor Theorem to find the value of a.

P (x) = x^4 - 3x^3 + Ax^2 - 6x + 14

Question

Mathematics

Brie

31 March, 08:45

Given that (x - 2) is a factor of this polynomial, use the Factor Theorem to find the value of a.

P (x) = x^4 - 3x^3 + Ax^2 - 6x + 14

+4

Answers (1)

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Daniella Lutz · Answer 1

The factor theorem states that if (x-a) is a factor of P (x) the P (a) = 0 so we can write, for this polynomial:

2^ (4) - 3 (2) ^3 + A (2) ^2 - 6 (2) + 14 = 0

16 - 24 + 4A - 12 + 14 = 0

4A = - 16+24 + 12 - 14 = 6

A = 6/4 = 1.5

Given that (x - 2) is a factor of this polynomial, use the Factor Theorem to find the value of a.P (x) = x^4 - 3x^3 + Ax^2 - 6x + 14

Given that (x - 2) is a factor of this polynomial, use the Factor Theorem to find the value of a.

P (x) = x^4 - 3x^3 + Ax^2 - 6x + 14