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Polynomials

fx=x3-6 x2-19...

Question

f(x) = x³ −6x² − 19x + 84, g(x) = x − 7

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Solution

It is given that and

By the factor theorem, g(x) is the factor of polynomial f(x), if f (7) = 0.

Therefore, in order to prove that (x − 7) is a factor of f(x).

It is sufficient to show that f(7) = 0

Now,

Hence, (x − 7) is a factor of polynomial f(x).

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Similar questions

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x).

f(x) = $x^{3} - 6 x^{2}$ - 19x + 84, g(x) = x - 7

Show that $(x + 4), (x - 3)$ and $(x - 7)$ are factors of $x^{3} - 6 x^{2} - 19 x + 84$

Q. f(x) = x³ − 6x² + 2x − 4, g(x) = 1 − 2x

Q. f(x) = x³ − 6x² + 11x − 6, g(x) = x² − 3x + 2

Q. Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following :

(i) f(x) = x³ − 6x² + 11x − 6, g(x) = x² + x + 1
(ii) f(x) = 10x⁴ + 17x³ − 62x² + 30x − 3, g(x) = 2x² + 7x + 1
(iii) f(x) = 4x³+ 8x + 8x² + 7, g(x) = 2x² − x + 1
(iv) f(x) = 15x³ − 20x² + 13x − 12, g(x) = 2 − 2x + x²

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