Q. 2 B5.0( 6 Votes )

# Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:

f(x) = x^{3} + 3x^{2} + 3x + 1, g(x) = x + 1

Answer :

By Factor Theorem, we know that,

If p(x) is a polynomial and a is any real number, then g(x) = (x – a) is a factor of p(x), if p(a) = 0

For checking (x+1) to be a factor, we will find f(–1)

⇒ f(–1) = (–1)^{3} + 3(–1)^{2} + 3(–1) + 1

⇒ f(–1) = – 1 + 3 – 3 + 1

⇒ f(–1) = 0

As, f(–1) is equal to zero, therefore, g(x) = (x+1) is a factor f(x)

Rate this question :

Factorize

x^{3} – 2x^{2} – x + 2

Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:

f(x) = x^{3} – 4x^{2} + x + 6, g(x) = x – 2

Factorize

x^{3} + 13x^{2} + 32x + 20

If x^{2} – x – 6 and x^{2} + 3x – 18 have a common factor (x – a) then find the value of a.

Determine which of the following polynomials has (x + 1) as a factor.

x^{4} + 2x^{3} + 2x^{2} + x + 1

Factorize

y^{3} + y^{2} – y – 1

Factorise

9a^{2} + 4b^{2} + 16c^{2} + 12ab - 16bc - 24ca