Q2 of 86 Page 48

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

f(x) = x3 + 3x2 + 3x + 1, g(x) = x + 1

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)


More from this chapter

All 86 →
1

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

x3 – x2 –(3 – √3 ) x + √3

 2

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

f(x) = 5x3 + x2 – 5x – 1, g(x) = x + 1

 2

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

f(x) = x3 – 4x2 + x + 6, g(x) = x – 2

 2

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

f(x) = 3x3 + x2 – 20x + 12, g(x) = 3x–2