Question

2. Use the Factor Theorem to determine whether g(x) is factor of f(x) in a
following cases:
(1) f(x) = 5x + x2 – 5x – 1, g(x) = x + 1
(i) f(x) = x2 + 3x² + 3x + 1, g(x) = x + 1
(i) f(x) = x2 - 4x² + x + 6, g(x) = x - 2
(iv) f(x) = 3x? + x2 – 20x + 12, g(x) = 3x - 2
(v) f(x) = 4x + 20x² + 33x + 18, g(x) = 2x + 3​

Answer 1

Answer:

Given polynomial f(x)=5x

3

+x

2

−5x−1 the factor of g(x)=x+1

If x+1 is factor then x+1=0 or x=−1

Replace x in f(x) by −1 we get

f(x)=5x

3

+x

2

−5x−1 g(x)=x+1

f(−1)=5(−1)

3

+(−1)

2

−5(−1)−1

⇒f(−1)=−5+1+5−1

⇒f(−1)=0

So f(−1) is zero by g(x)=x+1 then g(x)=x+1 is factor of f(x)=5x

3

+x

2

−5x−1