Question

Use the Factor Theorem to determine whether g(x) is factor f(x) in each of the
following cases:
(i)f(x)=5x³+x²-5x-1,g(x)=x+1

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Answer 1

Since g(x) = x + 1

x + 1 = 0

→ x = -1

Now, for checking whether given polynomial f(x) is a factor of g(x) or not, we shall use factor theorem.

So, we will substitute the value of x as -1 in the given polynomial.

g(x) = 5x³ + x² - 5x - 1

⇒ g(-1) = 5(-1)³ + (-1)² - 5(-1) - 1

⇒ g(-1) = -5 + 1 + 5 - 1

⇒ g(-1) = -5 + 5 + 1 - 1

⇒ g(-1) = 0

So, The given g(x) is a factor of f(x)

Know more:

• Factor theorem states that a polynomial f(x) has a factor (x - a) if and only if f(a) = 0

Here this condition is satisfied. So (x + 1) is a factor.