Question

Find the factors of f(x) given that x = 5 is a zero.

Answer 1

• If x = 5 is a zero of the given polynomial, then,
• (x - 5) is a factor of the polynomial. [Since, x = 5 or, x - 5 = 0]
• Now, divide the polynomial with (x - 5) using long division method. (See the picture)
• We get (x^2 - x - 6) as the quotient.
• Now, factorise the above polynomial:
• (x^2 - x - 6)
• = (x^2 - 3x + 2x - 6)
• = x(x - 3) + 2(x - 3)
• = (x - 3)(x + 2)
• Therefore, x^3 − 6x^2 − x + 30 = (x − 5)(x − 3)(x + 2)

Answer:

B.(x − 5)(x − 3)(x + 2)

Hope you could get an idea from here.

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