Question

For what value of a is (x-5) a factor of x³-3x²+ax-10.

Answer 1

Let, f (x) = x³ - 3x² + ax - 10 be the given polynomial.

By factor theorem,  If (x – 5) is a factor of f (x) then f (5) = 0  :

Now,

f (x) = x³ - 3x² + ax - 10

⇒f (5) = (5)³– 3 (5)² + a (5) – 10

⇒0 = 125 - 3 × 25 + 5a - 10

⇒0 = 125 – 75 + 5a – 10

⇒0 = 5a + 40

⇒-5a = 40

⇒a = - 40/5

⇒a = - 8

Hence, (x – 5) is a factor of f (x), if a = - 8.

 

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Answer 2

Answer:

When (x-5) a factor of p(x) = x³-3x²+ax-10, p(5) = 0

Thus:

p(5) = (5)³-3(5)²+a(5)-10 = 0

=> 125 - 75 + 5a - 10 = 0

=> 5a = 85 - 125

=> 5a = -40

=> a = -8

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