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

1.	For what value of a is (x - 5) a factor of x3 - 3x2 + ax - 10.
Answer» 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 – 75 + 5a – 10 0 = 5a + 40 a = -8 Hence, (x – 5) is a factor of f (x), if a = - 8.

Answer»

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 – 75 + 5a – 10

0 = 5a + 40

a = -8

Hence,

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

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