Question

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

Answer 1

let p(x) = x³- 3x² + ax - 10

since x-5 is a factor of p(x) x= 5

then

=> p(5) = 0

=> 5³ - 3x5² + 5a - 10 = 0

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

=> 5a = -40

=> a. = -8

Answer 2

Step-by-step explanation:

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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