Question

Find the value of ‘a’ such that (x – 4) is a factor of 5x^3
– 7x^2
– ax - 8​

Answer 1

Answer:

a=4

Step-by-step explanation:

Answer 2

Given that, (x−4) is a factor of 5x

3

−7x

2

−ax−28

To find out: The value of a

Let the given polynomial be p(x).

According to the factor theorem, if (x−a) is a factor of f(x), then f(a)=0.

∴ p(4)=0

Hence, p(4)=5(4)

3

−7(4)

2

−a(4)−28=0

⇒5(64)−7(16)−4a−28=0

⇒320−112−4a−28=0

⇒320−140−4a=0

⇒180−4a=0

⇒4a=180

⇒a=

4

180

∴ a=45

Hence, if (x−4) is a factor of 5x

3

−7x

2

−ax−28, then the value of a is 45.