Find the value of a such that (x-4) is a factor of 5x3 - 7x2 - ax -

1.	Find the value of a such that (x-4) is a factor of 5x3 - 7x2 - ax - 28.
Answer» Let f(x) = 5x³ - 7x² - ax - 28 be the given polynomial. From factor theorem, If (x -4) is a factor of f (x) then f (4) = 0 f (4) = 0 0 = 5 (4)³ – 7 (4)² – a (4) – 28 0 = 320 – 112 – 4a – 28 0 = 180 – 4a 4a = 180 a = 45 Hence, (x – 4) is a factor of f (x) when a = 45.

Find the value of a such that (x-4) is a factor of 5x3 - 7x2 - ax - 28.

Answer»

Let f(x) = 5x³ - 7x² - ax - 28 be the given polynomial.

From factor theorem,

If (x -4) is a factor of f (x) then f (4) = 0

f (4) = 0

0 = 5 (4)³ – 7 (4)² – a (4) – 28

0 = 320 – 112 – 4a – 28

0 = 180 – 4a

4a = 180

a = 45

Hence,

(x – 4) is a factor of f (x) when a = 45.