Question

find the value of a if (x -4) is a factor of 5x³-7x² - 8 x - 28​

Answer 1

Answer

148

Explanation

5(4)^3-7(4)^2-8(4)-28

5(64)-7(16)-32-28

320-112-32-28

=148

Answer 2

Step-by-step explanation:

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

By factor theorem,  If (x - 4) is a factor of f (x) then f (4) = 0  :

Now, f (x) = 5x³ - 7x² - ax - 28  

=> f (4) = 5(4)³ - 7(4)² + a (4) - 28

=> 0 = 5 × 64 - 7 × 16 + 4a - 28

=> 0 = 320 - 112 + 4a - 28

=> 0 = 180 -  4a  

=> 5a = 180

=> a = 180/5

=> a = 45

Hence, (x – 4) is a factor of f (x), if a is 45.