Question

The expression (ax3 + bx2 – 5x +2a) is exactly divisible by

(x2 – 3x – 4). Calculate the value of a and b and factorize the expression

completely.​

Answer 1

Answer:

0 is the answer

please keep in bainleast

Answer 2

Answer:

Step-by-step explanation:

x² - 3x - 4 => (x - 4)(x + 1)

If the expression, ax³ + bx² - 5x + 2a is exactly divisible by x² - 3x - 4, then it is also divisible by both x - 4 and x + 1

so, if f(x) = ax³ + bx² - 5x + 2a, then f(4) = f(-1) = 0...by the factor theorem.

Hence, a(4)³ + b(4)² - 5(4) + 2a = 0 and a(-1)³ + b(-1)² - 5(-1) + 2a = 0

=> 64a + 16b - 20 + 2a = 0 and -a + b + 5 + 2a = 0

so, 66a + 16b = 20 and a + b = -5

or, 33a + 8b = 10...(1) and a + b = -5...(2)

Hence, 33a + 8(-5 - a) = 10

i.e. 25a - 40 = 10

so, a = 2 => b = -7

Therefore, f(x) = 2x³ - 7x² - 5x + 4