If the polynomial ax³ + 4x² + 3x − 4 and x³ – 7x + a leaves the same remainder, when divided by (x − 2), then find the value of a.​

Correct option is B

Given:

Two polynomials:

f(x) = $$ax^3 + 4x^2 + 3x - 4$$​​

g(x) = $$x^3 - 7x + a$$​​

Both leave the same remainder when divided by (x−2)(x - 2)

Concept Used:

Remainder Theorem:

The remainder when a polynomial f(x) is divided by (x - c) is f(c)

Formula Used:

If remainders are same, then:

f(2) = g(2)

Solution:

Computing f(2):

f(2) = $$a(2)^3 + 4(2)^2 + 3(2) - 4$$​ = 8a + 16 + 6 - 4 = 8a + 18

Computing g(2):

g(2) =$$(2)^3 - 7(2) + a$$​ = 8 - 14 + a = -6 + a

Now equating:

8a + 18 = -6 + a

8a - a = -6 -18

7a = -24

a = $$-\frac{24}{7}$$​​