If the polynomials ax3 + 3×2 − 13
Question:

If the polynomials $a x^{3}+3 x^{2}-13$ and $2 x^{3}-5 x+a$ when divided by $(x-2)$ leave the same remainder, Find the value of a

Solution:

Here, the polynomials are

$f(x)=a x^{3}+3 x^{2}-13$

$p(x)=2 x^{3}-5 x+a$

equate, x – 2 = 0

x = 2

substitute the value of x in f(x) and p(x)

$f(2)=(2)^{3}+3(2)^{2}-13$

= 8a + 12 – 13

= 8a – 1 ….. 1

$p(2)=2(2)^{3}-5(2)+a$

= 16 – 10 + a

= 6 + a …. 2

f(2) = p(2)

⟹ 8a – 1 = 6 + a

⟹ 8a – a = 6 + 1

⟹ 7a = 7

⟹ a = 1

The value of a = 1