Question

The polynomials (ax^3 + 3x^2 -3) and (2x^3 -5x + a) when divided by (x-4) leave the same remainder. Find the value of 'a'?
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Answer 1

Step-by-step explanation:

$a {x}^3 + 3 {x}^{2} - 3 \: and \:2 {x}^{3} - 5 x + a \:$

when divided by (x-4) leave the remainder.

Substitute x=4 in this two polynomials.

$a {(4)}^3 + 3( {4)}^{2} - 3 =2 {(4)}^{3} - 5(4) + a$

$= > 64a + 48 - 3 = 128 - 20 + a = >$

$= > 64a - a = 108 - 45 = > 63a =$

$63 = > a = 1$

Hope it helps you.

Answer 2

Step-by-step explanation:

a {x}^3 + 3 {x}^{2} - 3 \: and \:2 {x}^{3} - 5 x + a \:

when divided by (x-4) leave the remainder.

Substitute x=4 in this two polynomials.

a {(4)}^3 + 3( {4)}^{2} - 3 =2 {(4)}^{3} - 5(4) + a

= > 64a + 48 - 3 = 128 - 20 + a = >

= > 64a - a = 108 - 45 = > 63a =

63 = > a = 1