Question

Find a quadratic polynomial divisible by x + 1 and x + 2 and leaving a remainder 4 when divided by x + 3.​

Answer 1

$\huge\mathfrak\blue{Answer:-}$

Given:

A quadratic polynomial ( x ) is divisible by x + 1 and x + 2 and leaving a remainder 4 when divided by x + 3

To Find:

The quadratic polynomial ( x )

Solution:

We have been given that ( x + 1 ) and ( x + 2) are the factors of the polynomial.

Now, p ( x ) = ( x + 1 ) ( x + 2 )

= x^2 + 2x + x + 2

= x^2 + 3x + 2

Now dividing x^2 + 3x + 2 by (x + 3)

[Division shown in attachment]

we do not get 4 as the remainder, so we multiply the equation by 2. We get,

2x^2 + 6x + 4

And on dividing 2x^2 + 6x + 4 by (x+3) we get 4 as the remainder.

[Division shown in attachment]