Question

Divide p(x) by g(x), where p(x)=
$x + 3x^{2} - 1$
and g(x)=1+x.​

Answer 1

I hope it will help u please read the caption in the phou

Answer 2

Given that,

p(x) = x + 3x² - 1

g(x) = 1 + x

But here, before doing anything else, we've to see first that all the terms of p(x) and g(x) are in standard form or not.

Standard form for quadratic equations and linear equations are different which are stated below,

Standard form for linear equations,

$\boxed{\bold{x + a}}$

Standard form for quadratic equations,

$\boxed{\bold{x^2 + x + a}}$

Now, by comparing both the standard forms to g(x) and p(x), we find that they aren't in the standard form.

So, we've to just rearrange the terms. Remember not to change their signs.

So, by rearranging the terms of p(x) in standard form we gotta,

p(x) = 3x² + x - 1

g(x) = x + 1

Now by dividing p(x) by g(x) we gotta,

Quotient = q(x) = 3x - 2

Remainder = r(x) = 1

Do refer the above attachment.