Question

give examples of polynomials p (x),g (x),q (x),and r (x),which satisfy the division algorithm and 1. deg p (x)=q (x)​

Answer 1

Step-by-step explanation i hope friend my answer is helpfull to you friend

Answer 2

Here, the given polynomials

$p (x),g (x),q (x), r (x)$

As we have to give the example for which it satisfies the division algorithm,

$deg$ $p (x)=q (x)$

We have the formula for the division algorithm,

⇒$Dividend = Divisor$ × $Quotient + Remainder$

$p (x) =$ Dividend,

$g(x)=$Divisor

$q(x)=$quotient

$r(x)=$remainder

Now, we have to give examples of polynomials

( 1 ) $deg$ $p (x)=q (x)$

Let's assume that $2x+4$ by 2

So, $p(x) = 2x+4$

$g(x) =2$

$q(x) = x+2$

$r(x) =0$

By using formula,

⇒$p(x)=g(x)$ × $q(x) +r(x)$

Substitute the values, we get

⇒ $2x+4=2$  × $(x+2) +0$

⇒ $2x+4=2x+4$

Hence, the given condition is satisfied,

$deg$ $p (x)=q (x)$