Divide Using Long Polynomial Division (25M^2-20M+4)÷(5M-2)

$(25 M^{2} - 20 M + 4) \div (5 M - 2)$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$5 M$

$2$

$25 M^{2}$

$20 M$

$4$

Step 2

Divide the highest order term in the dividend $25 M^{2}$ by the highest order term in divisor $5 M$ .

					$5 M$
	$5 M$	-	$2$		$25 M^{2}$	-	$20 M$	+	$4$

Step 3

Multiply the new quotient term by the divisor.

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $25 M^{2} - 10 M$

Step 5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 6

Pull the next terms from the original dividend down into the current dividend.

Step 7

Divide the highest order term in the dividend $- 10 M$ by the highest order term in divisor $5 M$ .

Step 8

Multiply the new quotient term by the divisor.

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 10 M + 4$

Step 10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 11

Since the remander is $0$ , the final answer is the quotient.

$5 M - 2$