Find the Factors Using the Factor Theorem 2x^2-24x+54 , x-3

$2 x^{2} - 24 x + 54$ , $x - 3$

Divide $\frac{2 x^{2} - 24 x + 54}{x - 3}$ using synthetic division and check if the remainder is equal to $0$ . If the remainder is equal to $0$ , it means that $x - 3$ is a factor for $2 x^{2} - 24 x + 54$ . If the remainder is not equal to $0$ , it means that $x - 3$ is not a factor for $2 x^{2} - 24 x + 54$ .

Place the numbers representing the divisor and the dividend into a division-like configuration.

$3$	$2$	$- 24$	$54$
	\xa0		\xa0

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$3$	$2$	$- 24$	$54$
	\xa0		\xa0
	$2$

Multiply the newest entry in the result $(2)$ by the divisor $(3)$ and place the result of $(6)$ under the next term in the dividend $(- 24)$ .

$3$	$2$	$- 24$	$54$
	\xa0	$6$	\xa0
	$2$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$3$	$2$	$- 24$	$54$
	\xa0	$6$	\xa0
	$2$	$- 18$

Multiply the newest entry in the result $(- 18)$ by the divisor $(3)$ and place the result of $(- 54)$ under the next term in the dividend $(54)$ .

$3$	$2$	$- 24$	$54$
	\xa0	$6$	$- 54$
	$2$	$- 18$

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$3$	$2$	$- 24$	$54$
	\xa0	$6$	$- 54$
	$2$	$- 18$	$0$

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$(2) x - 18$

Simplify the quotient polynomial.

$2 x - 18$

The remainder from dividing $\frac{2 x^{2} - 24 x + 54}{x - 3}$ is $0$ , which means that $x - 3$ is a factor for $2 x^{2} - 24 x + 54$ .

$x - 3$ is a factor for $2 x^{2} - 24 x + 54$

The final factor is the only factor left over from the synthetic division.

$2 x - 18$

The factored polynomial is $(x - 3) (2 x - 18)$ .

$(x - 3) (2 x - 18)$

Find the Factors Using the Factor Theorem 2x^2-24x+54 , x-3

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