Simplify (x^2-11x+28)/(2x^3-16x^2)

$\frac{x^{2} - 11 x + 28}{2 x^{3} - 16 x^{2}}$

Step 1

Factor $x^{2} - 11 x + 28$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $28$ and whose sum is $- 11$ .

$- 7, - 4$

Write the factored form using these integers.

$\frac{(x - 7) (x - 4)}{2 x^{3} - 16 x^{2}}$

Step 2

Factor $2 x^{2}$ out of $2 x^{3} - 16 x^{2}$ .

Factor $2 x^{2}$ out of $2 x^{3}$ .

$\frac{(x - 7) (x - 4)}{2 x^{2} (x) - 16 x^{2}}$

Factor $2 x^{2}$ out of $- 16 x^{2}$ .

$\frac{(x - 7) (x - 4)}{2 x^{2} (x) + 2 x^{2} (- 8)}$

Factor $2 x^{2}$ out of $2 x^{2} (x) + 2 x^{2} (- 8)$ .

$\frac{(x - 7) (x - 4)}{2 x^{2} (x - 8)}$

Simplify (x^2-11x+28)/(2x^3-16x^2)

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