How do you divide $(2 x^{2} + 7 x - 15) \div (x + 5)$ $(2x^2+7x-15)div(x+5)$ using synthetic division?

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How do you divide $(2 x^{2} + 7 x - 15) \div (x + 5)$ $(2x^2+7x-15)div(x+5)$ using synthetic division?

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Answer 1 · 2017-07-15T21:14:24

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

Explanation:

You can compare coefficients by seeing a quadratic ( $x^{2}$ $x^2$ ) divided by a linear (single power of x) will result in a linear factor in the form $(a x + b)$ $(ax+b)$

$2 x^{2} + 7 x - 15 = (x + 5) (a x + b)$ $2x^2+7x-15 = (x+5)(ax+b)$

If you compare coefficients, $x \times a x$ $xtimesax$ must be $2 x^{2}$ $2x^2$ so $a = 2$ $a=2$

Similarly, $5 \times b$ $5timesb$ must equal $- 15$ $-15$ so $b = - 3$ $b=-3$

I would use algebraic division but I don't know how to do the formatting yet!! I'll update my answer when I find out how to show the 'bus stop method'

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How do you divide $(2 x^{2} + 7 x - 15) \div (x + 5)$ $(2x^2+7x-15)div(x+5)$ using synthetic division?

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How do you divide (2x2+7x−15)÷(x+5)(2x^2+7x-15)div(x+5) using synthetic division?

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How do you divide $(2 x^{2} + 7 x - 15) \div (x + 5)$ $(2x^2+7x-15)div(x+5)$ using synthetic division?