Mister Exam
Factor polynomial x+8*x^2+20*x+96
The solution
You have entered
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2 x + 8*x + 20*x + 96
$$\left(20 x + \left(8 x^{2} + x\right)\right) + 96$$
x + 8*x^2 + 20*x + 96
Factorization
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/ ______\ / ______\ | 21 I*\/ 2631 | | 21 I*\/ 2631 | |x + -- + ----------|*|x + -- - ----------| \ 16 16 / \ 16 16 /
$$\left(x + \left(\frac{21}{16} - \frac{\sqrt{2631} i}{16}\right)\right) \left(x + \left(\frac{21}{16} + \frac{\sqrt{2631} i}{16}\right)\right)$$
(x + 21/16 + i*sqrt(2631)/16)*(x + 21/16 - i*sqrt(2631)/16)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(20 x + \left(8 x^{2} + x\right)\right) + 96$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 8$$
$$b = 21$$
$$c = 96$$
Then
$$m = \frac{21}{16}$$
$$n = \frac{2631}{32}$$
So,
$$8 \left(x + \frac{21}{16}\right)^{2} + \frac{2631}{32}$$
$$\left(20 x + \left(8 x^{2} + x\right)\right) + 96$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 8$$
$$b = 21$$
$$c = 96$$
Then
$$m = \frac{21}{16}$$
$$n = \frac{2631}{32}$$
So,
$$8 \left(x + \frac{21}{16}\right)^{2} + \frac{2631}{32}$$
Combining rational expressions
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96 + x*(21 + 8*x)
$$x \left(8 x + 21\right) + 96$$
96 + x*(21 + 8*x)