Factor completely. x^3-8x^2-2x+16

Mathematics

1 answer:

amm18124 years ago

8 0

Step-by-step explanation:

${x}^{3 } - 8 {x}^{2} - 2x + 16 \\ = {x}^{2} (x - 8) - 2(x - 8) \\ = (x - 8)( {x}^{2} - 2) \\ = (x - 8)( {x}^{2} - { \sqrt{2} }^{2} ) \\ = (x - 8)(x + \sqrt{2} )(x - \sqrt{2} )$

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Answer:

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Step-by-step explanation:

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3 years ago

PROVE THAT: cos 20° - sin 20° = \sqrt{2}sin25°

Lemur [1.5K]

Answer:

See below.

Step-by-step explanation:

$\cos(20)-\sin(20)=\sqrt{2}\sin(25)$

First, use the co-function identity:

$\sin(90-x)=\cos(x)$

We can turn the second term into cosine:

$\sin(20)=\sin(90-70)=\cos(70)$

Substitute:

$\cos(20)-\cos(70)=\sqrt{2}\sin(25)$

Now, use the sum to product formulas. We will use the following:

$\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})$

Substitute:

$\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)$