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alex41 [277]
3 years ago
9

Is x^4-1 a factor of P(x)=x^5+5x^4-x-5

Mathematics
1 answer:
sasho [114]3 years ago
7 0

Answer:

  yes

Step-by-step explanation:

The other factor is (x+5), so the product is ...

  (x^4 -1)(x +5) = x^5 +5x^4 -x -5 = P(x)

(x^4 -1) is a factor of P(x).

_____

It is not a <em>primitive</em> factor, because it can be factored as ...

  x^4 -1 = (x^2 -1)(x^2 +1) = (x -1)(x +1)(x^2 +1)

The complete factorization of P(x) to real numbers is ...

  P(x) = (x -1)(x +1)(x +5)(x^2 +1)

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The equation of the line that is parallel to given line and passes through the point (-8, -3) is: y = 5x+37

Step-by-step explanation:

Given equation of line is:

y=5x-3

The general form of equation of line in slope-intercept form is written as:

y = mx+b

Here m(co-efficient of x) is the slope of the line and b is the y-intercept.

Comparing the given equation with the general form we get

m = 5

Two parallel lines have same slope so the slope of any line parallel to given line will also be 5.

Let m1 be the slope of required line parallel to y=5x-3

Then m1=5

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y = m_1x+b

y=5x+b

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Putting the value of b and m1, we get

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