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sattari [20]
3 years ago
7

What is the remainder R when the polynomial p(x) is divided by (x + 1)? Is (x + 1) a factor of p(x)? p(x) = -3x4 + 2x3 - x2 + 6

Mathematics
1 answer:
vodka [1.7K]3 years ago
7 0

Answer:

(x+1) is a factor with remainder 0.

Step-by-step explanation:

We divide (x+1) into the polynomial -3x^4+2x^3-x^2+6 through long division or synthetic. We choose long division and look for what will multiply with (x+1) to make the polynomial -3x^4+2x^3-x^2+6 .

(x+1)(-3x^3)=-3x^4-3x^3

We subtract this from the original -3x^4-(-3x^4)+2x^3-(-3x^3)-x^2+6.

This leaves 5x^3-x^2+6. We repeat the step above.

(x+1)(5x^2)=5x^3+5x^2.

We subtract this from 5x^3-(5x^3)-x^2-(5x^2)+6=-6x^2+6. We repeat the step above.

(x+1)(-6x)=-6x^2-6x.

We subtract this from -6x^2-(-6x^2)+0x-(-6x)+6=6x+6. We repeat the step above.

(x+1)(6)=-6x+1.

We subtract this from 6x-(6x)+6-(6)=0. There is no remainder. This means (x+1) is a factor.


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Answer:

\sf y = \bold -\frac{2}{5} x -3

Explanation:

part A identification for slope:

\sf 2x + 5y = 15

\sf 5y = -2x + 15

\sf y = \frac{-2x + 15}{5}

\sf y = -\frac{2 }{5} x+3

comparing with slope intercept form: y = mx + b

we can find that here the slope is \bold -\frac{2}{5}

part B, solving the equation:

if the line is parallel, then the slope will be same.

given coordinates: ( - 10, 1 )

using the equation:

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\sf y - 1 = \bold -\frac{2}{5} (x --10)

\sf y = \bold -\frac{2}{5} x -4 + 1

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Extra information:

check the image below. this proves that the line is parallel and passes through point (-10, 1). the blue line is question line and red the answer line.

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