What is the end behavior of y=-2x^13+25x^8-3 as x approaches infinity?

1 answer:

6 0

Odd degree and negative leading coefient
means it goes from the top left to bottom right
goes infinitely down

as x aproaches infinity, y approaches neagtive infinity

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what is the quotient when x3 − 5x2 2x 5 is divided by x − 2? x2 − 3x − 4 x2 − 7x 16 x2 − 3x − 4 − 3 over the quantity of x minus

nekit [7.7K]

The correct answer is: 
x²-3x-4 - $\frac{3}{x-2}$ .

Explanation: 
To divide these polynomials, the dividend, x³-5x²+2x+5, goes under the box, and the divisor, x-2, goes outside of the box.

We first want to find what we multiply x by to make x³; x*x²=x³, so we write x² over -5x² in the box.

Now we multiply our divisor, x-2, by x²: 
x*x²=x³
-2*x²=-2x².

This goes under x³-5x² in the box.

Now we subtract: 
(x³-5x²)-(x³-2x²)=-3x².

This goes below the 2x² we wrote, and we bring down 2x.

Now we see what we multiply x by to make -3x²;
x*-3x=-3x², so we write -3x beside x² in the quotient (at the top).

We multiply our divisor, x-2, by -3x: 
x*-3x=-3x²
-2*-3x=6x.

We write -3x²+6x under our -3x²+2x and subtract:
(-3x²+2x)-(-3x²+6x)=-4x.

Write this below 6x. Bring down +5.

Now we see what we multiply x by to make -4x;
x*-4=-4x, so write -4 beside -3x in the quotient.

Multiply our divisor, x-2, by -4: 
x*-4=-4x;
-2*-4=8;

write -4x+8 below -4x+5 and subtract:
(-4x+5)-(-4x+8)=-3.

This gives us the quotient x²-3x-4 with a remainder of -3, so we write our full answer as x²-3x-4-(3/x-2).

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