Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

Given:

divided by

To find:

The remainder.

Solution:

divided by

Remainder theorem:

If a polynomial p(x) is divide by x - a, then the remainder is p(a).

Subtract 2 from both sides, we get

substitute x = -2 in p(x).

The remainder is 55.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

the infinity sign

step-by-step explanation: