What is the remainder when f(x) = x2 + 14x − 8 is divided by (x − 4)?

The remainder is 64.

Step-by-step explanation:

By definition, when we divide a polynomial f(x) by the remainder will be:

In this case we know that f(x) is:

And we need to find the remainder when it is divided by .

Therefore,  substituting into f(x), we get that the remainder is:  

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.

you're missing vital information, add to it so we can solve this problem for you.

step-by-step explanation: