Use the Factor Theorem to prove x^3 - 13x - 12 is divisible by x^2 – X – 12

See Below.

Step-by-step explanation:

We want to prove that:

We can factor the divisor:

According to the Factor Theorem, if we have a polynomial P(x) divided by a binomial in the form of (x - a) and if P(a) = 0, then the binomial is a factor of P(x).

Our two binomial factors our (x - 4) and (x + 3). Thus, a = 4 and a = -3.

Evaluate the polynomial for both of these factors:

And:

Since both yielded zero, the original polynomial is divisible by both (x - 4) and (x + 3) or x² - x - 12. Hence:

4.0 ft

step-by-step explanation:

4.0 ft

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet