Without actual division show that f(x) = (x3 − 3x2 − 13x + 15) is exactly divisible by g(x) = (x2 + 2x − 3).

see explanation

Step-by-step explanation:

Note that the sum of the coefficients of g(x)

1 + 2 - 3 = 0

Hence x = 1 is a root of g(x) and (x - 1) is a factor

Note the sum of the coefficients of f(x)

1 - 3 - 13 + 15 = 0

hence x = 1 is a root of f(x) and (x - 1) is a factor

Since (x - 1) is a factor of both

Then f(x) is also divisible by x² + 2x - 3

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