Please can you help me answer this

a) The factors of x² + 3·x are x and (x + 3)

x² + 3·x = x·(x + 3)

b) The factors of 2·x² - 8·x are 2, x and (x - 4)

2·x² - 8·x = 2·x·(x - 4)

c) The factors of 6·x + 9·x³ are 3, x and (2 + 3·x²)

6·x + 9·x³ = 3·x·(2 + 3·x²)

d) The factors of 12·x³ - 4·x² are 4, x², and (3·x - 1)

12·x³ - 4·x² = 4·x²·(3·x - 1)

Step-by-step explanation:

The question relates to resolving a polynomial into its factors;

a) For the polynomial (quadratic) equation, x² + 3·x, we have;

x² + 3·x = x·(x + 3)

Therefore, x² + 3·x in factorized form is x·(x + 3)

b) For the polynomial (quadratic) equation, 2·x² - 8·x, we have;

2·x² - 8·x = 2·x·(x - 4)

Therefore, 2·x² - 8·x in factorized form is 2·x·(x - 4)

c) For the polynomial (cubic) equation, 6·x + 9·x³, we have;

6·x + 9·x³ = 3·x × (2 + 3·x²)

Therefore, 6·x + 9·x³ in factorized form is 3·x·(2 + 3·x²)

d) For the polynomial (cubic) equation, 12·x³ - 4·x², we have;

12·x³ - 4·x² = 4·x²·(3·x - 1)

Therefore, 12·x³ - 4·x² in factorized form is 4·x²·(3·x - 1).

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

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