Is the binomial a factor of the polynomial function? f(x)=x^3+5x^2-9x-45 select yes or no for each binomial: (x-5) (x+3) (x-15)

No, Yes, No

Step-by-step explanation:

to determine if the given binomials are factors of  f(x)

if (x - a) is a factor of a polynomial then f(a) = 0

f(5) = 5³ + 5(5)² - 9(5) - 45 = 125 + 125 - 45 - 45 = 160 ≠ 0

⇒ (x - 5) is not a factor

f(- 3) = (- 3)³ + 5(- 3)² - 9(- 3) - 45 = - 27 + 45 + 27 - 45 = 0

⇒ (x + 3) is a factor

f(15) = 15³ + 5(15)² - 9(15) - 45 ≠ 0

⇒ (x - 15) is not a factor

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step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .