Factor each polynomial. fill in the missing expressions to show the results.
8x3 + 27
a = __ b= -
= (( ) +-0))+ (12)
= (_ - _x+_)
x3 - 4x2 - 9x + 36
= x2(x – 4) - _(x-4)
| = (x² - 9) ( )
= (_ (_ )(x - 4)
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step-by-step explanation:

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!