Erik is building a cubby bookshelf, that is, a book shelf divided into storage holes (cubbies) instead of shelves. He wants the height of the bookshelf to be x2−4x−45 and the width to be x2+7x+10. Each cubby hole in the bookshelf will have a height of x+2 and width of x−9
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Step-by-step explanation:

Factor your equations using the fact that x²-Sx+P represents the general equation where S is the sum of roots and P the product of roots.

What roots will have the sum  S=4 and product P= -45 ,

will have 5 and -9, S=5-9=-4✅ and P=5*(-9)=-45✅

x²-4x-45 = (x-root1) (x-root2) = (x+5)(x-9)

S=-7 and P=10 , so the roots are -5 and -2

x²+7x+10= (x+5)(x+2)

I am not sure what is your question yet you frobably need to factor the 2 given equation so you will have a bookshelf of (x+5)(x-9) by (x+5)(x+2)

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!