Factor the polynomial, x2 + 5x + 6 completely (show work)

a. (x + 6)(x + 1)
b. (x + 3)(x + 2)
c. (x - 3)(x - 2)
d. (x-6)(x + 1)

Choice b.

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Step-by-step explanation:

The highest power of the variable in this polynomial is . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to . The discriminant of this polynomial is .

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Similarly:

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By the Factor Theorem, if is a root of a polynomial, then would be a factor of that polynomial. Note the minus sign between and .

Verify that indeed expands to the original polynomial:

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step-by-step explanation: