Question

In the polynomial, x^2 - 13x + 30, you would need to find the factors of positive 30 to correctly factor this polynomial. Please write down all the factors of positive 30 and then circle the correct factors that you would use when factoring the given polynomial.

a) (x - 15), (x + 2)
b) (x - 30), (x + 1)
c) (x - 3), (x - 10)
d) (x - 5), (x - 6)

Answer 1

To factor the polynomial x^2 - 13x + 30, we need to find the factors of positive 30 and choose the correct ones that give us -13x.

Step-by-step explanation:

Solution:

To factor the polynomial x^2 - 13x + 30, we need to find the factors of positive 30. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30. Now we need to identify which combination of factors will give us -13, the coefficient of the x term.

If we choose (x - 3) and (x - 10) as factors, we can expand it using FOIL method: (x - 3)(x - 10) = x^2 - 10x - 3x + 30 = x^2 - 13x + 30. Therefore, the correct factors to factor the given polynomial are (x - 3) and (x - 10). So, the answer is option c) (x - 3), (x - 10).