Question

question 1 of 10
which of the binomials below is a factor of this trinomial?
x² - 9x + 18
a. x + 2
b. x - 2
c. x + 3
d. x - 3

Explanation:

Step1: Factor the trinomial

To factor \(x^2 - 9x + 18\), we need two numbers that multiply to \(18\) and add up to \(-9\). The numbers are \(-6\) and \(-3\) because \((-6)\times(-3)=18\) and \((-6)+(-3)=-9\). So, we can factor the trinomial as:

$$ x^2 - 9x + 18=(x - 6)(x - 3) $$

Step2: Identify the factor

From the factored form \((x - 6)(x - 3)\), we can see that \(x - 3\) (option D) is a factor. We can also check by substituting the root (value of \(x\) that makes the binomial zero) into the trinomial. For \(x - 3 = 0\), \(x = 3\). Substitute \(x = 3\) into \(x^2 - 9x + 18\):

$$ 3^2-9\times3 + 18=9 - 27 + 18=0 $$

Since the result is zero, \(x - 3\) is a factor.

Answer:

D. \(x - 3\)