Question

Which of the binomials below is a factor of this trinomial?

x2 - 13x + 30


A. x - 5

B. x + 3

C. x - 3

D. x + 5

Answer 1

C. x - 3

Explanation:

Given the trinomial:
`x^2-13x+30`

We factorize the trinomial to determine which of the given options is a factor.

Step 1: Multiply the first and last term of the trinomial.

`30 * x^2=30x^2`

Step 2: Write out factor pairs of 30

• 1 X 30
• 2 X 15
• 3 X 10
• 5 X 6

Step 3: Determine which pair added together will give the middle term, -13

These are -3 and -10

Step 4: Replace -13x with -3x and -10x

`x^2-3x-10x+30`

Step 5: Factorize

`\implies x(x-3)-10(x-3)\\\implies (x-3)(x-10)`

Therefore, one of the factors is x-3. The correct option is C.