Question

question 25 of 25
what is the factorization of the trinomial below?
$x^2 - 5x + 4$

a. $(x + 4)(x - 1)$
b. $(x - 2)(x - 2)$
c. $(x + 2)(x - 2)$
d. $(x - 4)(x - 1)$

Explanation:

Step1: Recall factoring trinomials

For a trinomial \(x^2 + bx + c\), we need two numbers that multiply to \(c\) and add to \(b\). Here, the trinomial is \(x^2 - 5x + 4\), so we need two numbers that multiply to \(4\) and add to \(-5\).

Step2: Find the numbers

The numbers that multiply to \(4\) and add to \(-5\) are \(-4\) and \(-1\) (since \((-4)\times(-1)=4\) and \(-4 + (-1)=-5\)).

Step3: Write the factorization

Using these numbers, the factorization of \(x^2 - 5x + 4\) is \((x - 4)(x - 1)\). We can also check by expanding each option:

• Option A: \((x + 4)(x - 1)=x^2+3x - 4\) (not equal to \(x^2 - 5x + 4\))
• Option B: \((x - 2)(x - 2)=x^2-4x + 4\) (not equal to \(x^2 - 5x + 4\))
• Option C: \((x + 2)(x - 2)=x^2-4\) (not equal to \(x^2 - 5x + 4\))
• Option D: \((x - 4)(x - 1)=x^2-5x + 4\) (matches the trinomial)

Answer:

D. \((x - 4)(x - 1)\)