Question
factor this expression
x^2-5x+4
A. (x-5)(x+4)
B. (x+5)(x-1)
C. (x+1)(x+4)
D. (x-1)(x-4)
E. (x-3)(x-2)
x^2-5x+4
A. (x-5)(x+4)
B. (x+5)(x-1)
C. (x+1)(x+4)
D. (x-1)(x-4)
E. (x-3)(x-2)
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \( x^2 - 5x + 4 \), we need to find two numbers that multiply to the constant term (4) and add up to the linear coefficient (-5).
The two numbers that meet these criteria are -4 and -1 since:
- \( -4 \times -1 = 4 \)
- \( -4 + (-1) = -5 \)
Thus, we can factor the expression as follows:
\[
x^2 - 5x + 4 = (x - 4)(x - 1)
\]
Looking at your options, this matches:
**D. (x-1)(x-4)**
So, the correct answer is **D. (x-1)(x-4)**.
The two numbers that meet these criteria are -4 and -1 since:
- \( -4 \times -1 = 4 \)
- \( -4 + (-1) = -5 \)
Thus, we can factor the expression as follows:
\[
x^2 - 5x + 4 = (x - 4)(x - 1)
\]
Looking at your options, this matches:
**D. (x-1)(x-4)**
So, the correct answer is **D. (x-1)(x-4)**.