Question
Factor.
x, squared, minus, 14, x, plus, 45
x
2
−14x+45
x, squared, minus, 14, x, plus, 45
x
2
−14x+45
Answers
GPT-4o mini
To factor the quadratic expression \(x^2 - 14x + 45\), we need to find two numbers that multiply to 45 (the constant term) and add to -14 (the coefficient of the linear term).
The two numbers that satisfy these conditions are -5 and -9, because:
- \(-5 \times -9 = 45\)
- \(-5 + -9 = -14\)
Now we can write the expression as:
\[
x^2 - 14x + 45 = (x - 5)(x - 9)
\]
Thus, the factored form of the expression is:
\[
(x - 5)(x - 9)
\]
The two numbers that satisfy these conditions are -5 and -9, because:
- \(-5 \times -9 = 45\)
- \(-5 + -9 = -14\)
Now we can write the expression as:
\[
x^2 - 14x + 45 = (x - 5)(x - 9)
\]
Thus, the factored form of the expression is:
\[
(x - 5)(x - 9)
\]