Question
2xsquared-22x+60
Answers
GPT-4o mini
To simplify the expression \( 2x^2 - 22x + 60 \), we can start by factoring it if possible.
1. First, factor out the greatest common factor (GCF) from all terms, which is 2:
\[
2(x^2 - 11x + 30)
\]
2. Next, we will try to factor the quadratic \( x^2 - 11x + 30 \). We need to find two numbers that multiply to 30 (the constant term) and add up to -11 (the coefficient of \( x \)).
The numbers that work here are -5 and -6, because:
\[
-5 \times -6 = 30 \quad \text{and} \quad -5 + -6 = -11
\]
3. Therefore, we can factor \( x^2 - 11x + 30 \) as:
\[
(x - 5)(x - 6)
\]
4. Now, substituting this back, we get:
\[
2(x - 5)(x - 6)
\]
Thus, the fully factored form of the expression \( 2x^2 - 22x + 60 \) is:
\[
2(x - 5)(x - 6)
\]
1. First, factor out the greatest common factor (GCF) from all terms, which is 2:
\[
2(x^2 - 11x + 30)
\]
2. Next, we will try to factor the quadratic \( x^2 - 11x + 30 \). We need to find two numbers that multiply to 30 (the constant term) and add up to -11 (the coefficient of \( x \)).
The numbers that work here are -5 and -6, because:
\[
-5 \times -6 = 30 \quad \text{and} \quad -5 + -6 = -11
\]
3. Therefore, we can factor \( x^2 - 11x + 30 \) as:
\[
(x - 5)(x - 6)
\]
4. Now, substituting this back, we get:
\[
2(x - 5)(x - 6)
\]
Thus, the fully factored form of the expression \( 2x^2 - 22x + 60 \) is:
\[
2(x - 5)(x - 6)
\]