Question
xsquared+11x+30
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 + 11x + 30 \), we are looking for two numbers that multiply to \( 30 \) (the constant term) and add to \( 11 \) (the coefficient of the linear term).
The pairs of factors of \( 30 \) are:
- \( 1 \) and \( 30 \) (sum is \( 31 \))
- \( 2 \) and \( 15 \) (sum is \( 17 \))
- \( 3 \) and \( 10 \) (sum is \( 13 \))
- \( 5 \) and \( 6 \) (sum is \( 11 \))
The pair \( 5 \) and \( 6 \) meets the required conditions.
Thus, we can factor the expression as:
\[
x^2 + 11x + 30 = (x + 5)(x + 6)
\]
So, the factored form of the expression is \( (x + 5)(x + 6) \).
The pairs of factors of \( 30 \) are:
- \( 1 \) and \( 30 \) (sum is \( 31 \))
- \( 2 \) and \( 15 \) (sum is \( 17 \))
- \( 3 \) and \( 10 \) (sum is \( 13 \))
- \( 5 \) and \( 6 \) (sum is \( 11 \))
The pair \( 5 \) and \( 6 \) meets the required conditions.
Thus, we can factor the expression as:
\[
x^2 + 11x + 30 = (x + 5)(x + 6)
\]
So, the factored form of the expression is \( (x + 5)(x + 6) \).