Question
Factor completely.
5w2+40w+35
5w2+40w+35
Answers
GPT-4o mini
To factor the expression \(5w^2 + 40w + 35\), we can start by factoring out the greatest common factor (GCF) from the entire expression.
1. The GCF of the coefficients \(5\), \(40\), and \(35\) is \(5\).
2. Factor out \(5\) from the entire expression:
\[
5(w^2 + 8w + 7)
\]
Next, we need to factor the quadratic \(w^2 + 8w + 7\).
3. We look for two numbers that multiply to \(7\) (the constant term) and add up to \(8\) (the coefficient of \(w\)). The numbers \(1\) and \(7\) fit this requirement:
- \(1 \times 7 = 7\)
- \(1 + 7 = 8\)
4. Therefore, we can write:
\[
w^2 + 8w + 7 = (w + 1)(w + 7)
\]
Putting it all together, the complete factorization of the original expression is:
\[
5(w + 1)(w + 7)
\]
So, the completely factored form of \(5w^2 + 40w + 35\) is:
\[
\boxed{5(w + 1)(w + 7)}
\]
1. The GCF of the coefficients \(5\), \(40\), and \(35\) is \(5\).
2. Factor out \(5\) from the entire expression:
\[
5(w^2 + 8w + 7)
\]
Next, we need to factor the quadratic \(w^2 + 8w + 7\).
3. We look for two numbers that multiply to \(7\) (the constant term) and add up to \(8\) (the coefficient of \(w\)). The numbers \(1\) and \(7\) fit this requirement:
- \(1 \times 7 = 7\)
- \(1 + 7 = 8\)
4. Therefore, we can write:
\[
w^2 + 8w + 7 = (w + 1)(w + 7)
\]
Putting it all together, the complete factorization of the original expression is:
\[
5(w + 1)(w + 7)
\]
So, the completely factored form of \(5w^2 + 40w + 35\) is:
\[
\boxed{5(w + 1)(w + 7)}
\]