Question
Factor x squared minus 13 x plus 36.
Question content area bottom
Part 1
x squared minus 13 x plus 36equals(xminus4)(x
▼
)
Question content area bottom
Part 1
x squared minus 13 x plus 36equals(xminus4)(x
▼
)
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 - 13x + 36 \), we want to express it in the form \((x - p)(x - q)\) where \( p \) and \( q \) are the roots of the equation.
1. We need two numbers that multiply to \( 36 \) (the constant term) and add to \( -13 \) (the coefficient of the linear term).
2. The numbers that fit these criteria are \(-9\) and \(-4\) because:
- \(-9 \times -4 = 36\)
- \(-9 + -4 = -13\)
Thus, we can factor the expression as follows:
\[
x^2 - 13x + 36 = (x - 9)(x - 4)
\]
So, the complete factorization is:
\[
x^2 - 13x + 36 = (x - 9)(x - 4)
\]
1. We need two numbers that multiply to \( 36 \) (the constant term) and add to \( -13 \) (the coefficient of the linear term).
2. The numbers that fit these criteria are \(-9\) and \(-4\) because:
- \(-9 \times -4 = 36\)
- \(-9 + -4 = -13\)
Thus, we can factor the expression as follows:
\[
x^2 - 13x + 36 = (x - 9)(x - 4)
\]
So, the complete factorization is:
\[
x^2 - 13x + 36 = (x - 9)(x - 4)
\]