Sure, let's factor the quadratic expression \( w^2 - 14w + 24 \).
To factor a quadratic expression of the form \( w^2 + bw + c \), we need to find two numbers that multiply to \( c \) (which is 24 in this case) and add up to \( b \) (which is -14 in this case).
1. List the pairs of factors of 24:
- \( 1 \times 24 \)
- \( 2 \times 12 \)
- \( 3 \times 8 \)
- \( 4 \times 6 \)
2. Determine which pair of factors when added together gives -14 (since the term in the equation is \(-14w\)).
- \( -2 \times -12 \) gives 24, and \(-2 + (-12) = -14\).
So, the correct pair of factors is -2 and -12.
3. Write the factored form using these factors:
\[
w^2 - 14w + 24 = (w - 2)(w - 12)
\]
None of the provided options are correct. The correct factorization should be:
\[
(w - 2)(w - 12)
\]
4.
Factor the expression.
w2 – 14w + 24
(w – 12)(w + 2)
(w + 2)(w + 12)
(w – 12)(w – 2)
(w – 1)(w – 24)
1 answer