Question

Factor the expression completely.
14k2–49k+35


please?

Answer 1

To factor the expression \( 14k^2 - 49k + 35 \) completely, we can start by looking for a common factor in all the terms:

1. The coefficients are 14, -49, and 35. The greatest common factor (GCF) of these numbers is 7.

2. We can factor out 7 from the expression:

\[
14k^2 - 49k + 35 = 7(2k^2 - 7k + 5)
\]

Next, we need to factor the quadratic expression \( 2k^2 - 7k + 5 \).

3. To factor \( 2k^2 - 7k + 5 \), we look for two numbers that multiply to \( 2 \times 5 = 10 \) and add up to \( -7 \). The numbers that satisfy this are \( -2 \) and \( -5 \).

4. We can rewrite the middle term \( -7k \) as \( -2k - 5k \):

\[
2k^2 - 2k - 5k + 5
\]

5. Now we can group the terms:

\[
= (2k^2 - 2k) + (-5k + 5)
\]

6. Factor out the common factors in each group:

\[
= 2k(k - 1) - 5(k - 1)
\]

7. Now, we can factor out the common binomial \( (k - 1) \):

\[
= (2k - 5)(k - 1)
\]

Putting it all together, we have:

\[
14k^2 - 49k + 35 = 7(2k - 5)(k - 1)
\]

Thus, the expression factored completely is:

\[
\boxed{7(2k - 5)(k - 1)}
\]