Factor: 14z2 - 49z + 35

I got 7(z^2-7z+5) but I got it wrong? Please correct me.

If you expand your answer, you don't get back what you started with.

So you knew you were wrong.

the common factor is 7, you had that

correct answer:
= 7(2z^2 - 7z + 35)

To correctly factorize the expression 14z^2 - 49z + 35, we need to find two numbers that multiply to give 35 and add up to -49.

First, we can factorize the constant term 35. The factors of 35 are 1, 5, 7, and 35. We need to find a pair of factors whose sum is -49.

By trial and error, we can determine that the factors -7 and -5 satisfy these conditions because -7 + (-5) = -12 and (-7)(-5) = 35.

So, we can rewrite the expression as:

14z^2 - 49z + 35
= 14z^2 - 7z - 42z + 35 (splitting the -49z term using the factors)
= 7z(2z - 1) - 7(2z - 1) (factoring out the greatest common factor from each pair of terms)
= (2z - 1)(7z - 7) (rearranging the terms)

Thus, the correct factorization of 14z^2 - 49z + 35 is (2z - 1)(7z - 7).