I am down to 5 out of 49 problems that I can't figure out. Help is very much appreciated. Thanks !

Factor Completely

3c^2 -42c +147 =

= 3(c^2 - 13c + 49)

nothing else happening here.

Thank you Reiny

To factor a quadratic expression like 3c^2 - 42c + 147, we need to look for two binomials whose product equals this expression.

Step 1: Check for a common factor:
In this case, there is a common factor of 3 among all three terms. We can factor out 3 from each term:
3(c^2 - 14c + 49).

Step 2: Factor the quadratic expression (c^2 - 14c + 49):
To factor this quadratic expression, we need to find two numbers whose product is 49 and whose sum is -14 (the coefficient of the middle term).
After examining the factors of 49, we find that -7 and -7 satisfy these conditions.

So, we can rewrite the quadratic expression as:
3(c - 7)(c - 7).

Therefore, the completely factored form of the expression 3c^2 - 42c + 147 is:
3(c - 7)(c - 7).