factor completely. -49x^2-35x-6
Please help with this, I know you multiply the two outer numbers which =-294, I am just having trouble finding a pair of factors of 294 that sum add up to 35. thanks
-49x^2-35x-6
-(49x^2+35x+6)
-(7x+2)(7x+3)
To factor the expression -49x^2 - 35x - 6 completely, let's break it down step by step.
We need to find two numbers whose product is equal to the product of the coefficient of the x^2 term (-49) and the constant term (-6). In this case, (-49) * (-6) equals 294.
So, we need to find two numbers that multiply to give 294 and add up to the coefficient of the x term (-35). Let's examine the factors of 294:
1 * 294 = 294
2 * 147 = 294
3 * 98 = 294
6 * 49 = 294
7 * 42 = 294
14 * 21 = 294
Since the coefficient of the x term is negative (-35), we need to find a pair of factors whose sum is also negative. From the options above, only 7 and 42 have a sum of 35, but since the x term is negative, we need to use the negative values (-7 and -42).
Now we can rewrite the expression -35x by splitting it into -7x and -42x. Therefore, the expression -49x^2 - 35x - 6 can be rewritten as:
-49x^2 - 7x - 42x - 6
Now, we can factor by grouping. Take out the greatest common factor from the first two terms and the second two terms separately:
-7x(7x + 1) - 6(7x + 1)
Now, we can see that we have a common factor, which is (7x + 1). We can factor it out:
(-7x - 6)(7x + 1)
So, the completely factored form of -49x^2 - 35x - 6 is (-7x - 6)(7x + 1).