Question 33232: How can do you factor a trinomial? x^2 - 11x - 60
Thank you
Found 2 solutions by sarah_adam, mszlmb:
Answer by sarah_adam(201)   (Show Source):
Answer by mszlmb(115)  (Show Source):
You can put this solution on YOUR website! Check this out in case I do it wrong myself!
Your equation  is very simple to factor because  is not multiplied by anything. I'll tell you how to solve those at the end.
I'll use the substitutes A, B, and C, defined  . Your A=1 B=-11 C=-60.
Basically, the only hard part is finding the two numbers that ADD to B and MULTIPLY to A*C. [Let the numbers be X and Y:  , and  ]. In your equation, X+Y=-11 and XY=-60. We know one number is positive, and one negative.
How do we know that? Since it's product (XY) is negative, we know that one is negative and one positive (because (+ times +) and (- times -) both have negative answers. We also know that the bigger number is negative because the sum is negative, it makes sense.
Now, what numbers add up to -11 and multiply to -60? First, we find the numbers that add up to 11 and multiply to 60. It's simpler.  , but 10*1=10, not 60. 10*6=60, but  . How about 15? No, 15*4=60, but 15+4, and 15-4=11. Ha! It equals 11! We know from earlier that we only have one negative and its the larger number, now you know why. -15+4=4-15=-11, and as we concluded 4*-15=*60!
Now that we've found the numbers, we put them in the equation, previously  . We change the -11x to +4x-15x (it's the same). The equation now yields  . Now, you see that  and -15x both have something in common with 4x and -60. and 4X are both divisible by X, so  is replaced by x(x+4). -15x and -60 have a negative 15 in common (-60= -15*4). So we replace -15x-60 by -15(x+4). Our entire equation is now x(x+4)-15(x+4).
Put the x+4's together and what's leftover? x-15. there's your equation:
(X+4)(X-15)
Any questions IM me.
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