Find two numbers that add to make -1 (the coefficient of our second term) and multiply to make 12 (the third term):
-4 * 3 = 12
-4 + 3 = -1
So negative four and three are the numbers we want. Now break the middle term down, using those two numbers:
x2 - x - 12
= x2 + 3x - 4x - 12
We now have a common factor (x + 3), that we can factor out of both the first two and the last two terms:
= x(x + 3) - 4(x + 3)
And we can group those like terms together, giving us the final answer:
= (x - 4)(x + 3)
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: (1 plus or minus the square root of 1201) divided by 24.
x = 1.4856436209302881
x = -1.4023102875969549
(x + 2)(x - 7)
x2+2x-63 = (x-7)(x+9) when factored
two factors is a binomial three factors is a trinomial four of more is a polynomial the product of any of these is just a polynomial
2(x + 2)(x - 2)(x2 + 2x + 4)(x2 - 2x + 4)
-4
-x2 + 2x + 48 = (-x - 6)(x - 8)
-x2 + 2x + 48 = (x +6)(8 - x)
-x2 + 2x + 48 = (-x - 6)(x - 8)
2x^2
(x+6)*(x-4)
-2x3 + 2x2 + 12x =(-2x) (x2 - x - 6) =(-2x) (x+2) (x-3)
I assume your problem is: -2x3-2x2+12x-2x(x2-x-6)-2x(x-3)(x+2)
-2x3 + 2x2 + 12x = -2x(x2 - x - 6) = -2x(x2 + 2x - 3x - 6) = -2x[ x(x + 2) - 3(x + 2) ] = -2x(x - 3)(x + 2)
-x2 - 11x + 26= -x2 - 13x + 2x + 26= (2x - x2) + (26 - 13x)= x(2 - x) + 13(2 - x)= (2 - x)(x + 13)
Simplifying x2 + -2x + -63 Reorder the terms: -63 + -2x + x2 Factor a trinomial. (-7 + -1x)(9 + -1x) Final result: (-7 + -1x)(9 + -1x)
(x + 2)(x - 7)
-x2 - 11x + 26 = -(x2 + 11x - 26) = -(x2 - 2x + 13x - 26) = -[ x(x - 2) + 13(x - 2) ] = -(x + 13)(x - 2) = (x + 13)(2 - x)