| A | B |
|---|
| x^2 -3x - 28 | x^2 -3x -28 Find two numbers that multiply to give us -28 and add to give us -3: -7 and 4: (x-7)(x+4) |
| 6x^2 + x - 15 | 6x^2 + x - 15 We need two numbers that multiply to give us -90 (6 times -15) and adds to give us 1: -9 and 10: 6x^2-9x+10x-15=3x(2x-3)+5(2x-3) =(3x+5)(2x-3) |
| x^2 - 5x - 36 | x^2 - 5x - 36 Find two numbers with a product of -36 and a sum of -5: -9 and 4: (x-9)(x+4) |
| x^2 - 36 | x^2 - 36 This is a difference of squares. Put the square root of x^2 and the square root of 36 in plus minus form: (x+6)(x-6) Or think x^2+0x-36: Two numbers that multiply to give us -36 and add to give us 0 are -6 and 6: (x-6)(x+6) |
| 20x^2 - x - 12 | 20x^2-x-12 We want two numbers that multiply to give us 20 times -12 (-240) and adds to give us -1: -16 and 15: 20x^2-16x +15x-12=4x(5x-4)+3(5x-4) =(4x+3)(5x-4) |
| 21x^2 + 2x - 8 | 21x^2+2x-8 Look for two numbers that have a product 21 times -8 (-168) and a sum of 2: -12 and 14: 21x^2-12x+14x-8 =3x(7x-4)+2(7x-4) =(3x+2)(7x-4) |
| x^2 - 3x -54 | x^2-3x-54 Two numbers with a product of -54 and a sum of -3: -9 and 6: (x-9)(x+6) |
| 12x^2 + 29x - 8 | 12x^2+29x-8 Find two numbers with a product of -96 (12 times -8) and a sum of 29: -3 and 32: 12x^2-3x+32x-8=3x(4x-1)+8(4x-1) =(4x-1)(3x+8) |
| 18x^3+3x^2-10x | 18x^3+3x^2-10x=x(18x^2+3x-10) Find two numbers with a product of -180 (18 times -10) and a sum of 3: 15 and -12 x(18x^2+15x-12x-10)= x(3x(6x+5)-2(6x+5)) =x(3x-2)(6x+5) |
| 14x^3-x^2-3x | 14x^3-x^2-3x=x(14x^2-x-3) Two numbers that multiply to give us -42 (14 times -3) and add to give us -1 are -7 and 6: x(14x^2-x-3)=x(14x^2-7x+6x-3)= x((7x(2x-1)+3(2x-1)) =x(7x+3)(2x-1) |
| 6x^2-29x+20 | 6x^2-29x+20 Find two numbers that multiply to give us 120 (6x20) and add to give us -29: -24 and -5 6x^2-24x-5x+20=6x(x-4)-5(x-4) =(6x-5)(x-4) |
| 2x^2-98 | 2x^2-98=2(x^2-49) =2(x+7)(x-7) You could think: 2x^2+0x-98=2(x^2+0x-49) Now, we need two numbers that multiply to give us -49 and add to give us 0: -7 and 7 That gives us 2(x-7)(x+7) OR whenever you recognize a difference of squares just put the square roots in "plus and minus" form: 2(x^2-49)=2(x+7)(x+7) since the square roots of x^2 and 49 are x and 7. |
