x2 + 5xy - 18y2 can not be factored.
x2-64 = (x-8)(x+8)
3x2 = -9 (divide both sides by 3) x2 = -3 (x would have to be the square root of -3) x = ±√-3 x = ±√3i Since you want to solve by factoring: x2 = -3 add 3 to both sides x2 + 3 = 0 x2 - 3i2 = 0 x2 - (√3i)2 = 0 Factor: (x - √3i)(x + √3i) = 0 x - √3i = 0 or x + √3i = 0 x = √3i or x = -√3i
x2+6x+9 = x+3 x2+6x-x+9-3 = 0 x2+5x+6 = 0 Solve by factoring or with the help of the quadratic equation formula: (x+3)(x+2) = 0 Therefore: x = -3 or x = -2
To factor any term, divide by the LCF (largest common factor) of the term. For 5x2-45, the LCF is 5. 5x2-45 = 5(x2-9) It can, of course, be factored even further to become: 5(x2-9) = 45(x2/9 - 1) but when factoring, we usually don't need to go past 5(x2-9) (for example, you've figured out that x2 = 9, thus x = +/- 3.)
x2+7x-18 = (x-2)(x+9) when factored because -2*9 = -18 and 9x-2x = 7x
First, it is important to regroup, so I am going to rearrange this equation: (x4 - 7x2 - 18 - 3x3 + 27x I can now factor the first three terms and the last two terms: (x4 - 7x2 - 18) becomes (x2 - 9)(x2 + 2) -3x3 + 27x becomes -3x(x2 - 9); so the new equation looks like: (x2 - 9)(x2 + 2) - 3x(x2 - 9) From here, factor out what is common, in this case- x2- 9. Therefore, you will have (x2 - 9)(x2 + 2 - 3x), which can be rearranged to (x2 -9)(x2 - 3x + 2). Further factoring reveals (x + 3)(x - 3)(x - 1)(x - 2) as the final answer.
x2 - 14x + 49 = (x - 7)2
When the co-efficient of x2 is 1
(x+8)(x-4)
-(x - 1)(x2 + x + 1)
(x+5)(x-3)