SOLUTION: How would you factor these four problems: 1) x2- 64 2)x4-y4 3)x2-7X+10 4)2X2- 5x-3

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Question 49170: How would you factor these four problems:
1) x2- 64
2)x4-y4
3)x2-7X+10
4)2X2- 5x-3
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
1) x^2 - 64 find factors of -64 that sum to 0 : -8 and 8
x^2 - 8x + 8x - 64
(x^2 - 8x) + (8x - 64)
x(x - 8) + 8(x - 8)
(x + 8)(x - 8)
2) x^4 - y^4
Just as you see above: (a - b)(a + b) = a^2 - b^2
what are 'a' and 'b' for x^4 - y^4 in a^2 - b^2
a = x^2 and b = y^2
(x^2 - y^2)(x^2 + y^2)
3)x^2 - 7x + 10 find factors of 10 that sum to -7: -5 and -2
x^2 - 5x - 2x + 10
(x^2 - 5x) + (-2x + 10)
x(x - 5) - 2(x - 5)
(x - 2)(x - 5)
4) 2x^2 - 5x - 3 find factors of -6 that sum to -5: -6 and 1
2x^2 - 6x + x - 3
(2x^2 - 6x) + (x - 3)
2x(x - 3) + 1(x - 3)
(2x + 1)(x - 3)