x²+7x-8
(x+8)(x-1)
To factor x²+7x-8:
Step 1: Multiply the coefficient of x² (which is 1) and the constant term (which is -8):
1 x -8 = -8
Step 2: Find two numbers that multiply to -8 and add to 7 (the coefficient of x). The pair of numbers that will work are 8 and -1, since 8 x -1 = -8 and 8 + (-1) = 7.
Step 3: Rewrite the middle term 7x as the sum of these two numbers 8x-1x, and group the first two terms and the last two terms:
x² + 8x – 1x – 8
Step 4: Factor out the greatest common factor from the first two terms and the last two terms:
x(x + 8) – 1(x + 8)
Step 5: Factor out the common binomial factor (x + 8):
(x + 8)(x – 1)
Final answer: x² + 7x – 8 = (x + 8)(x – 1)
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