What are the roots of the polynomial x^2 + 2x - 8?

What are the roots of the polynomial x^2 + 2x - 8?

Step 1: Start with the polynomial x^2 + 2x - 8.
Step 2: Look for two numbers that multiply to -8 (the last number) and add to 2 (the middle number).
Step 3: The two numbers that work are 4 and -2 because 4 * -2 = -8 and 4 + (-2) = 2.
Step 4: Rewrite the polynomial using these numbers: x^2 + 4x - 2x - 8.
Step 5: Group the terms: (x^2 + 4x) + (-2x - 8).
Step 6: Factor out the common terms: x(x + 4) - 2(x + 4).
Step 7: Now, factor out (x + 4): (x + 4)(x - 2).
Step 8: Set each factor to zero: x + 4 = 0 and x - 2 = 0.
Step 9: Solve for x: From x + 4 = 0, we get x = -4. From x - 2 = 0, we get x = 2.
Step 10: The roots of the polynomial are x = -4 and x = 2.

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