Factor 3x² + 7x – 20. Enter the factor with the greater x-coefficient first.
(______ x + ______)(______ x + ______)
Factor 3x² + 7x – 20. Enter the factor with the greater x-coefficient first. (______ x + ______)(______ x + ______)
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To factor the quadratic expression (3x^2 + 7x – 20), we will look for two numbers that multiply to (3 times -20 = -60) and add to (7).
1. The pairs of factors of (-60) that add to (7) are (12) and (-5).
2. Rewrite the middle term using these numbers:
(3x^2 + 12x – 5x – 20).
3. Group the terms:
((3x^2 + 12x) + (-5x – 20)).
4. Factor by grouping:
(3x(x + 4) – 5(x + 4)).
5. Now factor out the common term ((x + 4)):
((3x – 5)(x + 4)).
Thus, the factored form is:
((3x – 5)(x + 4)).
So, you can write it as:
(3x – 5)(x + 4).