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 (3x² + 7x – 20), we need to find two numbers that multiply to (3 times -20 = -60) and add up to (7).
The two numbers that satisfy this are (12) and (-5) (since (12 times -5 = -60) and (12 + (-5) = 7)).
Next, we can rewrite the middle term of the quadratic:
[ 3x² + 12x – 5x – 20 ]
Now, we can group the terms:
[ (3x² + 12x) + (-5x – 20) ]
Factoring each group gives us:
[ 3x(x + 4) – 5(x + 4) ]
Now, we can factor out the common binomial, ((x + 4)):
[ (3x – 5)(x + 4) ]
So the factored form of (3x² + 7x – 20) is:
((3x – 5)(x + 4))
Since we want to enter the factor with the greater x-coefficient first:
The answer is: (3x – 5)(x + 4).