Factor each expression completely:
18b²+24b-10
Thanks in advance.
factor out a two first, then
2*(9b^2 + 12b -5)
2(3b+5)(3b-1)
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To factor the expression 18b² + 24b - 10 completely, you can follow these steps:
Step 1: Look for the greatest common factor (GCF) among the terms. In this case, the GCF is 2, so factor out a 2 from each term:
2(9b² + 12b - 5)
Step 2: Now you need to factor the trinomial inside the parentheses, 9b² + 12b - 5. To do this, look for two numbers that multiply to give -45 (the product of the leading coefficient and the constant term) and add up to the coefficient of the middle term, which is 12 in this case.
The factors of -45 that add up to 12 are 15 and -3. So, rewrite the trinomial using these factors:
2(9b² + 15b - 3b - 5)
Step 3: Group the terms in pairs:
2[(9b² + 15b) + (-3b - 5)]
Step 4: Factor out the greatest common factor from each pair:
2[3b(3b + 5) - 1(3b + 5)]
Step 5: Notice that the terms (3b + 5) are common in both pairs. Factor this common binomial out:
2(3b + 5)(3b - 1)
Therefore, the expression 18b² + 24b - 10 is completely factored as 2(3b + 5)(3b - 1).