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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Because he was outstanding in his field!

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).