Find each product :

Question

Find each product :

(3 x - 2) (4 x^{2} + 3 x - 5)

Accepted Answer

Welcome back. I'm so glad you're here. We're multiplying these two polynomial. We've got two x minus four in the first set of parentheses, times three X squared minus seven X plus eight in the second set of parentheses. So we're going to start by distributing this to X. And we're going to multiply it by the first term in the second set of parentheses, so two X times three X squared which will give us six X cubed. And now we'll stick with this two X. And will multiply it by the second term over here to X times negative seven X will give us negative 14 X squared. We'll stick with this two X for the final term over here. Two X times eight will give us plus 16 X. Now we can start distributing that negative four negative four times the first term over here, negative four times three X squared will give us negative 12 X squared. We can take the negative four times the middle term. So negative four times negative seven X will give us positive 28 X. And then we can take the final one, the negative four times the eight. And that will get us minus 32. And now it's just a matter of combining like terms. So we look at the six X cubed is the only X cubed. So we can carry that down negative 14 X. And over here we've got a negative 12 X. So we can say minus 26 X squared. And we've got this plus 16 X plus another 28 X. So that will be a plus 44 X. And then we carry down that minus 32 because that's the only term with no X. And we look over at our answer choices and that is going to match with answer choice a well done, we'll catch you on the next one.

Find each product : $(3 x - 2) (4 x^{2} + 3 x - 5)$

Key Concepts

Polynomial Multiplication

Distributive Property

Combining Like Terms

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