In Exercises 23–34, find each product using either a horizontal o...

Question

In Exercises 23–34, find each product using either a horizontal or a vertical format.

(x²+2x−1)(x²+3x−4)

Accepted Answer

Hello, today we're gonna be multiplying the following polynomials and simplifying the resulting product. So we are given Q squared plus four Q minus two. And we're going to multiply that by Q squared plus five Q minus three. So the way that we multiply this together is to go ahead and foil the two quantities together. And so what we're going to do is we're going to take the first term Q squared and multiply it with each term in the following quantity. So Q squared times Q squared is going to give us Q to the fourth power, then Q squared times five Q is going to give us five Q cubed. Next, we're going to multiply Q squared with negative three and that is going to give us negative three Q squared. Then we're going to repeat this process with the next term four Q. So we're gonna take four Q and multiply it with Q squared and four Q multiplied by Q squared is going to give us positive four Q cubed. Next we're gonna multiply four Q with five Q and that is going to give us a product of positive 20 Q squared. Then we're gonna multiply four Q with negative three. And that is going to give us negative 12 Q. Finally, we're going to distribute, I mean foil negative two with Q squared. So negative two times Q squared is going to give us negative two Q squared. Next negative two times five Q is going to give us negative 10-Q. And finally negative two times negative three is going to give us positive six. So what we now now have is a sum indifference of multiple terms. And the way that we can simplify this is to go ahead and add and subtract all the like terms together. So the first term is Q to the fourth and this is the only term that has an exponent of four. So we're gonna write down Q to the fourth as the first simplification. Next, let's go ahead and add all of the Q cube terms together. So we have five q cubed And we have four q cubed and five Q cubed plus four Q cubed is going to give us nine Q cubed. So the next term is going to be nine Q to the third power. Next, we're gonna combine all of the Q squared terms together. So we have negative three Q squared, 20 Q squared and negative two Q squared. So N three Q squared plus 20 Q squared minus two Q squared is going to give us 15 Q squared. So next simplification is going to be positive 15 Q squared, then we're going to add all the Q terms together. So we have negative 12 Q and we have negative 10-Q and negative 12 Q minus 10-Q is going to give us negative Q. And finally, we have the constant at the end which is six. And then we're gonna add that to the end of our simplification. And so this is going to simplify to a polynomial of five terms. We have Q to the fourth plus nine Q cubed plus 15 Q squared minus 22 Q plus six. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 23–34, find each product using either a horizontal or a vertical format. (x²+2x−1)(x²+3x−4)

Key Concepts

Polynomial Multiplication

Horizontal and Vertical Formats

Combining Like Terms

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