Video: US-SAT04S3-Q18-372148642606

The sum of −𝑥² + 2𝑥 + 35 and 4𝑥² + 6𝑥 − 9 can be written in the form 𝑎𝑥² + 𝑏𝑥 + 𝑐, where 𝑎, 𝑏, and 𝑐 are constants. What is the value of 𝑎 + 𝑏 + 𝑐?

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Video Transcript

The sum of negative 𝑥 squared plus two 𝑥 plus 35 and four 𝑥 squared plus six 𝑥 minus nine can be written in the form 𝑎𝑥 squared plus 𝑏𝑥 plus 𝑐, where 𝑎, 𝑏, and 𝑐 are constants. What is the value of 𝑎 plus 𝑏 plus 𝑐?

The word “sum” means add. This means that we need to add our two expressions: negative 𝑥 squared plus two 𝑥 plus 35 and four 𝑥 squared plus six 𝑥 minus nine. In order to do this, we must group or collect the like terms. These are terms with the same power of 𝑥. Our first step is to collect the 𝑥 squared terms. We have negative 𝑥 squared and four 𝑥 squared. Negative one plus four is equal to three. Therefore, negative 𝑥 squared plus four 𝑥 squared is equal to three 𝑥 squared.

Next, we can group the 𝑥 terms. We have positive two 𝑥 and positive six 𝑥. Two plus six is equal to eight. Therefore, the 𝑥 terms simplify to eight 𝑥. Finally, we have the constant terms. We have positive 35 and negative nine. 35 minus nine is equal to 26. Therefore, the constant terms simplify to 26. The sum of negative 𝑥 squared plus two 𝑥 plus 35 and four 𝑥 squared plus six 𝑥 minus nine is three 𝑥 squared plus eight 𝑥 plus 26.

We have now written this in the form 𝑎𝑥 squared plus 𝑏𝑥 plus 𝑐, where 𝑎 is the coefficient of 𝑥 squared, 𝑏 is the coefficient of 𝑥, and 𝑐 is our constant. 𝑎 is equal to three, 𝑏 is equal to eight, and 𝑐 is equal to 26. We have been asked to calculate the value of 𝑎 plus 𝑏 plus 𝑐. This means that we need to add three, eight, and 26. Three plus eight is equal to 11. Adding this to 26 gives us 37. The value of 𝑎 plus 𝑏 plus 𝑐 is 37.

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