Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**How to Factor \(3x^2 + 17x + 10\) by Grouping**

Complete the sentences to explain how to factor \(3x^2 + 17x + 10\) by grouping.

\[3x^2 + 17x + 10 = 3x^2 + \boxed{\quad}x + \boxed{\quad}x + 10\]

- The product of these coefficients must be \(\boxed{\quad}\).
- The sum of these coefficients must be \(\boxed{\quad}\).

In this example, we need to find two numbers that multiply to give the product of the first and last coefficients (in this case, \(3\) and \(10\)), and add up to the middle coefficient (\(17\)).

By solving these requirements, we proceed to factor the quadratic polynomial by grouping.
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Transcribed Image Text:**How to Factor \(3x^2 + 17x + 10\) by Grouping** Complete the sentences to explain how to factor \(3x^2 + 17x + 10\) by grouping. \[3x^2 + 17x + 10 = 3x^2 + \boxed{\quad}x + \boxed{\quad}x + 10\] - The product of these coefficients must be \(\boxed{\quad}\). - The sum of these coefficients must be \(\boxed{\quad}\). In this example, we need to find two numbers that multiply to give the product of the first and last coefficients (in this case, \(3\) and \(10\)), and add up to the middle coefficient (\(17\)). By solving these requirements, we proceed to factor the quadratic polynomial by grouping.
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