step 1 Given 5x squared plus 7x plus 2, consider A and C that multiplies to 10. And think of how we cou

Factor. 5 x 2+7 x+2

Name: Problem 2, Chapter 6: Elementary Algebra
Uploaded: 2022-01-29T22:00:47-08:00
Duration: 31 s
Channel: James Kiss
Description: Factor. 5 x 2+7 x+2

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Key Concepts

Quadratic Polynomial

A quadratic polynomial is a second-degree polynomial typically written in the form ax² + bx + c, where a, b, and c are constants and a is not zero. Understanding its structure is essential because it allows you to apply systematic methods to solve equations and factor them into products of binomials if possible.

AC Method (Product-Sum Approach)

The AC method is a factoring technique used for quadratic polynomials where you multiply the coefficient of x² (a) and the constant term (c) to find a target product. Then, you search for two numbers that multiply to this product (ac) and add up to the coefficient of x (b). This technique simplifies the process of splitting the middle term to factor by grouping.

Factoring by Grouping

Factoring by grouping is a method used after splitting the middle term in a quadratic polynomial. It involves dividing the polynomial into two groups that share a common factor in each group, and then extracting these common factors to rewrite the polynomial as a product of two binomials. This approach is particularly useful when direct factoring is not immediately apparent.

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