Question

Factor each expression completely. $$ 4 x^{2}-22 x+10 $$

   Factor each expression completely.
$$
4 x^{2}-22 x+10
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 63

Instant Answer

Solved by Expert Robert Leedy

01/17/2020

Step 1

We recognize every term is divisible by two. Factoring that out, we have: $$ 2(2x^{2}-11x+5) $$ Show more…

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Factor each expression completely. $$ 4 x^{2}-22 x+10 $$

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Key Concepts

AC Method

The AC method is a specific technique used for factoring quadratic expressions when the leading coefficient is not 1. It involves multiplying the leading coefficient (a) and the constant term (c), then finding two numbers that multiply to ac and add to the middle coefficient (b). After identifying these numbers, the expression is split and factored by grouping.

Quadratic Expressions

Quadratic expressions are polynomials of degree two, typically written in the form ax² + bx + c. They form the basis of many algebraic problems, and understanding their structure is key to solving equations and factoring methods.

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting the quadratic as a product of two binomials. This process can reveal the roots of the equation and is fundamental in simplifying expressions and solving quadratic equations.

Discriminant

The discriminant of a quadratic expression, given by b² - 4ac, is an important concept as it indicates the nature of the roots of the equation. A positive discriminant suggests two distinct real roots, which can help determine whether the trinomial can be factored over the real numbers.

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