Question

Factor each expression. $$ x^{2}+5 x+6 $$

   Factor each expression.
$$
x^{2}+5 x+6
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 8

Instant Answer

Solved by Expert Amrita Bhasin

08/08/2019

Step 1

Step 1: First, we need to find two numbers that multiply to 6 (the constant term) and add to 5 (the coefficient of the middle term). Show more…

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Factor each expression. $$ x^{2}+5 x+6 $$

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Key Concepts

Product-Sum Method

The product-sum method is a common strategy for factoring quadratics. It requires identifying two numbers that multiply to the constant term (c) and add up to the linear coefficient (b). Once these numbers are found, the quadratic can be factored into two binomials.

Quadratic Polynomial

A quadratic polynomial is an algebraic expression of degree two, typically written in the form ax² + bx + c. These expressions form parabolic curves when graphed, and their properties, such as vertex, axis of symmetry, and roots, are fundamental in algebra.

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting the quadratic as a product of two binomials. This method is particularly effective when the leading coefficient is 1, as it allows the exponential expression to be decomposed into factors that can be set equal to zero to find the roots.

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