Question

Factor each expression. $$ 3 x^{2}-4 x+1 $$

   Factor each expression. 
$$
3 x^{2}-4 x+1
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 78

Instant Answer

Solved by Expert Amrita Bhasin

08/08/2019

Step 1

We need to find two numbers that multiply to $3*1=3$ (the product of the coefficient of $x^{2}$ and the constant term) and add up to $-4$ (the coefficient of $x$). Show more…

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Factor each expression. $$ 3 x^{2}-4 x+1 $$

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Key Concepts

Quadratic Expression

A quadratic expression is a second-degree polynomial with the general form ax² + bx + c, where a, b, and c are constants and a is nonzero. This type of expression is ubiquitous in algebra and often represents parabolic curves when graphed.

Factoring Techniques for Quadratics

Factoring a quadratic expression involves rewriting it as a product of two binomials. Common methods include the trial and error method and the ac method, where the product of the coefficient of x² (a) and the constant term (c) is used to split the middle term. This process is essential for solving quadratic equations and simplifying expressions.

Discriminant and Factorability

The discriminant, given by b² - 4ac, is a tool used to determine the nature of the roots of a quadratic equation. A positive perfect square discriminant often indicates that the quadratic can be factored into binomials with integer coefficients, making the factoring process straightforward.

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