Textbook Question
Factor each trinomial, if possible. See Examples 3 and 4. 36x3+18x2-4x
990
views
0. Review of Algebra
Factoring Polynomials
1:17 minutesProblem 43
Textbook Question
In Exercises 1–68, factor completely, or state that the polynomial is prime. x² + 10x − y² + 25
Verified step by step guidance1
Identify the polynomial: \(x^2 + 10x - y^2 + 25\).
Rearrange the terms to group them: \((x^2 + 10x + 25) - y^2\).
Recognize that \(x^2 + 10x + 25\) is a perfect square trinomial, which can be factored as \((x + 5)^2\).
Rewrite the expression using the difference of squares formula: \((x + 5)^2 - y^2\).
Apply the difference of squares formula: \((a^2 - b^2) = (a - b)(a + b)\), where \(a = (x + 5)\) and \(b = y\), resulting in \((x + 5 - y)(x + 5 + y)\).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Polynomials
Factoring polynomials involves rewriting a polynomial expression as a product of simpler polynomials. This process is essential for simplifying expressions and solving equations. Common techniques include factoring out the greatest common factor, using special products like the difference of squares, and applying the quadratic formula when necessary.
Recommended video:
Guided course
07:30
Introduction to Factoring Polynomials
Difference of Squares
The difference of squares is a specific factoring pattern that applies to expressions of the form a² - b², which can be factored into (a + b)(a - b). In the given polynomial, recognizing the presence of a difference of squares can simplify the factoring process, especially when combined with other terms.
Recommended video:
06:24Solving Quadratic Equations by Completing the Square
Completing the Square
Completing the square is a method used to transform a quadratic expression into a perfect square trinomial. This technique is useful for factoring and solving quadratic equations. In the context of the given polynomial, it can help identify the structure of the expression and facilitate the factoring process.
Recommended video:
06:24Solving Quadratic Equations by Completing the Square
Related Videos
Related Practice