Question

Factor the trinomial completely by using any method. Remember to look for a common factor first. $$5 p^{2}-10 p+7$$

Name: Problem 30, Chapter 4: Intermediate Algebra
Uploaded: 2020-06-23T05:15:42-08:00
Duration: 1 min 54 s
Channel: Ankit Gupta
Description: Factor the trinomial completely by using any method. Remember to look for a common factor first. 5 p^2-10 p+7

   Factor the trinomial completely by using any method. Remember to look for a common factor first.
$$5 p^{2}-10 p+7$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 4, Problem 30

Instant Answer

Solved by Expert Ankit Gupta

06/23/2020

Step 1

In this case, the trinomial is $5p^{2}-10p+7$. The coefficients are $a=5$, $b=-10$, and $c=7$. Show more…

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Factor the trinomial completely by using any method. Remember to look for a common factor first. $$5 p^{2}-10 p+7$$

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Key Concepts

Common Factor

The first step in factoring any expression is to look for a common factor among all its terms. This simplifies the expression and can make further factoring easier by reducing the coefficients or variable powers involved.

Factoring Trinomials

Trinomials, which are quadratic expressions typically written in the form ax² + bx + c, are factored by identifying two numbers that multiply to the product of a and c and add to b. This method is straightforward when the trinomial factors nicely over the integers.

Quadratic Discriminant

The discriminant, given by b² – 4ac, is crucial in determining the nature of the roots of a quadratic equation. A negative discriminant indicates that the quadratic does not have real roots and therefore does not factor into linear factors over the real numbers.

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