Show how to factor out 4x^2 - 12x + 5.

Question:

Show how to factor out {eq}\; 4x^2 - 12x + 5 {/eq}.

Factorization of Quadratic Polynomials:

The following steps are followed to factorize the polynomial of the form {eq}ax^2 + bx + c: {/eq}

Step 1: Multiply the co-efficient of {eq}x^2 {/eq} and constant term.

Step 2: Split this product into two factors such that their sum is equal to the co-efficient of {eq}x. {/eq}

Step 3: The terms are grouped into pairs and factorize.

Answer and Explanation:

Co-efficient of {eq}x^2 = 4 {/eq}; Constant term {eq}= 5 {/eq}

Their product = {eq}4 \times 5 = 20 {/eq}

Co-efficient of {eq}x = -12 {/eq}

Therefore, product {eq}= 20; {/eq} sum {eq}= -12 {/eq}

Factors of 20 Sum of factors
-1, -20 -21
-4, -5 -9
-2, -10 -12
The required factors are -2, -10

Therefore, {eq}4x^2 - 12x + 5 {/eq} can be written as {eq}4x^2 - 2x -10x + 5 {/eq}

{eq}= 2x(2x - 1) - 5(2x - 1) {/eq}

{eq}= (2x - 1)(2x - 5) {/eq}

Therefore, the factors of {eq}4x^2 - 12x + 5 {/eq} are {eq}(2x - 1)(2x - 5). {/eq}


Learn more about this topic:

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Factoring Polynomial Expressions

from College Algebra: Help and Review

Chapter 8 / Lesson 4
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