Chapter 8: Q41. (page 515)

Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.
$12 x^{2} + 22 x - 14$ .

Short Answer

Expert verified

The factor of each trinomial is:

$2 (2 x - 1) (3 x + 7)$ .

Step by step solution

Step 1. State the concept for factorization of algebraic expressions.

The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
If x is a variable and m, n are positive integers, then $x^{m + n} = (x^{m} \times x^{n})$

Step 2. State the methods to factorize.

Factoring an algebraic expression means writing the expression as a product of factors.

To verify whether the factors are correct or not, multiply them and check if the result is the original algebraic expression.

Algebraic expressions can be factorized using the common factor method, regrouping like terms together, and also by using algebraic identities.

Step 3. Factorize the expression.

Factorizing the given trinomial:

$\begin{matrix} 12 x^{2} + 22 x - 14 = 2 (6 x^{2} + x .11 - 7) \\ = 2 (6 x^{2} + 14 x - 3 x - 7) \\ = 2 [2 x (3 x + 7) - 1 (3 x + 7)] \\ = 2 (2 x - 1) (3 x + 7) \end{matrix}$

Therefore, the factor is $2 (2 x - 1) (3 x + 7)$ .

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Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.
$12 x^{2} + 22 x - 14$ .

Short Answer

Step by step solution

Step 1. State the concept for factorization of algebraic expressions.

Step 2. State the methods to factorize.

Step 3. Factorize the expression.

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Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.12x2+22x−14.

Short Answer

Step by step solution

Step 1. State the concept for factorization of algebraic expressions.

Step 2. State the methods to factorize.

Step 3. Factorize the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Mechanics Maths

Probability and Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.
$12 x^{2} + 22 x - 14$ .