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Chapter 8: Q41. (page 515)

Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.

12x2+22x鈭�14.

Short Answer

Expert verified

The factor of each trinomial is:

2(2x鈭�1)(3x+7).

Step by step solution

01

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

  1. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
  2. If x is a variable and m, n are positive integers, thenxm+n=(xm脳xn)
02

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.

03

Step 3. Factorize the expression.

Factorizing the given trinomial:

12x2+22x鈭�14=2(6x2+x.11鈭�7)=2(6x2+14x鈭�3x鈭�7)=2[2x(3x+7)鈭�1(3x+7)]=2(2x鈭�1)(3x+7)

Therefore, the factor is 2(2x鈭�1)(3x+7).

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Most popular questions from this chapter

Find the greatest common factor of each set of monomials.

22b,33c

Find the greatest common factor of each set of monomials.

21xy,28x2y,42xy2

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

x2鈭�12x+36is an example of a perfect square trinomial.

Factor the polynomial mn+5m鈭�3n鈭�15.

Amn鈭�35

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Find each product.

2x+5y2x鈭�5y
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