Chapter 8: Q63. (page 516)

Factor each trinomial, if possible. If the polynomial cannot be factored, write prime.
$x^{4} - 1$

Short Answer

Expert verified

The factor of the polynomial is:

$(x - 1) (x + 1) (x^{2} + 1)$

Step by step solution

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

I. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.

II. 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.

Factorize the given polynomial by using the formula: $a^{2} - b^{2} = (a - b) (a + b)$ .

$\begin{matrix} x^{4} - 1 = ({(x^{2})}^{2} - 1^{2}) \\ = (x^{2} - 1) (x^{2} + 1) \\ = (x^{2} - 1^{2}) (x^{2} + 1) \\ = (x - 1) (x + 1) (x^{2} + 1) \end{matrix}$

Therefore, the factor is $(x - 1) (x + 1) (x^{2} + 1)$ .

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Factor each trinomial, if possible. If the polynomial cannot be factored, write prime.
$x^{4} - 1$

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 polynomial cannot be factored, write prime.x4−1

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

Applied Mathematics

Decision Maths

Geometry

Theoretical and Mathematical Physics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Factor each trinomial, if possible. If the polynomial cannot be factored, write prime.
$x^{4} - 1$