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Rewrite each expression without absolute value bars. |7 - π|
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 56
Factor each perfect square trinomial.
Guida verificata passo dopo passo1
Recognize that the given trinomial \(64x^2 - 16x + 1\) is a perfect square trinomial, which generally has the form \(a^2 - 2ab + b^2\).
Identify the square terms: \$64x^2$ is $(8x)^2$ and \(1\) is \$1^2$.
Check the middle term to confirm the pattern: the middle term should be \(-2 \times 8x \times 1 = -16x\), which matches the given middle term.
Write the trinomial as a square of a binomial: \((8x - 1)^2\).
Thus, the factorization of \(64x^2 - 16x + 1\) is \((8x - 1)^2\).
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Perfect Square Trinomial
A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. It takes the form a^2 ± 2ab + b^2, which factors into (a ± b)^2. Recognizing this pattern helps simplify factoring problems quickly.
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Solving Quadratic Equations by Completing the Square
Factoring Quadratic Expressions
Factoring quadratics involves rewriting the expression as a product of two binomials. For perfect square trinomials, this process is straightforward because the factors are identical binomials, making it easier to solve or simplify equations.
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06:08Solving Quadratic Equations by Factoring
Identifying Squares and Middle Term
To factor a perfect square trinomial, identify the square terms (first and last) and verify if the middle term equals twice the product of their square roots. This check confirms the trinomial is a perfect square and guides the correct binomial factors.
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06:24Solving Quadratic Equations by Completing the Square
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