0. Review of Algebra

Factoring Polynomials

Textbook Question
Factor each trinomial, if possible. See Examples 3 and 4. (2p+q)²-10(2p+q)+25
Textbook Question
Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. $6y^3(4y - 1)^{-3/7} - 8y^2(4y - 1)^{4/7} + 16y(4y - 1)^{11/7}$
Textbook Question
In Exercises 39–44, factor by introducing an appropriate substitution.(x + 1)² + 8(x + 1) + 7 (Let u = x+1.)
Textbook Question
In Exercises 1–68, factor completely, or state that the polynomial is prime. 11x⁵ − 11xy²
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Textbook Question
Factor using the formula for the sum or difference of two cubes. $x cubed minus 27$
Textbook Question
In Exercises 39–48, factor the difference of two squares. 36x²−49y²
Textbook Question
Factor out the greatest common factor. $9 x^{4} - 18 x^{3} + 27 x^{2}$
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Textbook Question
In Exercises 1–68, factor completely, or state that the polynomial is prime. 12x³ + 3xy²
Textbook Question
Write each rational expression in lowest terms. 8x² + 16 / 4x²
Textbook Question
Simplify each complex fraction. $$\frac{\frac{3}{p^2 - 16}$ + p}{$\frac{1}{p - 4}$}$
Textbook Question
In Exercises 23–34, factor out the negative of the greatest common factor.−4x³ + 32x² − 20x
Textbook Question
In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.36x² - 49y²
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Textbook Question
In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.x² + x − 30
Textbook Question
In Exercises 39–44, factor by introducing an appropriate substitution.x⁴ − 4x² − 5
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Textbook Question
Factor by any method. See Examples 1–7. $(x + y)^{3} - (x - y)^{3}$