Algebra (Aleks)

Factoring a quadratic with leading coefficient greater than 1: Problem type 2

14x^2 + 9x -5 1. p and q integers 2. pq = 14 • (-5) = -70 3. p+q = 9

Square root multiplication: advance

2 sqrt 72 • sqrt 98 1. Simplify the sqrt expression 2. Simplify the product = 168

Signed fraction division

3/20 / (-21/16) 1. Reciprocal (-16/21) 2. cancel (dividing by common factor) 3. Cancel (dividing by common factor) = -4/35

Solving a two-step equation with signed fraction

3/2w - 1/7 = -8/5 1. Eliminate all the fractions with multiplying both sides by LCD of the fraction 2. Distributive property on the left hand side 3. Cancelling by dividing by common factors 4. Simplifying 5. Solve for w w = -34/35

Simplifying a ratio of univariate monomials

30y^4/5y^7 1. Divide variable 2. Cancel the numerator and minus it on denominator = 6/y^3

Using distribution with double negation and combining like terms to simplify: Multivariate

3x - 4(4y - 3x) + 4y 1. Distributive property 2. Subtraction as addition of a negative 3. Commutative property 4. Combining like terms 5. Addition of a negative as subtraction 15x - 12y

Evaluating Expressions with exponents and zeros

a^0 = 1

Solving an equation written in factored form

(w + 7)(w - 8) = 0 Equal to 0 (w +7)(w - 8) = 0 w = -7, 8

Degree and leading coefficient of a univariate polynomial

-5 - 10w + w^6 1. Rewrite polynomial in standard Degree - exponent of its variable - no variable, 0 Leading coefficient - number multiplying the variable - no variable, the term itself Degree: 6 Leading coefficient: 1

Solving a linear equations with several occurrences of the variable: Variables on both sides and two distributions

-6(3x-1)+4x = 1+2(2x-5) 1. Distributive property to remove parentheses 2. Combining like terms on each side 3. Subtracting the variable of the left side to each side 4. Subtract constant of the right side to each side 5. Dividing the variable of the constant of the right side to each side 6. Simplify X = 5/6

Introduction to the LCM of two monomials

12a^4 and 9a^2 LCM of 12 and 9 is 36 LCM of a^4 and a^2 is a^4 LCM of both us 36 • a^4 = 36a^4 36a^4

Simplifying a ratio of factored polynomials: Linear factors

56(u-7)(2u-3) / 7(2u-3)(u+8) 1. Cancel the common factor 2. Rewrite 3. Cancel the common factor 8(u-7) / u+8

Simplifying a ratio of polynomials using GCF factoring

8w^2 - 12w / 4w^2 - 16 1. Factor the numerator and denominator 2. Get the GCF 3. Cancel common factors 4. Rewrite in factor form = 2w - 3 / w - 4

Multiplicative property of equality with signed fractions

9 = -3/4y (-4/3)•9 = (-4/3)•(-3/4)y *reciprocal* -12 = y

Rationalizing a denominator: Quotient involving square roots

Sqrt 2 / sqrt 3 Multiply the fraction with the same denominator and simplify Sqrt 6 / 3

Introduction to simplifying a product involving square roots using the distributive property

Sqrt 7 (sqrt 6 - 11) 1. Distributive property 2. Property sqrt a • sqrt b = sqrt ab 3. Multiplying under the sqrt sign

Square root multiplication: Basic

Sqrt a • sqrt b = sqrt ab 1. Product property of sqrts 2. Multiply under square root sign 3. Factoring out and perfect square 4. Product property of sqrts = 4 sqrt 3

Evaluating a function: linear and quadratic or cubic

Substitution property