Algebra Class: GCF and Factoring Techniques

False (B)

Prime Factorization and Listing Factors

<p>$(a + b)(a - b)$</p> Signup and view all the answers

<p>6 (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>$(x+5)(x-5)$</p> Signup and view all the answers

<p>GCF = The largest number that divides two or more numbers without a remainder Prime Factorization = Breaking down a number into its prime factors DOTS = The difference of two squares Factor = Numbers that divide evenly into a number</p> Signup and view all the answers

<p>$(x+4)(x-4)$ (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Solving Systems of Equations: Substitution or Elimination</p> Signup and view all the answers

<p>variable</p> Signup and view all the answers

<p>Elimination method (A)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Solve one equation for one variable</p> Signup and view all the answers

<p>constant</p> Signup and view all the answers

<p>$x^2 - 4$ = $(x+2)(x-2)$ $9x^2 - 1$ = $(3x+1)(3x-1)$ $4x^2 - 25$ = $(2x+5)(2x-5)$ $16x^2 - 49$ = $(4x+7)(4x-7)$</p> Signup and view all the answers

<p>4 (A)</p> Signup and view all the answers

The largest number that divides two or more numbers without leaving a remainder.

Breaking down a number into its prime factors, which are only divisible by 1 and themselves.

It's the difference between two perfect squares that can be factored into two binomials.

A binomial is an algebraic expression with two terms, like (x + 2) or (y - 3).

The formula for DOTS is 𝑎^2 - 𝑏^2 = (𝑎 + 𝑏)(𝑎 - 𝑏), where 'a' and 'b' are the square roots of the squares.

Finding the GCF by listing all the factors of each number and then selecting the largest common factor.

Finding the GCF by breaking down each number into its prime factors and then identifying the common prime factors and multiplying them.

Recognizing the two perfect squares in the expression and applying the DOTS formula (𝑎^2 - 𝑏^2 = (𝑎 + 𝑏)(𝑎 - 𝑏)) to factor it.

The formula for the difference of squares: (a + b)(a - b) = a^2 - b^2. To factor a binomial using this pattern, identify the squares and then apply the formula.

The process of finding the factors of an algebraic expression by using the formula: a^2 - b^2 = (a + b)(a - b).

A system of equations is a set of two or more equations that share the same variables. The goal is to find the values for the variables that satisfy all equations simultaneously.

A method for solving systems of equations by isolating one variable in one equation and substituting it into the other equation.

The process of solving for one variable in a system of equations by manipulating the equations to have opposite coefficients for one variable and then adding or subtracting the equations to eliminate that variable.

The act of multiplying one or both equations in a system of equations by a constant to make the coefficients of one variable opposites, facilitating elimination.

When the coefficients of one variable in a system of equations are opposites, adding the equations eliminates that variable, simplifying the system.

After eliminating one variable in a system of equations, solving for the remaining variable to find the first solution to the system.

When the system of equations has been solved for one variable, substituting that value back into one of the original equations to find the second solution to the system.

The values of the variables that satisfy all equations in a system of equations simultaneously.