GMAT Algebra

• 1) Factoring by inspection
• 2) Plugging in the answer choices

• No - must be x²+2x-24=0
• Must = 0

• 1) Bring down the first sign
• 2) Look at the 2nd sign, if neg means different from the first sign
• 3) Figure out multiples of the last # & choose #s which also add/sub to middle #
• 4) Place the larger # on left

Use the substitution method when it is not easy to cancel out terms. But use the direct approach on all other problems (when you can cancel out terms by adding two equations together).

=1 (for x≠0)

• 1
• x^a

x^a

x^a+b

y^ax^b (can't combine non-like terms)

x^a-b

x^a∙b

x^a∙y^a

You can distribute the exponent to each variable

• (x^a)
• (y^a)

For division you can also distribute the exponent to each variable

7²⁴

Factor 4 so we have same base to solve

4³=2^x -> (2²)³ = 2^x -> 2⁶=2^x -> x=6

then the exponents must equal one another

(thus the goal is to make each side of the equation have the same prime #s and then equate the exponents)

x=5, y=4, z=5

the exponent rules

rely on your understanding of factoring to combine like terms and then use any necessary exponent rules

No - to add/subtract must have same base & same exponent.

(Try to change the add/sub into multiplication by factoring)

• Factor out 3⁵ from each #
• 3⁵(1+3³-3²-3) = 3⁵(1+27-9-3) = 16(3⁵)

x^a+b

same base, add exponents

x^a-b

When dividing same base, subtract exponents

x^a∙b

When raising a variable with an exponent to another power, multiply the exponents

x^1-a

Same as the exponent division rule (1 is just implied)

x⁹

In this case the parenthesis location is important. 3² = 9

x^a∙ya

• Distribute the exponent to each variable
• 12² = (3∙4)² = 3²∙4² = 144

(x ^1/b)^a = (x^a)^1/b = ^b√(x^a)

8²

(³√64)² = (4)² = 16

2√2

3√3

No, not standard

• 9√3 = 3
• 3

Isolate the unknown on one side of the equation

Infinite

One or None

• 1) Express one of the unknowns in terms of the other using one of the equations
• 2) Substitute the expression into the remaining equation, to cancel out one unknown.
• 3) Then solve for the unknown
• 4) Plug the solution for the one unknown back into one of the orig. equations & solve for the other unknown.

• 1) Make the coefficients of one of the unknowns the same, so that they cancel out when you add/subtract the equations together.
• 2) Add the equations together (leaving one unknown). Solve for it.
• 3) Plug the solution for the one unknown back into one of the equations and solve for the other unknown.

• 1) Substitition method
• 2) Direct method (cancel out an unknown)

• 1) Add/Subtract expressions to bring them all on one side and set = 0.
• 2) Try to factor out the side with all the expressions
• 3) Keep combining/simplifying until you see the solution(s) to make the expressions = 0.

roots

ax² + bx + c = 0

Two, One, or None.

f(x) is the corresponding output to the input (x).

The domain of the function. (i.e. the limitations/rules of what x can be).

a sequence and noted as a_n

• even roots = 2 solutions (+ and -)
• odd roots = 1 solution

x² + 2xy + y²

x² -2xy + y²

x²- y²