Quad Flashcards
(16 cards)
How would you solve 102 * 301 using QUAD tools?
FOIL the big numbers for easier math. (100 + 2) (300 + 1)
If the constant at the end of the Quad is positive then what is true about the factored pair?
They share the same sign!
How to solve 2x^2 - x - 15 = 0
DO NOT DIVIDE BY 2…
Allow middle term to guide process. It is the result of the Outside and Inside in FOIL. So they equal -1
We can do preliminary factoring, we know so far that (2x - _) (x + _)… 15 is the constant resulting from a product. Meaning options are 1, 3, 5 and 15. Now can plug and play
What are the 3 special products? and how would you convert them to their distributed form?
- Square of a sum: (x + y)^2 =
X^2 + 2xy + y^2 - Square of a difference: (x - y) ^2=
X^2 - 2xy + y^2 - Difference of squares: (x+y) (x-y)=
X^2 - y ^2
Identify which special product this is, explain signals and solve
a^2 - 4ab + 4b^2
square of a difference
- The first and last term are perfect squares.
- The negative term indicates that the factor will include a minus symbol
So take square root of the squared terms. That will create a factor pair, then put a minus between them because of second sign.
Middle term will be twice the product of their square roots AND be negative
Identify which special product this is, explain signals and solve
x^2 + 8x + 16
Square of a sum
- perfect squares for first and third term
- Take square root and boom that’s your factor pair
(x + 4)^2
Middle term will be twice the product of their square roots = 2( x * 4)
Identify which special product this is, explain signals and solve
(1 + radical 2) (1 - radical 2)
Difference of squares
- Same pair except one has a subtraction sign instead of a plus
- In FOIL the inner and outer term will always cancel
When DOS is observed… square the first number and square the second. Then put a minus sign between them.
1 - 2 = -1
When is difference of squares useful?
When needed to rationalize the denominator and simplify
if fraction has a positive radical in denominator, you can multiply it by the negative version of it over itself.
5 / (3 + radical 2)… multiply by (3 - radical 2) / (3 - radical 2)
What are huge signals that I can do easy factoring?
- quad set up, a term has an exponent and it’s being combined with another term which equals zero OR could be manipulated very easily to equal zero
- There are perfect squares and it could be one of 3 special products
GMAT Trap is…
disguised quads like…
3W^2 = 6w or 36/B = B -5
If you treat like normal algebra you will miss the second root
If you can factor a variable out and the resulting quad equals zero…
X = zero is always a solution
Time saver with perfect squares
Exp. (z + 3) ^ 2 = 25
Take root of both sides BUT remember the square exponent hides the signage of the base.
So!!
z + 3 = +5
Z = 3 = -5
Factor (what special product??)
a^2 -1 =
Square of difference
(a -1)^2
(a + 1)(a - 1)
Distribute (what special product??)
(a + b) ^2
Square of a sum
a^2 + 2ab + b^2
If you’re given
A^2 + B^2 = 9 + 2ab
what special product??
You can recognize square of a difference
A^2 -2ab + B^2 = 9
Simply by factoring into the square of a difference form
(a -B) ^2 = 9, A-B = +3 OR -3
Quad traps…
When you could factor it but it isn’t worth it because of a radical sign… instead estimate like radical 3 is 1.7
