Math · 12 · Advanced Math

Advanced Algebra

Notes

Equivalent expressions: expand, factor or combine — or test one value in both.
Rational equations: multiply by the LCD; reject any value that zeros a denominator.
Radical equations: isolate the root, square both sides, then check every answer.
Zero at $x=a$ ⇔ factor $(x-a)$ ⇔ $p(a)=0$ .
Remainder of $p(x)\div(x-a)$ is just $p(a)$ .
Match coefficients: if $ax^2+bx+c\equiv 3x^2+5x-2$ , then $a=3$ , $b=5$ , $c=-2$ .

Difference of squares

a^2-b^2=(a+b)(a-b)

Factor theorem

p(a)=0\iff(x-a)\ \text{is a factor of}\ p(x)

Remainder theorem

p(x)=(x-a)q(x)+p(a)

Adding fractions

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}

Square root

\sqrt{x^2}=|x|

Equivalent-expression question: plug x = 2 into the original and every choice. If two match, try x = 3.

10 official SAT questions on Advanced Algebra, easiest first.