Equating Coefficients Flashcards

All 4 cards in this deck

What does the symbol $\equiv$ mean in algebra?

It shows an identity — the two sides are equal for every value of the variable.

What does "equating coefficients" in an identity mean?

The coefficients of each power of $x$ (and the constant terms) must be equal on both sides.
e.g. in $ax^2+\ldots \equiv 5x^2+\ldots$, $a=5$

What are the steps to find unknown constants in an identity?

e.g. $x^2+6x+11 \equiv (x+a)^2+b$

1. Expand the side with the unknowns: $x^2+2ax+a^2+b$
2. Equate coefficients of $x$: $2a=6$, so $a=3$
3. Equate constants: $9+b=11$, so $b=2$

Apart from comparing coefficients, what other method finds unknown constants in an identity?

Substitute convenient values of $x$ into both sides.
e.g. putting $x=0$ compares the constant terms