Algebra

Topic overview

P3 algebra questions often hide binomial expansion, partial fractions, and factor and remainder theorems in the parametric conditions. First confirm the target coefficient or identity, then decide how far to expand.

Key concepts

(1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+\cdots

When $n$ is not a positive integer, the expansion is usually valid only for $|x|<1$ . If the expression first has a constant multiple or a linear substitution, adjust both the coefficients and the range of convergence.

Key points

◆Expand only to the order required by the question
◆Translate the parameter conditions into equations for the coefficients
◆Finally, state the valid range

Worked examples

Try each example yourself before checking the explanation.

1Finding parameters from coefficients

In $(1+kx)^{-1/2}$ the coefficient of $x^2$ is $3/2$ , and $k>0$ ; find $k$ .

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