Algebra and Algebraic Techniques
In the Bagrut mathematics exam, the algebra domain checks whether you can manipulate expressions fluently and justify each step. Questions mix factoring, exponents, radicals, rational expressions, and polynomial division, often as the first stage of a larger function or calculus problem.
Core rules
- Factor before you cancel: common factor, difference of squares a²−b²=(a−b)(a+b), trinomials, and grouping.
- For rational expressions, state restrictions where the denominator is zero; the simplified expression must keep them.
- Exponent laws: a^m·a^n=a^(m+n), a^m/a^n=a^(m−n), (a^m)^n=a^(mn), a^(−n)=1/a^n.
- √(a²)=|a|, not automatically a.
- Remainder theorem: the remainder of P(x) divided by x−c is P(c).
Worked example
Simplify (x²−9)/(x²+5x+6) ÷ (x−3)/(x+2). Factor: x²−9=(x−3)(x+3), x²+5x+6=(x+2)(x+3). The division becomes [(x−3)(x+3)]/[(x+2)(x+3)] · (x+2)/(x−3)=1, with x≠−2,−3,3. The restrictions come from the original denominators and the divisor, not from the cancelled factors alone.
Traps
Cancelling a term such as x+3 inside a sum instead of a factor is invalid. Dropping domain restrictions loses marks in Bagrut. Sign errors when factoring x²−9 or when subtracting rational expressions are common. Do not distribute a square root over a sum.