Expression structure
A numerical coefficient is the signed number multiplying a specified pronumeral part. State exactly which term is meant when products and single pronumerals both occur
- Keep the sign In an expanded expression, separate terms at addition and subtraction signs. Keep each sign with its term \(\displaystyle -3x^2+5x-7\)
- A product stays together The factors in a product form one term. A plus sign inside brackets does not split an outer product \(\displaystyle 4xy=4\times x\times y\)
- Invisible ones A pronumeral written without a number has numerical coefficient one or negative one \(\displaystyle -x=(-1)\times x\)
- Constants and zero terms A constant has no pronumeral. If none is written, the constant term is zero. A zero-coefficient term vanishes \(\displaystyle 0x=0\)
Worked example
Identify the terms and numerical coefficients in this expanded expression
- \(\displaystyle 5a^2,\quad-3ab,\quad a,\quad-8\)There are four signed terms; the constant is negative eight
- \(\displaystyle 5a^2=5\times a^2\)The squared term has numerical coefficient five
- \(\displaystyle -3ab=(-3)\times ab\)The product term has numerical coefficient negative three
- \(\displaystyle a=1\times a\)The standalone a term has numerical coefficient one
Common mistakes
Difficulty levels
Questions about this topic
Why can a coefficient be negative?+
It includes the sign of its term. Negative three x is negative three multiplied by x.
Do several tiles mean several terms?+
No. Tiles of the same pronumeral part represent one term with a larger coefficient
What if a constant is missing?+
The constant term is zero. A term with zero coefficient contributes nothing and can be omitted
Can I split at a sign inside brackets?+
First identify the outer operations. A bracket multiplied by another factor is a single outer term until expanded
Why specify the standalone term?+
An expression can contain both l and wl. Asking for the numerical coefficient of the standalone l term avoids confusing it with the product term
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 3: Algebra and indices