# A-Level Maths Polynomials

Everything you need to know about polynomials for A-Level Maths. **Save countless hours of time!**

**Polynomials** **Topics for A-Level Maths**

This module will teach you the following:

### Year 1

- Polynomial expressions
- Arithmetic operations on polynomials
- Graphs of polynomials

### Year 2

- Simplifying algebraic fractions

**What’s Included?**

We’ve created **52 modules **covering every Maths topic needed for A level, and each module contains:

- An editable PowerPoint lesson presentation
- Editable revision handouts
- A glossary which covers the key terminologies of the module
- Topical mind maps for visualising the key concepts
- Printable flashcards to help students engage active recall and confidence-based repetition
- A quiz with accompanying answer key to test knowledge and understanding of the module

As a premium member, once rolled out you get access to the entire library of A-Level Maths resources. For now, we have made the first five topics completely free of charge for you to get a taste of what’s to come.

**A Level Maths Resources Mapped by Exam Board**

**A Level Maths Resources Mapped by Exam Board**

Once completed our modules can be used with both UK and international A Level examination board specifications.

We will put together comprehensive mapping documents which will show you exactly which modules align to the specification you are teaching or learning.

## What Are Polynomials?

## Polynomial expressions

Quadratic expression consists of a coefficient of x^{2}. It is in the form of ax^{2}+bx+c=0 where a is a non-zero number, b and c can be any real number.

Cubic expression consists of coefficient of x^{3}. It is in the form of ax^{3} + bx^{2} + cx + d = 0 where a is a non-zero number, b, c and d can be any real number. For example: 3x^{3} – 2x^{2} + x – 1, p^{3} – 1 and z^{3} – 2z^{2} + 1.

The above described expressions are called polynomials. The order of a polynomial is equal to the highest power of variable it contains. For example, order of a quartic expression is 4.

Turning points:

- A n-order polynomial has a maximum of n-1 turning points.
- At repeated roots, the curve touches the x-axis at those points

Arithmetic operations of polynomials:

- Addition or subtraction: like terms
- Multiplication: term by term
- Division: long division method

Finding nature of curves:

- To find the nature of curves:
- x→∞, substitute a large positive value for x.
- x→ -∞, substitute a large negative value for x.

Graphs of polynomials:

- Shape of curve varies with respect to:
- Order of the polynomial
- Sign of the highest power of the variable.

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