# A-Level Maths Polynomials

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

## PolynomialsTopics 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

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.

## Polynomial expressions

Quadratic expression consists of a coefficient of x2. It is in the form of ax2+bx+c=0 where a is a non-zero number, b and c can be any real number.

Cubic expression consists of coefficient of x3. It is in the form of ax3 + bx2 + cx + d = 0 where a is a non-zero number, b, c and d can be any real number. For example: 3x3 – 2x2 + x – 1, p3 – 1 and z3 – 2z2 + 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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