Factorising Polynomials and Identities

Name: Factorising Polynomials and Identities
Author: StemPy Lab

Just as 12 is 3 times 4, a polynomial can be a product of smaller polynomials. Here we learn the factor theorem, how to factorise quadratic and cubic polynomials, and the algebraic identities that help us calculate fast.

3 lessons, about 1 h 10 min3 simulations10 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The factor theorem
The factor theorem says that x minus a is a factor of p(x) if and only if p(a) is 0. To test a divisor such as x plus 2, use a equal to minus 2. It can be used to find an unknown constant, and to find the other factor by synthetic division. For a polynomial with whole number coefficients, a whole number zero must divide the constant term, so only those numbers need to be tried. Once one factor is found, the quotient has a lower degree and is easier to factorise.
1 simulation2 practice questions1 Python program3 problems1 Python lab
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Lesson 2about 25 min
Factorising polynomials
To factorise is to write a polynomial as a product of polynomials of lower degree. First take out any common factor, then use identities such as the difference of two squares and the perfect squares. For a quadratic ax squared plus bx plus c, split the middle term using two numbers with product ac and sum b, then group. For a cubic, find one zero with the factor theorem, divide it out, and factorise the quadratic that is left. A factorisation can be checked by multiplying the factors back, or by comparing the zeroes with the coefficients.
1 simulation2 practice questions1 Python program3 problems
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Lesson 3about 20 min
Algebraic identities
An algebraic identity is true for every value of the variables. The identities for squares, cubes and the difference of squares help us expand, factorise and calculate quickly.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set1 note
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Factorising and Identities: Challenge Paper

10 questions · 20 min

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Factorising Polynomials and Identities

Course outline (3 lessons)

The factor theorem

Factorising polynomials

Algebraic identities

Test Your Learning

Your teacher

Discussion (0)

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