G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

Year 10 Interactive Maths - Second Edition


Factors of Quadratic Trinomials of the Type ax² + bx + c

Factorise (factorize) the quadratic trinomial by experimenting with its linear factors using the cross multiplication method.

The linear factors (7x + 1) and (x + 2) do not produce the middle term of 9x.

 72 + 1 = 14x+ x = 15x.  We reject this pair as the middle term is 9x.

The linear factors (7x + 2) and (x + 1) produce the middle term of 9x.

So 7x^2 + 9x + 2 = (7x+2)(x+1)  

Note:

The solution is read across.


Use of a Common Factor

If a quadratic trinomial has a common factor, take it out and place it in front of the brackets.  Then use the cross-multiplication method to factorise the quadratic trinomial.

Example 10

Factorise (factorize) 12x^2 - 14x - 6.

Solution:
Take out the common factor of 2 and then factorise (factorize) the quadratic trinomial by experimenting with its linear factors using the cross multiplication method.

The factors 6x and x don't produce the middle term.

The linear factors (2x - 3) and (3x + 1) produce the middle term -7x.

So 12x^2 - 14x - 6 = 2(2x-3)(3x+1)

Check:
Check by expanding 2(2x-3)(3x+1).
Note:

The common factor 2 was taken out first to make the factorisation simpler.


Example 11

Factorise (factorize) 18a^2 + 3a - 6.

Solution:

Take out the common factor of 3 and then factorise (factorize) the quadratic trinomial by experimenting with its linear factors using the cross multiplication method.

The factors 6a and a don't produce the middle term.

Now try the factors 2a and 3a.

The linear factors (2a - 1) and (3a + 2) produce the middle term a.

So 18a^2 + 3a - 6 = 3(2a-1)(3a+2)

Check:

Check by expanding 3(2a-1)(3a+2).


Note:

The common factor 3 was taken out first to make the factorisation simpler.


| Home Page | Order Maths Software | About the Series | Maths Software Tutorials |
| Year 7 Maths Software | Year 8 Maths Software | Year 9 Maths Software | Year 10 Maths Software |
| Homework Software | Tutor Software | Maths Software Platform | Trial Maths Software |
| Feedback | About mathsteacher.com.au | Terms and Conditions | Our Policies | Links | Contact |

Copyright © 2000-2022 mathsteacher.com Pty Ltd.  All rights reserved.
Australian Business Number 53 056 217 611

Copyright instructions for educational institutions

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.
If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number.