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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Factorization of Quadratic Expressions

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:factorization_of_quadratic_expressions/3548/


Example 1.

Factorize:


    
Example 2.

Simplify:


    
3.

Simplify:


    
4.

Simplify:


    
5.

Simplify:


    
6.

We simplify:


    
7.

Simplify:


    
8.
Prove that:

.

    

9.

A number n divides a dividend to give a quotient of 7 and remainder 1. If also divides the dividend to give a quotient 5 and remainder of 3. Find n and the dividend.

    
10.
Prove that:

    
11.
Prove that:

.

    
12.
Show that:

    
13.
Show that:

    
14.
Show that:

    
15.
Show that:

    
16.
Show that:

    
17.

Find a number that divides the difference of the squares of two consecutive odd numbers, where the two consecutive odd numbers are and .

    
18.

If and are divisible by . Prove that is also divisible by .

    

19.

Prove that is divisible by 9 if is divisible by 6 and is a multiple of 5.

    
20.

Prove that:


If n is not divisible by 3, then its square reduced by 1 is divisible by 3.

    
21.

If is a perfect square, find the minimum even number which satisfies the expression.

    
22.

Prove that if n is a number, then is divisible by 4.