What are quadratic expressions?
A quadratic expression is a mathematical expression, where the highest power of the first term is "2". To be able to determine whether an expression is a quadratic expression or not you can see if the highest exponent or degree of the first term is 2. The expression must have a power of 2, No lower and no higher.
For example: x^2 - 5x + 4
x^2 - 5x + 4
x^2 - 4x - x + 4
x (x-4) -1 (x-4)
(x-1) (x-4)
Step by Step guide -
Step 1 - Identify if the given question is a quadratic expression.
Step 2 - Identify the terms in the expressions. ( a,b, and c term)
Step 3 - Write them out.
step 4 - Now find the "ac" term.
Step 5 - Identify which two numbers when multiplied equate to the "ac" term and when added or subtracted equate to the "b" term.
Step 6 - Rewrite the a term and the two numbers you found and rewrite the c term.
Step 7 - Bracket the first two terms and the last two terms of the expression written.
Step 8 - Take out what's common from the first bracket and use your result to factor out what's inside the bracket.
Step 9 - Repeat step 8 for the second bracket.
Step 10 - Ensure that the brackets are the same.
Step 10 - After results are found you are now going to place the two terms on the outside in a bracket, and rewrite one of the brackets.
Written example -
x^2 - 2x - 35
a = 1, b = -2, c = -35, ac = -35 ( step 3 )
-7 + 5 ( step 5 )
x^2 - 7x + 5x - 35
x ( x-7) +5 (x-7)
(x+5) (x-7)
Diagram Example 2 -
2x^2 + 9x + 9 :
Common mistakes often made by students :
1. They don't identify if the expression is quadratic.
2. They forgot to find the "ac" term.
3. Have non-identical brackets.
Ways to fix these common mistakes :
1. Ensure you always identify if the given expression is quadratic before solving.
2. Always remember to find the ac term because this is what helps to find the two numbers needed to replace the B term.
3. Always check to ensure that your brackets are the same.
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