You factorize a quadratic expression
Rule
Find the roots of the expression,
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If the equation doesn’t have any solutions, the expression can’t be factorized.
Example 1
Factorize
Use the quadratic formula. Here, we have
This means that
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which tells us that the factorized expression is
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Example 2
Factorize
To factorize an expression by completing the square, we have to first use one of the algebraic identities to complete the square, and then the third algebraic identity to finish the factorization.
Example 3
Factorize
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If a quadratic equation only has one real solution, the quadratic expression is a complete square. That’s something we can look for when we attack a new quadratic equation.
Example 4
Factorize
Use the quadratic formula. Here, we have
Because we only have one solution, the factorized expression becomes
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Example 5
Factorize