## FACTOR USING A QUADRATIC PATTERN

Factor using a quadratic pattern :

To factor equation using quadratic pattern we have to convert the given equation in the form of quadratic equation ax² + bx + c known as quadratic equation. Then we have factorize this quadratic equation.

Example 1 :

Factor x⁴ + 10 x² + 25 completely.

Solution :

To factor the above equation let us take x² = t

=  (x²)² + 10 x² + 25

=  t² + 10 t + 25

=  t² + 5 t + 5 t + 25

Factor out t from first and second terms and factor out 5 from third and fourth terms

=  t (t + 5) + 5 (t + 5)

=  (t + 5) (t + 5)

Example 2 :

Factor 5 x - 29 x² + 20 completely.

Solution :

To factor the above equation let us take x² = t

=  5 (x²)² - 29 x² + 20

=  5 t² - 29 t + 20

=  5 t² - 25 t - 4 t + 20

Factor out 5 t from first and second terms and factor out -4 from third and fourth terms

=  5 t (t - 5) - 4 (t - 5)

=  (t - 5) (5 t - 4)

Example 3 :

Factor 3 x - 10 x² + 8 completely.

Solution :

To factor the above equation let us take x² = t

=  3 (x²)² - 10 x² + 8

=  3 t² - 10 t + 8

=  3 t² - 6 t - 4 t + 8

Factor out 3 t from first and second terms and factor out -4 from third and fourth terms

=  3 t (t - 2) -4 (t - 2)

=  (t - 2) (3 t - 4)

Example 4 :

Factor 18 x - x² - 4 completely.

Solution :

To factor the above equation let us take x² = t

=  18 (x²)² - x² - 4

=  18 t² - t - 4

=  18 t² - 9 t + 8 t - 4

Factor out 9 t from first and second terms and factor out 4 from third and fourth terms

=  9 t (2 t - 1) + 4 (2 t - 1)

=  (2 t - 1) (9 t + 4)

After having gone through the stuff given above, we hope that the students would have understood "Factor using a quadratic pattern".

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