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Equations- Factorization of a polynomial equation – Exercise 5602

Exercise

Factor the quadratic equation

4p^2-21p-18=0

Final Answer


(p-6)(4p+3)

Solution

4p^2-21p-18=0

It’s a quadratic equation. Our equation coefficients are

a=4, b=-21, c=-18

We solve it with the quadratic formula. Putting the coefficients in the formula gives us

p_{1,2}=\frac{21\pm \sqrt{{21}^2-4\cdot 4\cdot (-18)}}{2\cdot 4}=

=\frac{21\pm \sqrt{729}}{8}=

=\frac{21\pm 27}{8}

Hence, we get the solutions:

p_1=\frac{21+27}{8}=6

p_2=\frac{21-27}{8}=-\frac{6}{8}=-\frac{3}{4}

Thus, the factorizing of the quadratic equation is

4p^2-21p-18=

=4(p-6)(p+\frac{3}{4})=

=(p-6)(4p+3)

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