Equations- Factorization of a polynomial equation – Exercise 5602

Exercise

Factor the quadratic equation

$4p^2-21p-18=0$

Final Answer

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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

$4p^2-21p-18=$

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

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