The factor of the cubic expression x³ + 5x² − 3x − 15 is (x + 5)(x² - 3) option (D) is correct.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
A cubic expression:
= x³ + 5x² − 3x − 15
To find the first factor we will use the trial and error method:
Plug x = 5 in the above expression:
= (-5)³ + 5(-5)² − 3(-5) − 15
= -125 + 125 + 15 − 15
= 0
x = -5 is the zero of the above expression:
Or
(x + 5) is the factor of the cubic expression x³ + 5x² − 3x − 15
To get other factor:
(x³ + 5x² − 3x − 15) ÷ (x + 5)
After dividing:
= (x³ - 3)
The factor of the cubic expression x³ + 5x² − 3x − 15 is:
= (x + 5)(x² - 3)
Thus, the factor of the cubic expression x³ + 5x² − 3x − 15 is (x + 5)(x² - 3) option (D) is correct.
Learn more about quadratic equations here:
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