[tex]64x^4+24x^3-72x^2=(8x^2)(8x^2)+(8x^2)(3x)-(8x^2)(9)\\\\=8x^2(8x^2+3x-9)=(*)\\-------------------------------\\Quadratic\ formula\\ax^2+bx+c\\\\8x^2+3x-9\\a=8,\ b=3,\ c=-9\\\Delta=b^2-4ac\to\Delta=3^2-4(8)(-9)=9+288=297=(9)(33)\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\to x_1=\dfrac{-3-\sqrt{(9)(33)}}{2(8)}=\dfrac{-3-3\sqrt{33}}{16}\\\\x_2=\dfrac{-b+\sqrt\Delta}{2a}\to x_2=\dfrac{-3+\sqrt{(9)(33)}}{2(8)}=\dfrac{-3+3\sqrt{33}}{16}\\--------------------------------[/tex]
[tex](*)=8x^2\left(x-\dfrac{-3-3\sqrt{33}}{16}\right)\left(x-\dfrac{-3+3\sqrt{33}}{16}\right)[/tex]
Answer:
After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )
Step-by-step explanation:
Given Polynomial:
[tex]6x^4+24x^3-72x^2[/tex]
we need to completely factorize the polynomial.
Consider,
[tex]6x^4+24x^3-72x^2[/tex]
GCF = 6x², By taking it common out
[tex]=6x^2(x^2+4x-12)[/tex]
[tex]=6x^2(x^2+6x-2x-12)[/tex]
[tex]=6x^2(x(x+6)-2(x+6))[/tex]
[tex]=6x^2(x+6)(x-2)[/tex]
Therefore, After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )
