Mathematics: Factor the polynomial 6x4 + 24x3 − 72x2 completely by first factoring out the gcf, and then factoring the rest of the expression.

Factor the polynomial 6x4 + 24x3 − 72x2 completely

Ответ:

july00

11.03.2022

Mathematics

After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )

Step-by-step explanation:

Given Polynomial:

6x^4+24x^3-72x^2

we need to completely factorize the polynomial.

Consider,

6x^4+24x^3-72x^2

GCF = 6x², By taking it common out

=6x^2(x^2+4x-12)

=6x^2(x^2+6x-2x-12)

=6x^2(x(x+6)-2(x+6))

=6x^2(x+6)(x-2)

Therefore, After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )

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Ответ:

ethanyayger

11.03.2022

Mathematics

$64x^4+24x^3-72x^2=(8x^2)(8x^2)+(8x^2)(3x)-(8x^2)(9)\\\\=8x^2(8x^2+3x-9)=(*)\\-------------------------------\\Quadratic\ formula\\ax^2+bx+c\\\\8x^2+3x-9\\a=8,\ b=3,\ c=-9\\\Delta=b^2-4ac\to\Delta=3^2-4(8)(-9)=9+288=297=(9)(33)\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\to x_1=\dfrac{-3-\sqrt{(9)(33)}}{2(8)}=\dfrac{-3-3\sqrt{33}}{16}\\\\x_2=\dfrac{-b+\sqrt\Delta}{2a}\to x_2=\dfrac{-3+\sqrt{(9)(33)}}{2(8)}=\dfrac{-3+3\sqrt{33}}{16}\\--------------------------------$