Mathematics: F (x) = 8x^4 – 64 Factor completely

7x² = 9 + x Subtract x from both sides7x² - x = 9 Subtract 9 from both sides7x² - x - 9 = 0 Use the Quadratic Formulaa = 7 , b = -1 , c = -9x = Plug in the a, b, and c valuesx = Cancel out the double negativex = Square -1x = Multiply 7 and -9x = Multiply -4 and -63x = Multiply 2 and 7x = Add 1 and 252x = Split up the x = The approximate square root of 253 is 15.905973.x ≈ Add and subtractx ≈ Dividex ≈ Round to the nearest hundredthx ≈...

F (x) = 8x^4 – 64 Factor completely - id84648499846, gabbiej

Ответ:

dlatricewilcoxp0tsdw

06.02.2022

Mathematics

8(x^4 - 8)

Step-by-step explanation:

Factor out an 8, since both 8 and 64 are divisible by 8:

f(x) = 8x^4 - 64

f(x) = 8(x^4 - 8)

So, the equation factored completely is 8(x^4 - 8)

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Ответ:

amazing05

06.02.2022

Mathematics

$\huge\boxed{f(x)=8(x-\sqrt[4]8)(x+\sqrt[4]8)(x^2+2\sqrt2)}$

$\huge\boxed{f(x)=8(x-2)(x^2+2x+4)}$

Step-by-step explanation:

$f(x)=8x^4-64\qquad|\text{distribute}\\\\f(x)=8(x^4-8)=8\bigg[(x^2)^2-\left(\sqrt8\right)^2\bigg]\qquad|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\f(x)=8(x^2-\sqrt8)(x^2+\sqrt8)=8\bigg[x^2-\left(\sqrt[4]8\right)^2\bigg](x^2+\sqrt8)\\\\|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\f(x)=8(x-\sqrt[4]8)(x+\sqrt[4]8)(x^2+\sqrt8)\\\\\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2$

taking into account the correction from the comment

$f(x)=8x^3-64=8(x^3-8)=8(x^3-2^3)\\\\\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\f(x)=8(x-2)(x^2+(x)(2)+2^2)=8(x-2)(x^2+2x+4)$

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Ответ:

yareli42

14.07.2020

Mathematics

7x² = 9 + x Subtract x from both sides
7x² - x = 9 Subtract 9 from both sides
7x² - x - 9 = 0 Use the Quadratic Formula

a = 7 , b = -1 , c = -9

x = $\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$ Plug in the a, b, and c values
x = $\frac{- (-1) \pm \sqrt{(-1)^2 - 4(7)(-9)} }{2(7)}$ Cancel out the double negative
x = $\frac{1 \pm \sqrt{(-1)^2 - 4(7)(-9)} }{2(7)}$ Square -1
x = $\frac{1 \pm \sqrt{1 - 4(7)(-9)} }{2(7)}$ Multiply 7 and -9
x = $\frac{1 \pm \sqrt{1 - 4(-63} }{2(7)}$ Multiply -4 and -63
x = $\frac{1 \pm \sqrt{1 + 252} }{2(7)}$ Multiply 2 and 7
x = $\frac{1 \pm \sqrt{1 + 252} }{14}$ Add 1 and 252
x = $\frac{1 \pm \sqrt{253} }{14}$ Split up the $\pm$
x = $\left \{ {{ \frac{1 + \sqrt{253} }{14} } \atop { \frac{1 - \sqrt{253} }{14} }} \right.$
The approximate square root of 253 is 15.905973.
x ≈ $\left \{ { \frac{1 + 15.905973}{14} } \atop { \frac{1 - 15.905973}{14} }} \right$ Add and subtract
x ≈ $\left \{ {{ \frac{16.905973}{14} } \atop { \frac{14.905973}{14} }} \right.$ Divide
x ≈ $\left \{ {{1.2075} \atop {1.0647}} \right.$ Round to the nearest hundredth
x ≈ $\left \{ {{1.21} \atop {1.06}} \right.$

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F (x) = 8x^4 – 64

Factor completely

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