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Let f(x) = 8x3 − 22x2 − 4 and g(x) = 4x − 3. Find f of x over g of x.

2x2 − 4x − 3 − 13 over quantity 4x minus 3
2x2 − 4x − 3 − quantity of 4 x minus 3 over 13
2x2 − 7x − 1
2x2 − 7x − 5 + quantity of x minus 4 over quantity of 4 x minus 3

Respuesta :

lublana

Given that [tex] f(x)=8x^3-22x^2-4 [/tex] and [tex] g(x)=4x-3 [/tex]

Question says to find f of x over g of x which simply means divide value of f(x) by value of g(x)

Dividing them gives:

[tex] \frac{f(x)}{g(x)}=\frac{8x^3-22x^2-4}{4x-3} [/tex]

Denominator is already in factored form which can't divide numerator means it can't be simplified more.

Hence final answer is [tex] \frac{f(x)}{g(x)}=\frac{8x^3-22x^2-4}{4x-3} [/tex].

other part of question is not clear so i will skip them.

LudwigGR

Answer:

The correct answer is the first one.

Step-by-step explanation:

We have the functions [tex]f(x) = 8x^3-22x^2-4[/tex] and [tex]g(x) = 4x-3[/tex]. Then, the fraction is

[tex]\frac{f(x)}{g(x)} = \frac{8x^3-22x^2-4}{4x-3}[/tex].

If we want to give a ‘‘simplified’’ expression for this quotient we must do a a division of polynomials. The algorithm is the analogue for the division of integers. Attached there is an image of the procedure.

After the completion of the division algorithm we obtain

[tex] \frac{f(x)}{g(x)} = \frac{(4x-3)(2x^2-4x-3)-13}{4x-3} = 2x^2-4x-3 - \frac{13}{4x-3}[/tex].

Ver imagen LudwigGR

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