What is the quotient of $(3 x^{4} - 4 x^{2} + 8 x - 1) \div (x - 2)$ $(3x^4-4x^2+8x-1)div(x-2)$ ?

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What is the quotient of $(3 x^{4} - 4 x^{2} + 8 x - 1) \div (x - 2)$ $(3x^4-4x^2+8x-1)div(x-2)$ ?

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Answer 1 · 2017-07-05T17:38:24

$3 x^{3} + 6 x^{2} + 8 x + 24$ $3x^3+6x^2+8x+24$

Explanation:

One way of dividing is to use the divisor as a factor in the numerator.

$consider the numerator$ $"consider the numerator"$

$3 x^{3} (x - 2) + 6 x^{3} - 4 x^{2} + 8 x - 1$ $color(red)(3x^3)(x-2)color(magenta)(+6x^3)-4x^2+8x-1$

$= 3 x^{3} (x - 2) + 6 x^{2} (x - 2) + 12 x^{2} - 4 x^{2} + 8 x - 1$ $=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(magenta)(+12x^2)-4x^2+8x-1$

$= 3 x^{3} (x - 2) + 6 x^{2} (x - 2) + 8 x (x - 2) + 16 x + 8 x - 1$ $=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(magenta)(+16x)+8x-1$

$= 3 x^{3} (x - 2) + 6 x^{2} (x - 2) + 8 x (x - 2) + 24 (x - 2) + 48 - 1$ $=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(red)(+24)(x-2)color(magenta)(+48)-1$

$= 3 x^{3} (x - 2) + 6 x^{2} (x - 2) + 8 x (x - 2) + 24 (x - 2) + 47$ $=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(red)(+24)(x-2)+47$

$\Rightarrow quotient = 3 x^{3} + 6 x^{2} + 8 x + 24$ $rArr"quotient "=color(red)(3x^3+6x^2+8x+24)$

$remainder = 47$ $"remainder "=47$

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What is the quotient of $(3 x^{4} - 4 x^{2} + 8 x - 1) \div (x - 2)$ $(3x^4-4x^2+8x-1)div(x-2)$ ?

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Explanation:

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What is the quotient of (3x4−4x2+8x−1)÷(x−2)(3x^4-4x^2+8x-1)div(x-2)?

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What is the quotient of $(3 x^{4} - 4 x^{2} + 8 x - 1) \div (x - 2)$ $(3x^4-4x^2+8x-1)div(x-2)$ ?