How do you find the quotient of 3x^3 - 2x^2 +5 / x - 4?

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How do you find the quotient of 3x^3 - 2x^2 +5 / x - 4?

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Answer 1 · 2015-12-22T17:47:58

$3 x^{2} + 10 x + 40$ $3x^2+10x+40$

Explanation:

divide the term $3 x^{3} - 2 x^{2} + 5$ $3x^3-2x^2+5$ traditionally by $x - 4$ $x-4$
so you have $3 x^{3} - 2 x^{2} + 5$ $3x^3-2x^2+5$ = $x - 4 \cdot$ $x-4 *$ quotient + remainder

$x - 4 \cdot 3 x^{2} = 3 x^{3} - 12 x^{2}$ $x-4 * 3x^2 = 3x^3-12x^2$
Subtract this with the polynomial you get $10 x^{2} + 5$ $10x^2+5$
$x - 4 \cdot 10 x = 10 x^{2} - 40 x$ $x-4 * 10x = 10x^2-40x$
Subtract this from the polynomial in step 2 to get $40 x + 5$ $40x+5$
$x - 4 \cdot 40 = 40 x - 160$ $x-4 * 40 = 40x-160$
Subtract this from the polynomial in step 4 to get $165$ $165$

now the number cannot be divided further hence 165 is remainder
and $3 x^{2} + 10 x + 40$ $3x^2+10x+40$ is the quotient (sum of terms we used in steps 1, 3 and 5)

$3 x^{3} - 2 x^{2} + 5 = (x - 4) \cdot (3 x^{2} + 10 x + 40) + 165$ $3x^3-2x^2+5 = (x-4) * (3x^2+10x+40) +165$

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How do you find the quotient of 3x^3 - 2x^2 +5 / x - 4?

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