Divide (16x^5-56x^4+24x^3)/(8x^4)

Math
16×5-56×4+24x38x4
Simplify the numerator.
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Factor 8×3 out of 16×5-56×4+24×3.
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Factor 8×3 out of 16×5.
8×3(2×2)-56×4+24x38x4
Factor 8×3 out of -56×4.
8×3(2×2)+8×3(-7x)+24x38x4
Factor 8×3 out of 24×3.
8×3(2×2)+8×3(-7x)+8×3(3)8×4
Factor 8×3 out of 8×3(2×2)+8×3(-7x).
8×3(2×2-7x)+8×3(3)8×4
Factor 8×3 out of 8×3(2×2-7x)+8×3(3).
8×3(2×2-7x+3)8×4
8×3(2×2-7x+3)8×4
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅3=6 and whose sum is b=-7.
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Factor -7 out of -7x.
8×3(2×2-7(x)+3)8×4
Rewrite -7 as -1 plus -6
8×3(2×2+(-1-6)x+3)8×4
Apply the distributive property.
8×3(2×2-1x-6x+3)8×4
8×3(2×2-1x-6x+3)8×4
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
8×3((2×2-1x)-6x+3)8×4
Factor out the greatest common factor (GCF) from each group.
8×3(x(2x-1)-3(2x-1))8×4
8×3(x(2x-1)-3(2x-1))8×4
Factor the polynomial by factoring out the greatest common factor, 2x-1.
8×3((2x-1)(x-3))8×4
8×3(2x-1)(x-3)8×4
8×3(2x-1)(x-3)8×4
Cancel the common factor of 8.
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Cancel the common factor.
8×3(2x-1)(x-3)8×4
Rewrite the expression.
(x3(2x-1))(x-3)x4
(x3(2x-1))(x-3)x4
Cancel the common factor of x3 and x4.
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Factor x3 out of (x3(2x-1))(x-3).
x3((2x-1)(x-3))x4
Cancel the common factors.
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Factor x3 out of x4.
x3((2x-1)(x-3))x3x
Cancel the common factor.
x3((2x-1)(x-3))x3x
Rewrite the expression.
(2x-1)(x-3)x
(2x-1)(x-3)x
(2x-1)(x-3)x
Expand (2x-1)(x-3) using the FOIL Method.
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Apply the distributive property.
2x(x-3)-1(x-3)x
Apply the distributive property.
2x⋅x+2x⋅-3-1(x-3)x
Apply the distributive property.
2x⋅x+2x⋅-3-1x-1⋅-3x
2x⋅x+2x⋅-3-1x-1⋅-3x
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x by adding the exponents.
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Move x.
2(x⋅x)+2x⋅-3-1x-1⋅-3x
Multiply x by x.
2×2+2x⋅-3-1x-1⋅-3x
2×2+2x⋅-3-1x-1⋅-3x
Multiply -3 by 2.
2×2-6x-1x-1⋅-3x
Rewrite -1x as -x.
2×2-6x-x-1⋅-3x
Multiply -1 by -3.
2×2-6x-x+3x
2×2-6x-x+3x
Subtract x from -6x.
2×2-7x+3x
2×2-7x+3x
Split the fraction 2×2-7x+3x into two fractions.
2×2-7xx+3x
Split the fraction 2×2-7xx into two fractions.
2x2x+-7xx+3x
Cancel the common factor of x2 and x.
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Factor x out of 2×2.
x(2x)x+-7xx+3x
Cancel the common factors.
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Raise x to the power of 1.
x(2x)x1+-7xx+3x
Factor x out of x1.
x(2x)x⋅1+-7xx+3x
Cancel the common factor.
x(2x)x⋅1+-7xx+3x
Rewrite the expression.
2×1+-7xx+3x
Divide 2x by 1.
2x+-7xx+3x
2x+-7xx+3x
2x+-7xx+3x
Cancel the common factor of x.
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Cancel the common factor.
2x+-7xx+3x
Divide -7 by 1.
2x-7+3x
2x-7+3x
Divide (16x^5-56x^4+24x^3)/(8x^4)

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