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Math  /  Algebra

QuestionQuestion 34
Divide: −6x7−4x3−2x22x2\frac{-6 x^{7}-4 x^{3}-2 x^{2}}{2 x^{2}} □\square Question Help: Video

Studdy Solution

STEP 1

1. We are given a polynomial expression in the numerator and a monomial in the denominator.
2. The division involves dividing each term in the numerator by the term in the denominator.

STEP 2

1. Divide each term in the numerator by the term in the denominator.
2. Simplify each resulting term.

STEP 3

Identify each term in the numerator: −6x7-6x^7, −4x3-4x^3, and −2x2-2x^2.
Divide each term by the denominator 2x22x^2.
−6x72x2,−4x32x2,−2x22x2 \frac{-6x^7}{2x^2}, \quad \frac{-4x^3}{2x^2}, \quad \frac{-2x^2}{2x^2}

STEP 4

Simplify each term individually:
1. −6x72x2=−3x7−2=−3x5\frac{-6x^7}{2x^2} = -3x^{7-2} = -3x^5
2. −4x32x2=−2x3−2=−2x1=−2x\frac{-4x^3}{2x^2} = -2x^{3-2} = -2x^1 = -2x
3. −2x22x2=−1\frac{-2x^2}{2x^2} = -1

STEP 5

Combine the simplified terms to get the final result:
−3x5−2x−1 -3x^5 - 2x - 1

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