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------------------------------------------------ Divide [tex]45x^7[/tex] by [tex]-9x^4[/tex].

A. [tex]-5x^3[/tex]
B. [tex]-4x^3[/tex]
C. [tex]5x^3[/tex]
D. [tex]4x^3[/tex]

To divide 45x⁷ by -9x⁴, divide 45 by -9 to get -5, and subtract the exponent in the denominator from the one in numerator to get x^3. Therefore, the answer is a) -5x³..

Explanation:

The question asks to divide 45x⁷ by -9x⁴. To divide these two polynomials, you just need to carry two separate divisions, one with coefficients (45 by -9) and one with variable parts (x⁷ by x⁴).

Firstly, if you divide coefficient 45 by -9, you will get -5. Now, coming to the variable part which is x⁷ divided by x⁴, according to the subtraction rule of exponents, you just subtract the exponent in the denominator from the exponent in the numerator (which is 7-4), and you obtain x³.

Therefore, the result of the division of 45x⁷ by -9x⁴ is -5x³. So, the correct answer is option a) -5x³..

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