DIVISION OF POLYNOMIALS || GRADE 7 MATHEMATICS Q2
WOW MATH・2 minutes read
Dividing polynomials involves various rules like subtracting exponents and dividing coefficients first. The process includes dividing common factors and arranging terms in descending order for accurate results.
Insights
- Division of polynomials requires subtracting exponents with the same base and dividing coefficients first, as seen in various examples like -8a^4b^7 divided by 4a^4b^3c^2 resulting in -2a^0b^4c^5.
- Polynomial division by a monomial involves arranging terms in descending order and dividing each term, as demonstrated in 24x^3/8x resulting in 3x^2-2x+4, showcasing the step-by-step process of this mathematical operation.
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Recent questions
How do you divide polynomials?
When dividing polynomials, start by dividing the coefficients of the terms. Then, subtract the exponents of the variables with the same base. Arrange the terms in descending order and divide each term by the divisor. Remember to handle any remainders appropriately.
What happens when you divide expressions with exponents?
When dividing expressions with exponents, subtract the exponents of the variables with the same base. If an exponent becomes negative after subtraction, move the variable to the denominator. Any variable raised to the power of 0 equals 1. Handle coefficients and variables separately during division.
How do you divide a polynomial by a monomial?
To divide a polynomial by a monomial, arrange the terms in descending order. Divide each term of the polynomial by the monomial, ensuring to handle coefficients and exponents correctly. Simplify each term individually and combine them to form the final quotient.
What is the result of dividing negative numbers with exponents?
When dividing negative numbers with exponents, remember to handle the signs of the coefficients and the exponents properly. Subtract the exponents of the variables with the same base and simplify the expression accordingly. Pay attention to the rules of exponents to ensure accurate division.
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Summary
00:00
"Polynomial Division: Rules and Examples"
- Division of polynomials involves dividing monomials, polynomials, and multiple terms.
- Exponents with the same base are subtracted when dividing, like x^5y^2 divided by x^2y^7.
- Coefficients are divided first, as in -8a^4b^7 divided by 4a^4b^3c^2, resulting in -2a^0b^4c^5.
- Dividing -6x^4y^3 by 15y^2z gives -2x^4y/5z.
- For 2a^8b^4 divided by 6a^6b, common factors are divided, yielding a^2b^3.
- Any expression raised to 0 equals 1, as in 5x^3y^0 divided by x^2y^2 resulting in 5x.
- Negative 12m^4n^2 divided by 8m^4n^6 gives -3n^0b^2c^2.
- Exponents are subtracted when dividing, like 3^2x^8y^6 divided by x^12 resulting in x^4y^0.
- Polynomial division by a monomial involves arranging terms in descending order and dividing each term, like 24x^3/8x resulting in 3x^2-2x+4.
- Dividing 27x^3 by 3x gives 9x^2, with a remainder of -18x, leading to the quotient 9x^2-6x+4.
30:44
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