This is dividing polynomial by monomials
How do yu solve these?
1. 5mn divided by 5m^3n - 10m^2n^2
2. -10a^6 divided by -30a^9 + 20a^7
3. -2a divided by 8a^3 - 4a^2b + 6ab^2
Just divide each term
Also, you have the order reversed.
5m^3n - 10m^2n^2 divided by 5mn is
m^2 - 2mn
#2: 3a^3 - 2a
#3: -4a^2 + 2ab - 3b^2
Review your rules for adding/subtracting exponents
To divide a polynomial by a monomial, you can follow these steps:
Step 1: Simplify the expressions by canceling out common factors, if possible.
Step 2: Divide each term of the polynomial by the monomial.
Let's apply these steps to the given problems:
1. 5mn divided by 5m^3n - 10m^2n^2
First, let's simplify the polynomials:
5mn / 5m^3n - 10m^2n^2
Notice that 5 can be cancelled out in the numerator and denominator. Also, we can simplify the exponents. After simplifying, the expression becomes:
mn / m^3n - 2m^2n^2
Now divide each term by the monomial:
(mn / m^3n) - (2m^2n^2 / m^3n)
When dividing variables with the same base, subtract the exponent of the denominator from the exponent of the numerator. The expression simplifies to:
1/m^2 - 2mn
2. -10a^6 divided by -30a^9 + 20a^7
First, let's simplify the expression:
-10a^6 / -30a^9 + 20a^7
Again, we can simplify the expression by canceling out common factors:
-10a^6 / (-30a^9 + 20a^7)
Canceling out 10 from both the numerator and denominator:
-a^6 / (-3a^9 + 2a^7)
Now divide each term by the monomial:
(-a^6 / -3a^9) + (a^6 / 2a^7)
When dividing variables with the same base, subtract the exponent of the denominator from the exponent of the numerator. The expression simplifies to:
1/3a^3 + (1/2a)
3. -2a divided by 8a^3 - 4a^2b + 6ab^2
First, let's simplify the expression:
-2a / 8a^3 - 4a^2b + 6ab^2
Now divide each term by the monomial:
(-2a / 8a^3) - (-2a / 4a^2b) + (-2a / 6ab^2)
Divide the variables by subtracting the exponents:
-1/4a^2 - (-1/2b) - (1/3b^2)
And there you have it! The expression is simplified. Remember to check if there are any common factors that can be canceled out to further simplify the expression.