
www.VirtualNerd.com
How Do You Find a Missing Factor in a Monomial Equation?
Find the monomial to multiply 3x3y by to get 48x7y3
Summary
- We want to figure out what to multiply 3x3y by to get 48x7y3
- Divide 48x7y3 by 3x3y
- 48
÷ 3=16 - x7
÷ x3=x7-3=x4 - y3
÷ y=y3-1=y2 - 16x4y2 is the missing factor
- Check our result by multiplying it by 3x3y

Notes
-
-
- We want to figure out what to multiply 3x3y by to get 48x7y3
- So to do that, we need to divide 48x7y3 by 3x3y
-
- The left hand side is 48x7y3
- On the right we know we have 3x3y times some missing factor
-
- Think of it kind of like a multiplication equation, where the missing factor is the variable
- To solve a multiplication equation, we would divide both sides by what we know to get the variable by itself
- So here we divide 48x7y3 by 3x3y
-
- 48x7y3 is the dividend, so it goes under the division sign
- 3x3y is the divisor, so it goes out in front of the division sign
-
-
-
48
÷ 3=16 - So the 16 goes up top above the 48
-
48
-
- Remember, when we're dividing powers that have the same base we can just subtract their exponents
- So here we can subtract 7 and 3 to get the exponent for the result
-
x7
÷ x3=x7-3=x4
-
-
x7
÷ x3=x7-3=x4
-
x7
-
- Here we can subtract 3 and 1 to get the exponent for the result
- Remember, a number or variable without an exponent has a hidden exponent of 1
-
y3
÷ y=y3-1=y2
-
-
y3
÷ y=y3-1=y2
-
y3
-
-
- The result we got was 16x4y2
-
- This is the number we need to multiply 3x3y by to get 48x7y3
-
- We can check our answer by multiplying it by 3x3y to see if we get 48x7y3
-
- We can check our answer by multiplying it by 3x3y to see if we get 48x7y3
-
- We can check our answer by multiplying it by 3x3y to see if we get 48x7y3
-
- Multiply the numbers first
- 3•16=48
-
- Remember, when we're multiplying two powers with the same base we can just add the exponents
- So here we can add 3 and 4 to get the exponent for the result
- x3•x4=x3+4=x7
-
- Here we can add 3 and 4 to get the exponent for the result
- x3•x4=x3+4=x7
-
- Here we can add 1 and 2 to get the exponent for the result
- Remember, a number or variable without an exponent has a hidden exponent of 1
- y•y2=y1+2=y3
-
- So that must mean our result was correct!
-
- 16x4y2 is what we need to multiply 3x3y by to get 48x7y3