What is the remainder when 3a^2+6a+20 is divided by a-2.
Answer is 44. But I don't know how it comes. Please help.
To find the remainder when dividing a polynomial by another, we can use the polynomial long division method. Here's how you can find the remainder when dividing 3a^2 + 6a + 20 by a - 2:
Step 1: Set up the division:
Write the dividend (3a^2 + 6a + 20) and the divisor (a - 2) in long division format:
____________________________
a - 2 | 3a^2 + 6a + 20
Step 2: Divide the first term:
Divide the first term of the dividend (3a^2) by the first term of the divisor (a). The quotient is 3a.
3a
_______
a - 2 | 3a^2 + 6a + 20
Step 3: Multiply and subtract:
Multiply the quotient (3a) by the divisor (a - 2), and subtract the result from the dividend:
3a
_______
a - 2 | 3a^2 + 6a + 20
-(3a^2 - 6a)
___________
+ 12a + 20
Step 4: Repeat the process:
Bring down the next term (-12a) and repeat the division process:
3a + 12
________
a - 2 | 3a^2 + 6a + 20
-(3a^2 - 6a)
___________
12a + 20
-(12a - 24)
___________
+ 44
Step 5: Interpret the result:
After completing all the divisions, we have a remainder of +44. Therefore, the remainder when dividing 3a^2 + 6a + 20 by a - 2 is 44.
So the answer is indeed 44.