divid (3x2+x-5) ÷ (x-2)
Answers
Answer:
Given that Divide 3x^2+5x-13x
2
+5x−1 by (x+2)
TO VERIFY :
The division algorithm for the given polynomial.
SOLUTION :
First divide the given polynomial
3x-1
_________________
x+2) 3x^2+5x-13x
2
+5x−1
3x^2+6x3x
2
+6x
__(-)___(-)________
-x-1
-x-2
____(+)_(+)______
1
_________
Therefore the quotient is 3x-1 and remainder is 1
Now verify the division algorithm :
Dividend =quotient\times divisor + remainderDividend=quotient×divisor+remainder
3x^2+5x-1=(3x-1)\times (x+2)+13x
2
+5x−1=(3x−1)×(x+2)+1
By using Distributive property :
(x+y)(a+b)=x(a+b)+y(a+b)
3x^2+5x-1=(3x)(x+2)-1(x+2)+13x
2
+5x−1=(3x)(x+2)−1(x+2)+1
By using Distributive property :
a(x+y)=ax+ay
3x^2+5x-1=3x(x)+3x(2)-1(x)-1(2)+13x
2
+5x−1=3x(x)+3x(2)−1(x)−1(2)+1
3x^2+5x-1=3x^2+6x-x-2+13x
2
+5x−1=3x
2
+6x−x−2+1
Adding the like terms
3x^2+5x-1=3x^2+5x-13x
2
+5x−1=3x
2
+5x−1
Hence the Division Algorithm is verified.
Step-by-step explanation:
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/Answer:
Step-by-step explanation:
