x square - 5 x + 1/5 x minus 12 = to x square minus x minus 4 upon X + 4.
NO SPAM ANSWER PLZ
Answers
Answer:
Divide the polynomial 2x^4 -9x^3 +5x^2 + 3x-82x
4
−9x
3
+5x
2
+3x−8 by x^2 - 4 x + 1x
2
−4x+1
TO VERIFY :
The Division Algorithm for the given polynomial.
SOLUTION :
Given that divide the polynomial 2x^4 -9x^3 +5x^2 + 3x-8Given that divide the polynomial 2x^4 -9x^3 +5x^2 + 3x-82x
4
−9x
3
+5x
2
+3x−8 by x^2 - 4 x + 1x
2
−4x+1
___________________
x^2 - 4 x + 1x
2
−4x+1 ) 2x^4 -9x^3 +5x^2 + 3x-82x
4
−9x
3
+5x
2
+3x−8 ( 2x^2-x-12x
2
−x−1
2x^4-8x^3+2x^22x
4
−8x
3
+2x
2
__(-)__(+)___(-)_____________
-x^3+3x^2+3x−x
3
+3x
2
+3x
-x^3+4x^2-x−x
3
+4x
2
−x
__(+)___(-)___(+)____________
-x^2+4x-8−x
2
+4x−8
-x^2+4x-1−x
2
+4x−1
__(+)_(-)__(+)___________
-7
____________________
∴ the quotient is 2x^2-x-12x
2
−x−1 and remainder is -7
Now we ca verify the Division Algorithm
The formula for Division Algorithm is :
Dividend=quotient\times divisor+remainderDividend=quotient×divisor+remainder
Substitute the values in the formula we get
2x^4 -9x^3 +5x^2 + 3x-8=x^2 - 4 x + 1\times (2x^2-x-1)+(-7)2x
4
−9x
3
+5x
2
+3x−8=x
2
−4x+1×(2x
2
−x−1)+(−7)
=x^2(2x^2)+x^2(-x)+x^2(-1)-4x(2x^2)-4x(-x)-4x(-1)+1(2x^2)+1(-x)+1(-1)-7=x
2
(2x
2
)+x
2
(−x)+x
2
(−1)−4x(2x
2
)−4x(−x)−4x(−1)+1(2x
2
)+1(−x)+1(−1)−7
=2x^4-x^3-x^2-8x^3+4x^2+4x+2x^2-x-1-7=2x
4
−x
3
−x
2
−8x
3
+4x
2
+4x+2x
2
−x−1−7
Adding the like terms
=2x^4-9x^3+5x^2+3x-8=2x
4
−9x
3
+5x
2
+3x−8
∴ 2x^4-9x^3+5x^2+3x-8=2x^4-9x^3+5x^2+3x-82x
4
−9x
3
+5x
2
+3x−8=2x
4
−9x
3
+5x
2
+3x−8
Hence LHS = RHS
∴ the Division algorithm is verified.