2
. Find the remainder when 2x2 – 3x + 5 is divided by 2x - 3. Does it exactly divide the
polynomial ? State reason.
Find the remainder when 9x2 – 3x2 + x-5 is divided by x -
3
5. If the polynomials 2x' + ar? + 3x - 5 and x3 + x2 - 4x + a leave the same remainder
when divided by x-2, find the value of a.
6. If the polynomials x' + ax? +5 and x3 – 2x² +a are divided by (x + 2) leave the same
remainder, find the value of a.
7. Find the remainder when f(x)=x4 - 3x2 + 4 is divided by g(x)=x-2 and verify the
result by actual division.
8. Find the remainder when p(x) = x - 6x² + 14x - 3 is divided by g(x)= 1 - 2x and
verify the result by long division.
TXT
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2.
Answers
Find the remainder when 2x2 – 3x + 5 is divided by 2x - 3. Does it exactly divide the
polynomial ? State reason.
Answer:
1) Let 2x-3 = 0
then, x = 3/2
2x^2-3x+5
Now, we need to put this value in the polynomial (2 x 9/4) - 9/2 + 5
9/2 -9/2 + 5 = 5
which is not equals to zero. That means 2x - 3 doesn't divides the polynomial.
Find the remainder when 9x2 – 3x2 + x-5 is divided by x -3
Answer:
2) Let x-3 = 0
then x = 3
9x^3 – 3x^2 + x-5
Now, we need to put this value in the polynomial
9(3)^3 - 3(3)^2 + 3 - 5
243 - 27 - 2
243 - 29
214
which is not equals to zero. That means x - 3 doesn't divides the polynomial.
If the polynomials 2x' + ar? + 3x - 5 and x3 + x2 - 4x + a leave the same remainder
when divided by x-2, find the value of a.
Answer:
3) Let x-2 = 0
then x = 2
2x^3 + ax^2 + 3x - 5 = x^3 + x^2 - 4x + a
put x = 2
16 + 4a + 6 - 5 = 8 + 4 - 8 + a
3a = - 21
a = -7
If the polynomials x' + ax? +5 and x3 – 2x² +a are divided by (x + 2) leave the same
remainder, find the value of a.
Answer:
4) Let x + 2 = 0
then x = -2
x^2 + ax + 5 = x^3 + x^2 - 4x + a
4 - 2a + 5 = -8 + 4 + a
a = 13/3
Explanation:
Firstly by simple division and secondly by putting the value of x obtained from the second equation in the polynomial.
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