divisible by (x+3).
18. Without actual division, show that (x2-3x2 - 13x +15) is exactly
divisible by (x² + 2x - 3).
19. If (x + ax? + bx + 6) has (x - 2) as a factor and leaves a remainder 3 when
divided by (x-3), find the values of a and b.
20. Find the values of a and b so that the polynomial (r - 10x² + ax +b) is
exactly divisible by (x - 1) as well as (x - 2).
21. Find the values of a and b so that the polynomial (x4 + ax - 7x2 - 8x+b)
is exactly divisible by (x + 2) as well as (x+3).
22. If both (x - 2) and (x-1) are factors of px? + 5x+r, prove that p=r.
23. Without actual division, prove that 2x4 -5x + 2x2 - x+2 is divisible by
x² – 3x+2.
24. What must be added to 2x* -5x + 2x2-x-3 so that the result is exactly
divisible by (x - 2)?
25. What must be subtracted from (x* + 2x - 2x² + 4x +6) so that the result
is exactly divisible by (x² + 2x - 3)?
26. Use factor theorem to prove that (x + a) is a factor of (x"+a") for any odd
positive integer n.
Please please answer these questions very urgent please
Answers
Answer:
18 . X^2 + 2x - 3 = x^2 + 3x - x -3
= x(x + 3)-1(x + 3)
= (x + 3)(x - 1)
===============================
checking whether (x + 3) and (x - 1) are the factors or not,
==========================
Taking x + 3 = 0 So, x = -3
Putting the value of x in given equation,
x^3 - 3x^2 - 13x + 15 = 0
(-3)^3 - 3(-3)^2 - 13(-3) + 15 = 0
-27 - 3(9) + 39 + 15 = 0
-27 -27 + 39 + 15 = 0
-54 + 54 = 0
0 =0
Hence, (x + 3) is the factor,
=======================
checking for (x -1) x = 1
Putting the value of x in given equation,
x^3 - 3x^2 - 13x + 15 = 0
(1)^3 - 3(1)^2 - 13(1) + 15 =0
1 - 3 - 13 + 15 = 0
-15 + 15 = 0
0 =0
Hence, (x - 1) is also a factor.
=========================
Then, x^2 + 2x - 3 is the factor of given equation
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