Question

3. With the help of the remainder theorem,
find the remainder when the polynomial
x + x2 - 26x + 24 is divided by each of the
following divisors :
( 1 ) x + 1 (2)x-1
(3) x + 4
(4) x-4
(5) x + 6 (6)x - 6


4. If x + 5 is a factor of x3 + 13x2 + ax + 35, find the value of a.


5. If x + 2 is a factor of x3 + ax2 - x + 30, find the value of a.


6. On dividing x3 + ax2 + 19x + 20 by (x + 3), if
the remainder is a, then find the value of a.​

Answer 1

Answer:

$3)Given: P(x) = x + x^{2} - 26x + 24\\ a) x = -1\\ P(-1) = -1 + (-1)^{2} - 26(-1) + 24\\ = -1 + 1 + 26 + 24\\ =50\\\\b)x = 1\\ P(1) = 1 + (1)^{2} - 26(1) + 24\\ = 1 + 1 - 26 + 24\\ =0\\\\c) x = -4\\ P(-4) = -4 + (-4)^{2} - 26(-4) + 24\\ = -4 + 16 + 104 + 24\\ =140\\\\d) x = 4\\ P(4) = 4 + (4)^{2} - 26(4) + 24\\ = 4 + 16 - 104 + 24\\ =-60$

$e) x = - 6\\ P(-6) = -6 + (-6)^{2} - 26(-6) + 24\\ = -6 + 36 + 156 + 24\\ =222\\\\f) x = 6\\ P(6) = 6 + (6)^{2} - 26(6) + 24\\ = 6 + 36 - 156 + 24\\ = -90$

Answer 2

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