Question

3. With the help of the remainder theorem,
find the remainder when the polynomial
x3 + 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​

Answer 1

Answer:

1. 50

2. 0

3. 78

4.  2

5. 0

6. 120

Step-by-step explanation:

p(x) = x³ + x² - 26x + 24

1. On being divided by x + 1

p(-1) = (-1)³ + (-1)² -26×(-1) +24

= -1+1+26+24 = 50

2. On being divided by x - 1

p(1) = 1³ + 1² - 26×1 + 24 = 1 + 1 - 26 + 24

p(1) = 0

3. On being divided by x + 4

p(-4) = (-4)³ + (-4)² -26×(-4) +24

= -64 + 16 +102 +24

= 78

4. On being divided by x - 4

p(4) = 4³ + 4² - 26×4 + 24

= 64 + 16 -102 + 24

= 2

5. On being divided by x + 6

p(-6) = (-6)³ + (-6)² -26×(-6) +24

= -216 + 36 + 156 + 24

= 0

6. On being divided by x - 6

p(6) = 6³ + 6² - 26×6 + 24

=216 + 36 - 156 +24

= 120