Question

Examine the validity of the following polynomials:
(1) x +3 is a factor of x2 +10x +21.
(2) x-2 is a factor of x + 5x2 - 2x - 25.
(3) x+3 is a factor of x? + 6x2 + 3x - 12.
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Answer 1

1).

x + 3 = 0

x = -3

( -3 )^2 + 10 ( -3 ) + 21 = 0

-9-30+21=0

-39+21=0 ( remainder ) ( r )

r = -17

2) x=2

2+20-4-25=r

r = 22 - 29

r = -7

3).

x = 3

3 + 54 + 9 - 12 = r

r = 54