Question

using factor theorem Select the factor of the
Polynemia x³-5x+2
(a) x+2
b) x-2
(c)x-3
(d) x +4
​

Answer 1

Answer:

b)x-2

Step-by-step explanation:

x-2=0

x=2

x³-5x+2

(lets substitute the value of x in the above equation)

(2)³-5(2)+2

8-10+2

10-10

=0

∴x-2 is the factor of the given polynomial

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Answer 2

Answer:

Step-by-step explanation:

(a)x+2=0

x=-2

p(x) = x^3 - 5x + 2

p(-2) = (-2)^3 - 5(-2) + 2

p(-2)= (-8) - (-10) + 2

p(-2) = (-8) + 10 + 2

p(-2) = (-8) + 12

p(-2) = 4

which is not equal to zero

(b)x-2=0

x=2

p(x)=x^3 - 5x + 2

p(2) = (2)^3 - 5(2) + 2

p(2) = 8 - 10 + 2

p(2) = 10 - 10

p(2) = 0

Since the remainder is zero (x-2) is a factor of the polynomial p(x)

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