Question

Determine whether p(y) = 3x2 + 6x -24 has x-2 a factor(by using factor theorem)?
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Answer 1

Answer:

hope this may help you

Step-by-step explanation:

Let g(x)=x−2

Now,g(x)=x−2

=>x−2=0

=>x=2

(i)

Let p(x)=3x

2

+6x−24

Now, g(x) is a factor p(x) if p(2)=0

Thus, p(2)

=3(2)

2

+6(2)−24

=12+12−24

=0

Thus, g(x) is a factor of p(x)

(ii)

Let p(x)=4x

2

+x−2

Now, g(x) is a factor p(x) if p(2)=0

Thus, p(2)

=4(2)

2

+2−2

=16



=0

Thus, g(x) is not a factor of p(x)

So, (i) is the factor of x−2

Answer 2

the zero of x-2 = +2

therefore by factor theorem:

p(y) = $3x^{2}$ + 6x -24

p(2) = 3(2)^2 + 6(2) - 24

       = 12+12-24

       = 0

therefore x-2 is a factor