## Polynomial p is defined by p(x)=x3+5×2−2x−24p has a zero at x = 2. Factor p completely and find its zeros.​

Question

Polynomial p is defined by
p(x)=x3+5×2−2x−24p
has a zero at x = 2. Factor p completely and find its zeros.​

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2 weeks 2021-09-10T14:01:41+00:00 2 Answers 0 views 0

1. solution

p(x) has a zero at x = 2 and therefore x – 2 is a factor of p(x).

★ Divide p(x) by x – 2

→ p(x) / (x – 2) = (x² + 5 x² – 2 x – 24) / (x- 2)x2 + 7 x + 12

Using the division above, p(x) may now be written in factored form as follows:

→ p(x) = (x – 2)(x2 + 7 x + 12)

→ x² + 7 x + 12.

→ p(x) = (x – 2)(x + 3)(x + 4)

The zeros are found by solving the equation.

→ p(x) = (x – 2)(x + 3)(x + 4) = 0

For p(x) to be equal to zero, we need to have

→ x – 2 = 0 , or x + 3 = 0 , or x + 4 = 0

Solve each of the above equations to obtain the zeros of p(x).

→ x = 2 , x = – 3 and x = -4

### has a zero at x = 2. Factor p completely and find its zeros.

p(x) has a zero at x = 2 and therefore x – 2 is a factor of p(x).

⚘Divide p(x) by x – 2

→ p(x) / (x – 2) = (x² + 5 x² – 2 x – 24) / (x- 2)x2 + 7 x + 12

⚜Using the division above, p(x) may now be written in factored form as follows:

→ p(x) = (x – 2)(x2 + 7 x + 12)

→ x² + 7 x + 12.

→ p(x) = (x – 2)(x + 3)(x + 4)

The zeros are found by solving the equation.

→ p(x) = (x – 2)(x + 3)(x + 4) = 0

For p(x) to be equal to zero, we need to have

→ x – 2 = 0 , or x + 3 = 0 , or x + 4 = 0

Solve each of the above equations to obtain the zeros of p(x).

→ x = 2 , x = – 3 and x = -4

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