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

Answers ( )

    0
    2021-09-10T14:03:16+00:00

    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)

    Factor the quadratic expression

    → 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\sf

    0
    2021-09-10T14:03:17+00:00

     \huge \star \underline \red{question}

    Q..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.

     \huge \star \bold \red{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)

    Factor the quadratic expression

    → 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

     \large \star \underline \green{hope \: it \: helps \: u \: siso}

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