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ira [324]
3 years ago
6

Is the binomial a factor of the polynomial nominal function?

Mathematics
1 answer:
Sedbober [7]3 years ago
7 0

The factors for given equation f(x)=x^{3} +3x^{2} -25x-75.

  • (x-1) - No
  • (x-3) - No
  • (x+3) - Yes
  • (x-5) - Yes
  • (x+5) - Yes

<u>Step-by-step explanation:</u>

The given equation is f(x)=x^{3} +3x^{2} -25x-75 .

Add 0 at the end of the equation.

x^{3} +3x^{2} -25x-75 = 0.

Let us group the given equation,

(x^{3} +3x^{2}) -(25x-75) =0.

⇒ Group 1: x^{3} +3x^{2} .

Group 2: - 25x +75 .

Pull out factor from each group,

⇒ Group 1: (x+3)(x^{2}).

Group 2: (x+3) (-25).

Join the two group since both (x+3) is common in both groups.

(x+3)(x^{2} -25) =0.

One of the factor is (x+3).

Other factors are solved by the formula, a^{2}-b^{2} = (a+b) (a-b) .

(x+3)(x^{2} -25) = (x+5) (x-5) .

The other factors are (x+5) and (x-5).

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