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The legs of an isosceles triangle measure ( 2 x^4 + 2 x − 1 ) units each. The perimeter of the triangle is ( 5 x^4 − 2 x^3 + x − 3 ) units. Write a polynomial (in simplest standard form) that represents the measure of the base of the triangle.

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Answer:

The base is x^4 -2x^3 -3x-1

Step-by-step explanation:

We know the perimeter of a triangle is the sum of the three sides

P = s1+s2+s3

We know the perimeter is  5 x^4 − 2 x^3 + x − 3

and two of the legs are 2 x^4 + 2 x − 1  since it is an isosceles triangle

P = 2s1 + s3

Subtract 2s1 from each side

P-2s1 =2s1 +s3 -2S1

P -2s1 =s3

Substituting what we know

5 x^4 − 2 x^3 + x − 3 - 2(2 x^4 + 2 x − 1) = s3

Distribute the -2

5 x^4 − 2 x^3 + x − 3 - 4 x^4 -4 x + 2 = s3

Combine like terms

5 x^4-4x^4 − 2 x^3 + x  -4 x -3+ 2 = s3

x^4 -2x^3 -3x-1 =s3

The base is x^4 -2x^3 -3x-1

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