Using the Fundamental Theorem of Algebra. Complete the following exercises. Show your work. Determine how many, what type, and find the roots for f(x) = x^4 + 21x^2 − 100.

Determine how many, what type, and find the roots for f(x) = x^3 − 5x^2 − 25x + 125.

A) - Quartic polynomial

- has four roots

- roots are; f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)

B) - Cubic polynomial

- has 3 roots

- roots are; f(x) = (x - 5)²(x + 5)

Step-by-step explanation:

A) f(x) = x⁴ + 21x² − 100

The highest power in this polynomial is 4 and thus, it is called a quartic polynomial. This means that it will have 4 roots.

Factorizing this polynomial gives;

f(x) = (x² + 25)(x² - 4)

Equating to zero, we can find the roots. Thus, the roots are;

x = 5i

x = -5i

x = 2

x = -2

Thus, the completely factorized polynomial is;

f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)

B) f(x) = x³ − 5x² − 25x + 125

The highest power in this polynomial is 3. It is therefore a cubic polynomial with 3 roots.

Factorizing this polynomial gives;

f(x) = (x² - 25)(x - 5)

Equating to zero and Factorizing gives;

x = 5

x = -5

x = 5

Thus, completely factorized with the roots is;

f(x) = (x - 5)²(x + 5)

answer: idk

step-by-step explanation: sry idk

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.