1. Find the greatest common factor (GCF)
What is the largest number that divides evenly into 4x^2, -16x^4, and 10x^5?
It is 2.
What is the highest degree of x that divides evenly into 4x^2, -16x^4, and 10x^5?
It is x^2.
Multiply the results above, the GCF = 2x^2

2. Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2x^2(4x^2/2x^2 + -16x^4/2x^2 + 10x^5/2x^2)

3. Simplify each term in parentheses
2x(2-8x^2+5x^3)

Have a nice day :D

6 0

3 years ago

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i? f(x) = x2 – 2x + 2 f(x) = x3 – x

konstantin123 [22]

Answer:

$f(x)=x^{3}-3x^{2} +4x-2$

Step-by-step explanation:

we know that

The <u><em>conjugate root theorem</em></u> states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

In this problem we have that

The polynomial has roots 1 and (1+i)

by the conjugate root theorem

(1-i) is also a root of the polynomial

therefore

The lowest degree of the polynomial is 3

$f(x)=a(x-1)(x-(1+i))(x-(1-i))$

Remember that

The leading coefficient is 1

a=1

$f(x)=(x-1)(x-(1+i))(x-(1-i))\\\\f(x)=(x-1)[x^{2} -(1-i)x-(1+i)x+(1-i^2)]\\\\f(x)=(x-1)[x^{2} -x+xi-x-xi+2]\\\\f(x)=(x-1)[x^{2} -2x+2]\\\\f(x)=x^{3}-2x^{2} +2x-x^{2} +2x-2\\\\f(x)=x^{3}-3x^{2} +4x-2$

5 0

3 years ago

Read 2 more answers

In one game, the final score was Falcons 3, Hawks 1. What fraction and

dlinn [17]

Step-by-step explanation:

3over4 which is 75percent

4 0

2 years ago