Question

Prove Corollary 2

Corollary 2 Factor Theorem
Let F be a field, a E F, and f(x) E F[x]. Then a is a zero of f(x) if
and only if x – a is a factor of f(x).
Expand
Transcribed Image Text

Corollary 2 Factor Theorem Let F be a field, a E F, and f(x) E F[x]. Then a is a zero of f(x) if and only if x – a is a factor of f(x).

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Algebra

Other

Related Algebra Q&A

Find answers to questions asked by students like you.

Q: 4u° – 5.94u? + 284.592u – 1.52 on your graphing calculator on the interval Graph the function k(u) [...

A: Click to see the answer

Q: Find (a) ⟨A, B⟩, (b) ||A||, (c) ||B||, and (d) d(A, B) for the matrices in M2,2 using the inner prod...

A: We need to find   (a) ⟨A, B⟩, (b) ||A||, (c) ||B||, and (d) d(A, B) for the matrices in M2,2 using t...

Q: I am trying to find what h =

A: Click to see the answer

Q: A manufacturing company purchased a new diamond tipped saw blade for $7800 and it will depreciate on...

A: A manufacturing company purchased a new diamond-tipped saw blade for $7800 and it will depreciate on...

Q: Find the angle θ between the vectors.u = (3, 4), v = (5, −12), ⟨u, v⟩ = u ∙ v

A: Given vector: Formula used : By dot product equation:

Q: You have 3 figures that make up a sequence.  First is a single cube, next is two cubes pushed togeth...

A: Given Six faces painted in first figure To find faces painted in 200th figure

Q: Given the following functions, use function composition to determine if f(x) and g(x) are inverse fu...

A: Click to see the answer

Q: Write the equation of the line described. Through (9,3) and (-4,2) Lost on step 1 where does 1/13 co...

A: In the given solution picture, formula used and equation of line is correct. So we are explaining wh...

Q: While driving in France, a sales representative encounters a speed limit sign indicating 57km/h. Con...

A: Given: While driving in France, a sales representative encounters a speed limit sign indicating 57 k...

Q: Given the following functions, find each of the values: f(x) = x² + x – 12 + + ¤ = (x)6 (f + g)( – 4...

A: Click to see the answer

Q: FInd the average rate of change of the given function on the interval (1,7). G(x)=4x^2+4x

A: Click to see the answer

Q: Let |G| = 15. If G has only one subgroup of order 3 and only one oforder 5, prove that G is cyclic. ...

A: Note that for a non identity element a ∈ G, , |a| =3,5, or 15. Now let A= {a ∈ G | |a| = 3} and B = ...

Q: Flo sets a goal of walking 10,000 total steps per day. Flo's normal routine involves walking 4,000 s...

A: Given, Flo sets a goal of walking 10,000 total steps per day. Flo's normal routine involves walking ...

Q: Find the domain and range of the function graphed below. 5 2- -5 4 3 2 -1 -1 1 2 3 4 5 -2 -3- 4- -5+...

A: From the graph and find the values of the x for which the graph has defined y. Then find the maximum...

Q: solving an equation using the odd root property: Problem type 2 (w-6)3 -72=0

A: Click to see the answer

Q: With pictures and words, describe each symmetry in D3 (the set ofsymmetries of an equilateral triang...

A: Click to see the answer

Q: How do i solve this?

A: In a diamond problem, there are certain rules according to which the data is filled. These rules are...

Q: .

A: Given To find value of a for which system has unique solution

Q: e the graph of y=f(x) to answer the following -- a) Determine f(-5). b) Determine f(1). C) Find all ...

A: Click to see the answer

Q: Construct a truth table for       p V ~p What is special about its truth values?

A: Click to see the answer

Q: If q is false, what must be the truth value of the statement (P^~q)^q ?

A: Given, q is false.  

Q: Consider the following sets. A  =  {17} B  =  {10 + 7} C  =  {10, 7} D  =  {25} E  =  {...

A: a). Cardinality is the number of elements present in the given set.  

Q: Consider the following. (Assume that the coins are distinguishable and that what is observed are the...

A: Click to see the answer

Q: Find f-1(x) then: Algerbraicly prove that it is the inverse of f(x): f(x)=(x-4)/(3x+5)

A: Click to see the answer

Q: I need help with 18,19,20,21,22,23,24 Thank you so much

A: Since multiple questions are asked, we will solve the first question, that is, question 18. To get s...

Q: Write the domain in interval notation. (a) k (x) =-3 x+4 x+4 (b) j(x) = x+3 x+4 (C) p (x) =

A: Domain of a function is a set of all the input values it can take for which the function remains def...

Q: Describe The Simplex Method.

A: The simplex method is an algorithm or the set of instructions using which we can examine the corner ...

Q: Hi, I really need some help with this assignment, help will be appreciated! I took some shots below.

A: " Since you have asked multiple question, we will solve the first question for you. If you want any ...

Q: Solve the inequality. I need to see step by step to understand how to solve.

A: Click to see the answer

Q: I need help on this problem. Alg 2

A: Given  The graph of f(x) and g(x) The composition of f and g 

Q: solving a quadratic equation using a square root property (x+3)2-36=0

A: Given quadratic equation, Adding 36 to both sides of equation. ( x + 3 )2 - 36 + 36 = 36 ( x + 3 )2...

Q: Determine if each is an expression or an equation: Y+14.     X-6=21

A: Click to see the answer

Q: I just need help in checking over my work.

A: Click to see the answer

Q: Write the equation of the line passing through ( 3,5) that is perpendicular to 5x-6y=4.  What is ste...

A: Click to see the answer

Q: Renting a car cast $30 per day, or $600 per month. Renting daily is cheaper for a few days, but afte...

A: Given: The rental cost of a car per day = $30 and The rental cost of a car per month = $600  

Q: Given the function f(x) 62? – 4x + 1. Calculate the following values: f( – 2) = f( – 1) = %3D f(0) =...

A: Click to see the answer

Q: Draw the standard coordinate axes on th e same diagram as th e axes relative to u and v. Use these t...

A: Click to see the answer

Q: I am trying to figure out step by step on how to solve.

A: Click to see the answer