MHB How do you factor a cubic function?

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Cubic Function
AI Thread Summary
To factor the cubic function x^3 + 2x^2 + x, the expression can be rewritten as x(x^2 + 2x + 1), which further factors to x(x + 1)(x + 1) or x(x + 1)^2. Verifying the correctness of the factorization can be done by multiplying the factors back together. Understanding how to factor is crucial for students, as it is a valuable mathematical skill. Mastery of factoring aids in solving more complex problems in precalculus and beyond.
mathdad
Messages
1,280
Reaction score
0
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 44b.

Factor the expression.

x^3 + 2x^2 + x

x(x^2 + 2x + 1)

x(x + 1)(x + 1)

x(x + 1)^2

Correct?
 
Mathematics news on Phys.org
RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 44b.

Factor the expression.

x^3 + 2x^2 + x

x(x^2 + 2x + 1)

x(x + 1)(x + 1)

x(x + 1)^2

Correct?

yes . to check the corrcetness of the solution you can multiply it out and check
 
Factoring a very important. Students have no idea how valuable this skill is, honestly.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

MHB How do I factor this expression: 3(x + 5)^3 + 2(x + 5)^2?
Replies
3
Views
1K
MHB How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?
Replies
2
Views
1K
MHB Is it necessary to expand the quantity before factoring the expression?
Replies
6
Views
2K
MHB Is 27 - (a - b)^3 a Difference of Cubes in Precalculus?
Replies
9
Views
2K
MHB What is the domain for ax^(1/3) + b?
Replies
2
Views
1K
MHB Yes, your factorization is correct.
Replies
4
Views
1K
MHB Which method is easier and why?
Replies
4
Views
2K
MHB Is there more factoring to come?
Replies
2
Views
1K
MHB What is the domain for the expression 4/[(t - 1)•sqrt{t}]?
Replies
6
Views
2K
MHB How Can You Rewrite an Equation to Express y as a Function of x?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top