MHB How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Expression
AI Thread Summary
The expression 3(x + h)^4 - 48(x + h)^2 can be factored by first extracting 3(x + h)^2, resulting in 3(x + h)^2[(x + h)^2 - 16]. This further simplifies to 3(x + h)^2[(x + h) - 4][(x + h) + 4]. The discussion highlights the complexity of factoring problems found in Precalculus by David Cohen, particularly in Section 1.3, which includes many challenging examples. Participants express a commitment to sharing additional tricky factoring problems in future posts. The focus remains on mastering these advanced factoring techniques.
mathdad
Messages
1,280
Reaction score
0
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 32c.

Factor the expression.

3(x + h)^4 - 48(x + h)^2

Solution:

Factor out 3(x + h)^2.

3(x + h)^2[(x + h)^2 - 16]

Simplify the quantity in the brackets.

3(x + h)^2[(x + h) - 4][(x - h) + 4]

Is this right?
 
Mathematics news on Phys.org
RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 32c.

Factor the expression.

3(x + h)^4 - 48(x + h)^2

Solution:

Factor out 3(x + h)^2.

3(x + h)^2[(x + h)^2 - 16]

Simplify the quantity in the brackets.

3(x + h)^2[(x + h) - 4][(x - h) + 4]

Is this right?

right
 
Section 1.3 has what appears to be endless factoring questions. I will post many factoring problems in the coming days. I am talking about "tricky" factoring problems not factor 3a + a.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
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 »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Solving Function Expressions h(x): (x+a)2 +b & h-1 Range
Replies
7
Views
1K
MHB How Do I Factor This Expression?
Replies
6
Views
2K
MHB How do I factor this expression: 3(x + 5)^3 + 2(x + 5)^2?
Replies
3
Views
1K
MHB How do you factor a cubic function?
Replies
2
Views
2K
MHB Is it necessary to expand the quantity before factoring the expression?
Replies
6
Views
1K
MHB Yes, your factorization is correct.
Replies
4
Views
1K
MHB Is 27 - (a - b)^3 a Difference of Cubes in Precalculus?
Replies
9
Views
2K
MHB Is there more factoring to come?
Replies
2
Views
1K
MHB What is the domain for ax^(1/3) + b?
Replies
2
Views
1K
MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top