Factoring Expressions
Factoring Expressions - Related Videos
08:00
Analyzing Tumor Gene Expression Factors with the CorExplorer Web Portal
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2019
We introduce the CorExplorer web portal, an resource for exploration of tumor RNA sequencing factors found by the machine learning algorithm CorEx (Correlation Explanation), and show how factors can be analyzed relative to survival, database annotations, protein-protein interactions, and one another to gain insight into tumor biology and therapeutic interventions.
10:08
Flow Cytometry Analysis of Tissue Factor Expression in Human Platelets
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Cited by 3 •
2024
This article outlines the protocol for quantifying the percentage of Tissue Factor (TF)-positive platelets using whole blood flow cytometry, assessing the protein: (1) intracellularly in resting conditions, and (2) on the cell surface, in both resting and activated conditions. Guidance is also provided for evaluating TF-positive platelets in platelet-rich plasma.
11:42
Hemogenic Reprogramming of Human Fibroblasts by Enforced Expression of Transcription Factors
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Cited by 3 •
2019
This protocol demonstrates the induction of a hemogenic program in human dermal fibroblasts by enforced expression of the transcription factors GATA2, GFI1B and FOS to generate hematopoietic stem and progenitor cells.
08:51
Applying an Inducible Expression System to Study Interference of Bacterial Virulence Factors with Intracellular Signaling
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Cited by 10 •
2015
The method described here is used to induce the apoptotic signaling cascade at defined steps in order to dissect the activity of an anti-apoptotic bacterial effector protein. This method can also be used for inducible expression of pro-apoptotic or toxic proteins, or for dissecting interference with other signaling pathways.
03:45
Antibody Staining of Scale Melanocytes: A Technique to Detect Transcription Factors Expressed in Dorsal Scale-associated Melanocytes of Zebrafish Models
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2023
This video describes the antibody staining method to detect transcription factors expression in dorsal scale-associated melanocytes of zebrafish models. This immunostaining technique helps specifically identify the melanocyte-inducing transfection factor-A in the transgenic zebrafish.
FAQs
Finding the greatest common factor first exposes a shared numerical or algebraic part of every term. Removing that common part leaves a simpler expression inside parentheses, while multiplication by the factor preserves equivalence. This step can make later pattern recognition easier and often reduces the work required for further algebraic manipulation.
With a difference of two squares, each term must be a square and the operation between them must be subtraction. The expression can then be represented using two binomials with matching terms and opposite signs, whose middle terms cancel when multiplied. Expanding the result confirms that the factors reproduce the original expression.
For a quadratic trinomial, the useful structure lies in finding two factors whose product accounts for the quadratic and constant terms while their combined contribution produces the middle term. Once that structure is identified, the factored form can expose values that make the expression zero. This connects symbolic pattern recognition directly to solving polynomial equations.
An efficient workflow begins by checking for a greatest common factor, then testing recognizable patterns such as a difference of two squares or a quadratic trinomial. After selecting a candidate form, expand the factors and compare every resulting term with the starting expression. This check catches sign errors, missing factors, and incorrect middle terms.
Factoring Expressions can simplify a polynomial equation by turning one expression into a product of factors. Setting that product equal to zero allows attention to shift to the individual factors, whose zeros identify solution values. In this way, factoring provides an efficient route from symbolic form to the roots or zeros associated with a polynomial.
Factored forms are especially useful when studying functions because they can reveal zeros and other key features that may be less apparent in expanded form. The same representation supports graphing and algebraic modeling, while the underlying symbolic skills prepare students for later work in calculus and higher mathematics. Thus, factoring connects computation with interpretation.