[Video] Fundamentals of Factoring

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We go through common prerequisite topics about fundamentals of factoring. We look at common factors and factoring quadratic polynomials.

The following videos will cover topics about factoring polynomials:

Fundamentals of Factoring

Factoring Video Warning!

Introduction and Question 1: Factoring With Common Factors

(Click the arrow to the right to see the Introduction video and first question.)

Which of the following ways does $2x^2 + 6x$ factor?

Question 2: Factoring Quadratic Polynomials 1

(Click the arrow to the right to see the second question.)

Which of the following ways does $x^2-7x+12$ factor?

Question 3: Factoring Quadratic Polynomials 2

(Click the arrow to the right to see the third question.)

Which of the following ways does $x^2+16$ factor (over the real numbers)?

Advanced Factoring

Question 4: Factoring by Grouping

(Click the arrow to the right to see the fourth question.)

Factor $3x^3+x^2-3x-1$ completely. Please note that this is a different polynomial than the one in the above video.

Polynomial Long Division

Introduction and Question 5: Polynomial Long Division

(Click the arrow to the right to see the fifth question.)

How does $x^5 - 5x^3 + 4x$ factor if either $x=-1$ or $x=1$ is a root of the expression?

Synthetic Division

Introduction to Synthetic Division

(Click the arrow to the right an introduction to synthetic division.)

Question 6: Synthetic Long Division

(Click the arrow to the right to see the sixth question.)

Suppose you know that $x+3$ is a factor of the polynomial $f(x) = x^3 - 7x + 6$ . What is the result of dividing $f(x)$ by $x+3$ ?

Question 7: Imaginary Roots

(Click the arrow to the right to see the seventh question.)

What are all of the imaginary roots of $x^3 - 3x^2 + 6x - 4$ ?
Hint 1: The graph of the function in the video (when the question is posed) may have some useful information.
Hint 2: If you know one root of the polynomial, synthetic division may be useful.

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
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text	$\text{\blue{[?]}}$
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sqrt	$\sqrt{\blue{[?]}}$
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factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
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frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
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arctan	$\arctan\left(\blue{[?]}\right)$
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ln	$\ln\left(\blue{[?]}\right)$
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beta	$\beta$
gamma	$\gamma$
delta	$\delta$
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zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

Fundamentals of Factoring

Advanced Factoring

Polynomial Long Division

Synthetic Division

Wrap-up of Factoring Polynomials

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