Recognize and use the appropriate method to factor a polynomial completely
Before you get started, take this readiness quiz.
Factor
${y}^{2}-2y-24$ .
If you missed this problem, review
[link] .
Factor
$3{t}^{2}+17t+10$ .
If you missed this problem, review
[link] .
Factor
$36{p}^{2}-60p+25$ .
If you missed this problem, review
[link] .
Factor
$5{x}^{2}-80$ .
If you missed this problem, review
[link] .
Recognize and use the appropriate method to factor a polynomial completely
You have now become acquainted with all the methods of factoring that you will need in this course. (In your next algebra course, more methods will be added to your repertoire.) The figure below summarizes all the factoring methods we have covered.
[link] outlines a strategy you should use when factoring polynomials.
Factor polynomials.
Is there a greatest common factor?
Factor it out.
Is the polynomial a binomial, trinomial, or are there more than three terms?
If it is a binomial:
Is it a sum?
Of squares? Sums of squares do not factor.
Of cubes? Use the sum of cubes pattern.
Is it a difference?
Of squares? Factor as the product of conjugates.
Of cubes? Use the difference of cubes pattern.
If it is a trinomial:
Is it of the form
${x}^{2}+bx+c$ ? Undo FOIL.
Is it of the form
$a{x}^{2}+bx+c$ ?
If
$a$ and
$c$ are squares, check if it fits the trinomial square pattern.
Use the trial and error or “ac” method.
If it has more than three terms:
Use the grouping method.
Check.
Is it factored completely?
Do the factors multiply back to the original polynomial?
Remember, a polynomial is completely factored if, other than monomials, its factors are prime!
Factor completely:
$4{x}^{5}+12{x}^{4}$ .
Solution
$\begin{array}{ccccccc}\text{Is there a GCF?}\hfill & & & \text{Yes,}\phantom{\rule{0.2em}{0ex}}4{x}^{4}.\hfill & & & \hfill 4{x}^{5}+12{x}^{4}\hfill \\ & & & \text{Factor out the GCF.}\hfill & & & \hfill 4{x}^{4}\left(x+3\right)\hfill \\ \text{In the parentheses, is it a binomial, a}\hfill & & & & & & \\ \text{trinomial, or are there more than three terms?}\hfill & & & \text{Binomial.}\hfill & & & \\ \phantom{\rule{1em}{0ex}}\text{Is it a sum?}\hfill & & & & & & \text{Yes.}\hfill \\ \phantom{\rule{1em}{0ex}}\text{Of squares? Of cubes?}\hfill & & & & & & \text{No.}\hfill \\ \text{Check.}\hfill & & & & & & \\ \\ \phantom{\rule{1em}{0ex}}\text{Is the expression factored completely?}\hfill & & & & & & \text{Yes.}\hfill \\ \phantom{\rule{1em}{0ex}}\text{Multiply.}\hfill & & & & & & \\ \\ \\ \phantom{\rule{2.5em}{0ex}}4{x}^{4}\left(x+3\right)\hfill & & & & & & \\ \phantom{\rule{2.5em}{0ex}}4{x}^{4}\xb7x+4{x}^{4}\xb73\hfill & & & & & & \\ \phantom{\rule{2.5em}{0ex}}4{x}^{5}+12{x}^{4}\phantom{\rule{0.2em}{0ex}}\u2713\hfill & & & & & & \end{array}$
a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190
Usman
Stella bought a dinette set on sale for $725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount?
if you want the discounted price subtract $725 from $1299. then divide the answer by $1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2%
Orlando
you could also just divide $725/$1299 and then subtract it from 1. then you get the same answer.
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Niazmohammad
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found $7(+7). Totally you lost just $12 (-12)
Annushka
I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme
same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?
Use algebra to combine 39×5 and the half sum of travel of 59+30
Cherokee
What is the segment of 13? Explain
Cherokee
my weight is 49. So 3 times is 147
Cherokee
kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps