Rectangular poster has an area of (2x^2 - 9x + 10), which describe the dimension of the poster?

Question

geerky42 · Answer

I think you need to factor 2x² - 9x +10. Can you do it?

geerky42 · Answer

Ok so the rectangle has area of 2x² - 9x +10 and each multiple choice give you two factor (ax + b) etc. one of the answer will have two factors multipled together to be  2x² - 9x +10

So you need to factor 2x² - 9x +10. Do you know how to do it?

anonymous · Answer

No I don't remember how to factor it.

geerky42 · Answer

Ok so look at first term (2x²) it is a multiply of x and 2x, right?
And take a look at signs, it's (__ - __ +__)

So if you factor 2x² - 9x +10, it should look like (2x - __)(x - __) right?

anonymous · Answer

oh ok got it

geerky42 · Answer

So you can factor it now?

geerky42 · Answer

sorry, it's hard for me to explain how to factor...

jim_thompson5910 · Answer

one way to factor is to solve  2x^2 - 9x + 10 = 0  for x

then use the roots to find the factors

jim_thompson5910 · Answer

you can solve 2x^2 - 9x + 10 = 0 for x using the quadratic formula

saifoo.khan · Answer

https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_factoring/v/factoring-quadratic-expressions

campbell_st · Answer

here is a simple method for factoring a quadratic in the form 

$$ax^2 + bx + c = 0$$

multiply a and c

in your question is 2 x 10 = 20

find the factors of 20 that add to -9.... hint they are both negative

-4, -5

then write your binomials as 

(ax + factor 1)(ax + factor2) 
-------------------------   = 0
                    a

so you have 

(2x -4)(2x - 5)
-------------- = 0
           2
there is a factor that can be removed from the first binomial and cancelled witht he denominator

hope this helps
           2

jim_thompson5910 · Answer

using the quadratic formula, you can determine 2x^2 - 9x + 10 = 0 has the two solutions

x = 5/2 or x = 2

get everything to one side (and 0 on the right side) and use the zero product property to get

x - 5/2 = 0 or x - 2 = 0

2x - 5 = 0 or x - 2 = 0

(2x-5)(x-2) = 0


so this shows us that 2x^2 - 9x + 10 factors to (2x-5)(x-2)

geerky42 · Answer

Is this clear?? @avisos2830

campbell_st · Answer

so removing the common fractor you get

2(x -2)(2x - 5)
--------------   = 0
          2

leaves

(x -2)(2x -5) = 0

anonymous · Answer

Thanks for the help!