Question

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Show that 8x²-6x-275=0
thanks. ​​

Answer 1

Answer:

(4x -25), (2x + 11)

Step-by-step explanation:

STEP1: Equation at the end of step 1

(23x2 - 6x) - 275

STEP2: Trying to factor by splitting the middle term

 2.1     Factoring  8x2-6x-275 

The first term is,  8x2  its coefficient is  8 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  -275 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -275 = -2200 

Step-2 : Find two factors of  -2200  whose sum equals the coefficient of the middle term, which is   -6 .

     -2200   +   1   =   -2199     -1100   +   2   =   -1098     -550   +   4   =   -546     -440   +   5   =   -435     -275   +   8   =   -267     -220   +   10   =   -210     -200   +   11   =   -189     -110   +   20   =   -90     -100   +   22   =   -78     -88   +   25   =   -63     -55   +   40   =   -15     -50   +   44   =   -6   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -50  and  44 

                     8x2 - 50x + 44x - 275

Step-4 : Add up the first 2 terms, pulling out like factors :

                    2x • (4x-25)

              Add up the last 2 terms, pulling out common factors :

                    11 • (4x-25)

Step-5 : Add up the four terms of step 4 :

                    (2x+11)  •  (4x-25)

             Which is the desired factorization

Final result :

(4x - 25) (2x + 11)

Hope this helps a bit

Answer 2

$\\ \rm\hookrightarrow \dfrac{1}{2}(Sum\:of\: parallel\:sides)(Height)=133$

$\\ \rm\hookrightarrow \dfrac{1}{2}(x+5+3x-2)(2x-3)=133$

$\\ \rm\hookrightarrow 4x+3(2x-3)=266$

$\\ \rm\hookrightarrow 4x(2x-3)+3(2x-3)=266$

$\\ \rm\hookrightarrow 8x^2-12x+6x-9=266$

$\\ \rm\hookrightarrow 8x^2-6x-275=0$