Question

4x~2-31x-8=0 factorise by splitting the middle term.

Answer 1

Answer:

Step-by-step explanation:

Can bot solve it with splitting middle term but can solve like this:

4x2-31x-8=0  

Two solutions were found :

x = -1/4 = -0.250

x = 8

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22x2 -  31x) -  8  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4x2-31x-8  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -31x  its coefficient is  -31 .

The last term, "the constant", is  -8  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -8 = -32  

Step-2 : Find two factors of  -32  whose sum equals the coefficient of the middle term, which is   -31 .

     -32    +    1    =    -31    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -32  and  1  

                    4x2 - 32x + 1x - 8

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

                   4x • (x-8)

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

                    1 • (x-8)

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

                   (4x+1)  •  (x-8)

            Which is the desired factorization

Equation at the end of step  2  :

 (x - 8) • (4x + 1)  = 0  

Step  3  :

Theory - Roots of a product :

3.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

PLEASE MARK BRAINIEST