Question

I NEED HELP AS SOON AS POSSIBLE!

Answer 1

Answer:

Step-by-step explanation:

For 1 and 2, follow this explanation.

1) As it is the coeficient of x² is 1, we need to find two numbers whose Sum S(x)=3 and the same numbers whose product is 2, P(x)= 2

S(x) = (  ) + (  ) =3

P(x) = (   )  *  (   ) =2

S(x) = ( 2 ) + ( 1 ) =3

P(x) = (  2 )  *  ( 1  ) =2

These numbers in bold will be coeficients of x.

Rewrite the Trinomial x²+ 3x +2 as x² +2x+1x+2

So x²+3x+2 =x²+2x+1x+2

x² +2x+x+2   Put the x in evidence

x(x+2)+1(x+2)  Find the Maximum Common Divider

(x+1)(x+2)

2) x²+x-6=0

Applying the same procedure. Which two integer number whose sum is 1 and whose Product is -6?

S(x) = ( 3  ) + ( -2  ) =1

P(x) = ( 3  )  * ( -2  ) =-6

Rewrite

x²+x-6

x²+3x-2x-6      Group them

x(x+3)-2(x+3)   Common Term

(x+3)(x-2)

3) Since the a coeficient is ≠ 1, a little adjustment must be made on our algorithm for -2x²+4x+30=0

Firstly multiply a*c, in this case -2 * 30 = -60

Which two numbers multiplied by themselves will turn out to be -60 and whose sum is -60? Since we're working with integers factoring out may be very helpful.

P(x)=  ( 10  )  *   ( - 6 )  = -60

S(x) = (  10 )  +  (  -6 )  = 4

Rewriting

-2x²+10x-6x+30   Group them

2x(x+5) -6(x+5)

(2x-6)(x+5)   Inserting the -1 to finally adjust

-1(2x-6)(x+5)

4) Explanation is the same principle as a≠1

3x²+4x-4=0

P(x) = ( 6  )  *  (-2  ) = -12

S(x) = (  6 ) +  ( -2  )  = 4

3x²+4x-4 = 3x²+6x-2x-4

3x²+6x -2x+4

3x(x+2)-2(x-2)

(3x-2)(x+2)

The other ones are just applications of these, above.

Answer 2

I will give you the answer to number 1.
(x+2) . (x+1)

How to solve:

Step-1 : Multiply the coefficient of the first term by the constant  1 • 2 = 2 

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   3 .

     -2   +   -1   =   -3     -1   +   -2   =   -3     1   +   2   =   3   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  2 
                     x2 + 1x + 2x + 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+2)  •  (x+1)