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X^2+4x-4=0
Solve by factoring.​

User Vishnu N K
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6 votes

Answer:

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.

Explanation:

User JasonCG
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