Question

find the middle term split of 4x2 + 16x -84

Answer 1

Answer:

4x2-16x+16=0

One solution was found :

x = 2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(22x2 - 16x) + 16 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

4x2 - 16x + 16 = 4 • (x2 - 4x + 4)

Trying to factor by splitting the middle term

3.2 Factoring x2 - 4x + 4

The first term is, x2 its coefficient is 1 .

The middle term is, -4x its coefficient is -4 .

The last term, "the constant", is +4

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

Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4 .

-4 + -1 = -5

-2 + -2 = -4 That's it

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

x2 - 2x - 2x - 4

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

x • (x-2)

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

2 • (x-2)

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

(x-2) • (x-2)

Which is the desired factorization