Question

Punctuate the following sentences.
1. happy birthday to you everybody sang
2. this is the best birthday party I have ever had said Danny

Answer 1

Explanation:

Step by step solution :

STEP

1

:

Equation at the end of step 1

((22•3x2) - 72x) + 96 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

12x2 - 72x + 96 = 12 • (x2 - 6x + 8)

Trying to factor by splitting the middle term

3.2 Factoring x2 - 6x + 8

The first term is, x2 its coefficient is 1 .

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

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

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

Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is -6 .

-8 + -1 = -9

-4 + -2 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -2

x2 - 4x - 2x - 8

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

x • (x-4)

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

2 • (x-4)

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

(x-2) • (x-4)