2x^2(7x^4 + 4x + 2)

2(7x^6 + 4x^3 + 2x^2)

x^2(14x^4 + 8x + 4)

prime

C)(x − 3)2 = 25 C)Factor out 4 from 4x2 + 40x.

Step-by-step explanation:

1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.

___

2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.

Here, that looks like ...

4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4

4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation

4(x +5)² = 180 . . . . . . . . . . . written as a square

QUESTION 1

The given expression is

The greatest common factor is .

We factor to obtain;

QUESTION 2

The given quadratic equation is

We split the middle term to obtain

Factor by grouping;

Use zero product property;

QUESTION 3

The given system of equation is

If we multiply by 3, we obtain;

If we multiply by 4 we obtain;

Adding the last two equations will give us;

The y-variable is eliminated.

Multiply 3x+4y=−8

by 3. Multiply 7x−3y=6 by 4. Add the resulting equations together.

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