Factor completely 14x6 + 8x3 + 4x2.
2x^2(7x^4 + 4x + 2)
2(7x^6 + 4x^3 + 2x^2)
x^2(14x^4 + 8x + 4)
prime

Answers

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

12x^4+18x^3+45x^2

The greatest common factor is 3x^2.

We factor to obtain;

3x^2(4x^2+6x+15)

QUESTION 2

The given quadratic equation is

x^2+6x-72=0

We split the middle term to obtain

x^2+12x-6x-72=0

Factor by grouping;

x(x+12)-6(x+12)=0

(x+12)(x-6)=0

Use zero product property;

(x+12)=0\:\:or\:\:(x-6)=0

x=-12\:\:or\:\:x=6

QUESTION 3

The given system of equation is

3x+4y=-8

7x-3y=6

If we multiply 3x+4y=-8 by 3, we obtain;

9x+12y=-24

If we multiply 7x-3y=6 by 4 we obtain;

28x-12y=24

Adding the last two equations will give us;

37x=0

The y-variable is eliminated.

Multiply 3x+4y=−8

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

2x²(7x⁴ + 4x + 2)

Step-by-step explanation:

14x^6+8x^3+4x^2\\\\GCF(14,\ 8,\ 4) =2\\GCF(x^6,\ x^3,\ x^2)=x^2\\\\14x^6+8x^3+4x^2=(2x^2)(7x^4)+(2x^2)(4x)+(2x^2)(2)\\\\=2x^2(7x^4+4x+2)



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