More algebra 2 help please?

Question

Question 1 (Multiple Choice Worth 1 points)

Factor completely 3x3 – 21x2 – 27x

3x(x2 – 7x – 9)

3x(x + 1)(x – 9)

3(x2 – 7x – 9)

3(x3 – 21x2 – 27x)

Question 2 (Multiple Choice Worth 1 points)

Which of the following represents the area of a rectangle whose length is x – 7 and whose width is
x + 12?

x2 + 5x – 84

x2 – 84

x2 – 5x – 84

x2 – 84x + 5s

Question 3 (Multiple Choice Worth 1 points)

Which is a factor of 12x2– 46x – 8 ?

2

3x – 4

2x + 1

3x – 2

Question 4 (Multiple Choice Worth 1 points)

Simplify (x + 4)(x2 – 6x + 3)

x3 – 14x2 + 3x + 12

x3 – 6x2 – 17x + 12

x3 – 10x2 – 27x + 12

x3 – 2x2 – 21x + 12

Question 5 (Multiple Choice Worth 1 points)

Which of the following is a factor of 5x3 + 320?

5

x + 4

x2 – 4x + 16

All of the above

Question 6 (Multiple Choice Worth 1 points)

Simplify (5x3 – x + 14) – (3x2 – 9x + 4)

5x3 – 3x2 + 8x + 10

2x2 + 8x + 10

5x3 – 3x2 – 10x + 18

2x2 – 10x + 18

Question 7 (Multiple Choice Worth 1 points)

Identify the polynomial written in descending order.

9 – 14x – 7x2 + x3

x3 – 7x2 – 14x + 9

–7x2 + 9 + x3 – 14x

–14x + x3 + 9 – 7x2

Question 8 (Multiple Choice Worth 1 points)

Classify the expression 7x3 + 2x2 – 9x as a monomial, binomial, trinomial or polynomial.

monomial

binomial

trinomial

polynomial

Question 9 (Multiple Choice Worth 1 points)

Which is a factor of 3x2y2 + 6x2+ 12y2 + 24 ?

6

x2 + 2

y2 + 6

x2 + 4

Question 10 (Multiple Choice Worth 1 points)

Factor completely 25x2 – 144

(5x – 12)(5x – 12)

(5x – 12)(5x + 12)

(12x – 5)(12x – 5)

(12x – 5)(12x + 5)

Answer 1

1.

   3x³ - 21x² - 27x

Take out common term 3x

= 3x(x² - 7x - 9)

A is the right choice.

Answer 2

The length of the rectangle : l   = x - 7

The width of the rectangle  : b   = x + 12

The area of the rectangle   :l×b = (x - 7)(x + 12)

                                             = x² + 12x - 7x - 84

                                             = x² + 5x - 84

A is the right choice. 

Answer 3

3.

   12x² - 46x - 8

Take out common term 2 in the above expression

= 2(6x² - 23x - 8)

= 2.

A is the right choice.

 

Answer 4

4.

   (x + 4)(x² - 6x + 3)

Recall : Distributive property a ( b + c) = ab + ac

= x³ - 6x² + 3x + 4x² - 24x + 12

= x³ - 2x² - 21x + 12

D is the right choice.

Answer 5

5.

   5x^3 + 320

Take out common term 5 in the above expression

= 5(x^3 + 64)

= 5(x^3 + 4^3)

Recall : a^3 + b^3 = (a + b)(a^2 - ab + b^2)

= 5(x + 4)(x^2 - 4x + 16)

D is the right choice.

Answer 6

6.

(5x^3 - x + 14) - (3x^2 - 9x + 4)

Subtract same power terms in the above expression

5x^3 - 3x^2  + 8x + 10

A is the right choice.

Answer 7

7.

The polynomial written in descending order x³ - 7x² - 14x - 9

B is the right chice.

Answer 8

8.

7x³ + 2x² - 9x

This is a third degree expression then it is called a trinomial

C is the right choice.

Answer 9

9.

   3x²y² + 6x² + 12y² + 24

= 3x²(y² + 2) + 12(y² + 2)

Take out common term y² + 2

= (y² + 2)(3x² + 12)

= (y² + 2)3(x² + 4)

x² + 2 is the common factor

D is the right choice.

Answer 10

10.

    25x² - 144

 =(5x)² - (12)²

Recall : alzebra formula (a² - b²) = (a - b)(a + b)

=(5x - 12)(5x + 12)

B is the right choice.