$$x = 0$$; check that $$x \neq 2$$ and $$x \neq -2$$

Question 1

Which of the following is the correct complete factorization of $$14x^3w^2$ - 21x^2$w^3y$$ + $$35w^4x^2$y^2$$?

Accepted Answer

$$7x^2w^2$(2x - 3wy + 5w^2$y^2$$)$$

Question 2

Given the expression $$2a^3$$ - $$7ab^2$$ - $$7b^3$$, which of the following is its complete factorization?

Accepted Answer

$$(a + b)(2a^2$ - 2ab - 7b^2$)$$

Question 3

Which of the following is the correct factorization of $$x^3$$ + $$4x^2 - x - 4$?

Accepted Answer

$$(x + 4)(x^2$ - x - 4)$$

Question 4

If $$x^3$$ - $$2x^2 - 5x + 6$ is factored completely, which of the following is correct?

Accepted Answer

$$(x - 1)(x - 2)(x + 3)$$

Question 5

Which of the following is the correct factorization of $$2x^3$$ - $$3x^2 - 8x + 12$?

Accepted Answer

$$(x - 2)(2x^2$ + x - 6)$$

Question 6

Given the quadratic $$4x^2 - 25$, which of the following is its complete factorization?

Accepted Answer

$$(2x + 5)(2x - 5)$$

Question 7

Which of the following is the correct factorization of $$6x^2 - 5x$$ - $$x^3$$?

Accepted Answer

$$-x(x^2 - 6x + 5$$)$$

Question 8

Which of the following is the correct factorization of $$7x^2 - 49x$?

Accepted Answer

$$7x(x - 7)$$

Question 9

What is the complete factorization of $$15x^2 - 21x + 48x$?

Accepted Answer

$$3x(5x + 9)$$

Question 10

Which of the following is the correct factorization of $$x^2 - 2$?

Accepted Answer

$$(x + 2)(x - 2)$$

Question 11

Solve for $$x$$: $$2(x - 3) = 7x - 7$$

Accepted Answer

$$x = 1$$

Question 12

Solve for $$x$$: $$4x + 6 = -4(x - 6)$$

Accepted Answer

$$x = -3$$

Question 13

Solve for $$y$$: $$2x + 4y = 0$$

Accepted Answer

$$y = -\frac{x}{2}$$

Question 14

If $$f(x) = x^2$ - 4x + 3$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 15

Solve for the exact answer: $$\frac{4x}{x^2$ - 4} + \frac{2x}{x^2$ - 4} = 0. $$What must you check?

Accepted Answer

$$x = 0$$; check that $$x 
eq 2$$ and $$x 
eq -2$$

Question 16

Simplify and multiply: $$(2A - 5B)^2$

Accepted Answer

$$4A^2 - 20AB$$ + $$25B^2$$

Question 17

Simplify: $$\frac{3x^2$ + 2x - 8}{x^2$ - 4}$$

Accepted Answer

$$\frac{3x^2$ + 2x - 8}{(x + 2)(x - 2)}$$

Question 18

Divide and simplify: $$\frac{3x^2$ + 2x - 8}{x^2$ - 4} \div \frac{x^2$ + 2x - 8}{x^2$ - 4}$$

Accepted Answer

$$\frac{3x^2$ + 2x - 8}{x^2$ + 2x - 8}$$

Question 19

Perform the indicated operations and simplify: $$\frac{2x}{x^2$ - 2x} + \frac{2}{x^2$ - 2x}$$

Accepted Answer

$$\frac{2x + 2}{x^2$ - 2x}$$

Question 20

Perform the indicated operations and simplify: $$\frac{x^2$}{x^2$ - 2x} - \frac{2x}{x^2$ - 2x}$$

Accepted Answer

$$\frac{x^2$ - 2x}{x^2$ - 2x}$$

Review and Study Notes: Polynomial and Rational Functions (Chapter 6)

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