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Pre-Algebra : Polynomials

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Example Questions

Example Question #51 : Polynomials

Simplify the polynomial.

-2x(2x^2 - 3x + 4) =

Possible Answers:

-4x^3 +6x^2 +8x

-4x^3 -6x^2 - 8x

-4x^3 + 6x^2 - 8x

-4x^2 - 13x

4x^3 - 5x^2 - 8x

Correct answer:

-4x^3 + 6x^2 - 8x

Explanation:

-2x(2x^2-3x + 4) =

(-2x * 2x^2) + (-2x * -3x) + (-2x * 4) =

(-4x^3) + (6x^2) + (-8x) =

-4x^3 + 6x^2 - 8x

Variables without any exponents have an invisable 1 as their exponent.

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Example Question #52 : Polynomials

Simplify: $\frac{b^2-49}{b+7}$

Possible Answers:

-7b

The expression is already simplified.

b+7

b-7

Correct answer:

b-7

Explanation:

In order to simplify this, we need to rewrite the numerator by factorization.

To factor the numerator, we need to look at the factors of the integer value. The factors of the integer value when added together should result in the middle term of the polyinomial. In this particular case there is no middle term therefore, we are looking for a factor that when added together results in a zero term. This is also known as the differences of squares.

$\frac{b^2-49}{b+7} = \frac{(b+7)(b-7)}{b+7}$

Cancel the terms in the numerator and denominator.

The correct answer is: b-7

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Example Question #53 : Polynomials

Simplify: $\frac{x^2-49}{x-7}$

Possible Answers:

x-7

-7x

x+7

7-x

Correct answer:

x+7

Explanation:

In order to divide this polynomial, it is necessary to factor out the numerator.

To factor this polynomial find the two factors of the integer term, , that when added together results in the middle term of the polynomial, .

This particular type of polynomial is known as the difference of perfect squares.

$\frac{x^2-49}{x-7} = \frac{(x+7)(x-7)}{x-7} = x+7$

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Example Question #54 : Polynomials

Multiply: 3x^4(-2x^2+2x-1)

Possible Answers:

-x^6+5x^5-3x^4

-6x^6+6x^5-3x^4

-5x^6+5x^5-4x^4

x^4-x^2-2x-1

-6x^8+6x^4-3x^4

Correct answer:

-6x^6+6x^5-3x^4

Explanation:

Use the distributive property to expand this expression. When powers of similar bases are multiplied, their powers can be added.

3x^4(-2x^2+2x-1) = -6x^6+6x^5-3x^4

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Example Question #55 : Polynomials

Multiply: (3x^2-1)(-8x)

Possible Answers:

-24x^3+8x+1

-24x^3-8x-1

-24x^3+8x

3x^2-8x-1

-24x^2+8x

Correct answer:

-24x^3+8x

Explanation:

Use the distributive property to expand the expression.

(3x^2-1)(-8x) = (3x^2)(-8x)+(-1)(-8x) = -24x^3+8x

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Example Question #56 : Polynomials

Multiply:

(3x^2+4)(2x+8)

Possible Answers:

6x^3+24x^2+8x+12

30x^2+8x+32

6x^3+24x^2+8x+32

6x^3+32x^2+12

6x^2+32x+12

Correct answer:

6x^3+24x^2+8x+32

Explanation:

Use the FOIL method to simplify. FOIL stands for the finding the product of polynomials by multiplying their First, Outer, Inner, and Last terms together.

(3x^2+4)(2x+8) =

Firsts: (3x^2)(2x)

Outers: (3x^2)(8)

Inners: (4)(2x)

Lasts: (4)(8)

Multiply out each term and adding them results in the final polynomial.

Remember when multiplying like bases you add their exponents.

=(3x^2)(2x)+(3x^2)(8)+(4)(2x)+(4)(8)

=6x^3+24x^2+8x+32

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Example Question #57 : Polynomials

Multiply: (2x^2 +2)(3x^2+1)

Possible Answers:

5x^2+6x+1

6x^2+6x+1

6x^4+8x^2+2

6x^4+5x^2+2

5x^4+6x^2+2

Correct answer:

6x^4+8x^2+2

Explanation:

Use the FOIL method to expand the terms.

(2x^2 +2)(3x^2+1) = (2x^2)(3x^2) + (2x^2)(1) + (2)(3x^2)+(2)(1)

Multiply out each term.

$(2x^2)(3x^2) = 2\cdot x\cdot x\cdot 3\cdot x\cdot x = 6x^4$

(2x^2)(1) = 2x^2

$(2)(3x^2) = 2 \cdot 3 \cdot x\cdot x =6x^2$

(2)(1)=2

Combine like-terms and write out the expanded form.

The answer is: 6x^4+8x^2+2

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Example Question #58 : Polynomials

Solve the equation below.

$\frac{9x^7}{2x^4}$

Possible Answers:

4.5x^2^8

18x^2^8

18x^1^1

4.5x^3

11x^1^1

Correct answer:

4.5x^3

Explanation:

When dividing with exponents that have different bases, divide the bases then subtract the exponents.

$\frac{9x^7}{2x^4}$

9 / 2 = 4.5

7 - 4 = 3

4.5x^3

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Example Question #59 : Polynomials

Multiply the polynomials and simplify.

$(6x^{2})\cdot(4x^{4})=$

Possible Answers:

$10x^{6}$

$24x^{8}$

$10x^{8}$

$24x^{6}$

$24x^{2}$

Correct answer:

$24x^{6}$

Explanation:

To figure out the solution to this problem is to simply multiply the integers normally so

$6\times4=24$

The rule to multiply the same variables with exponents is to add the exponents together. For example,

$x^{2}\times x^{4}= x^{(2+4)}=x^{6}$

So,

$24\times x^{6}=24x^{6}$

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Example Question #1 : Power Rule Of Exponents

Simplify:

$\left ( 3x^{2}y \right )^{3}$

Possible Answers:

$9x^{2}y$

$27x^{6}y^{3}$

$3x^{5}y^{3}$

$3x^{2}y^{3}$

$9x^{6}y^{3}$

Correct answer:

$27x^{6}y^{3}$

Explanation:

Recall the Power Rule of Exponents: $\left ( x^{m} \right )^{n}=x^{m*n}$ .

To simplify the expression $\left ( 3x^{2}y \right )^{3}$ , use this rule to distribute the exponents:

$\left ( 3x^{2}y \right )^{3}=3^{3}x^{2*3}y^{3}=27x^{6}y^{3}$

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Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #51 : Polynomials

Example Question #52 : Polynomials

Example Question #53 : Polynomials

Example Question #54 : Polynomials

Example Question #55 : Polynomials

Example Question #56 : Polynomials

Example Question #57 : Polynomials

Example Question #58 : Polynomials

Example Question #59 : Polynomials

Example Question #1 : Power Rule Of Exponents

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