0. Review of Algebra

Polynomials Intro

0. Review of Algebra

# Polynomials Intro - Video Tutorials & Practice Problems

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## Introduction to Polynomials

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## Standard Form of Polynomials

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## Adding and Subtracting Polynomials

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Problem

ProblemPerform the indicated operation.

$\left(x^3+3x^2-7x\right)+2\left(x^3-5x^2+9x+4\right)$

A

$2x^3-2x^2+2x+6$

B

$3x^3-7x^2+11x+8$

C

$2x^3-2x^2+2x+4$

D

$3x^3-2x^2+2x+4$

5

Problem

ProblemPerform the indicated operation.

$\left(-2x^4+10x^3+6x-3\right)-\left(x^4-7x^2+8x+5\right)$

A

$-3x^4+10x^3+7x^2-2x-8$

B

$-3x^4+17x^3-2x-8$

C

$-3x^4+17x^2-2x-8$

D

$-x^4+10x^3-7x^2+14x+2$

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PRACTICE PROBLEMS AND ACTIVITIES (105)

- Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)^3 for x=4
- In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. 7/(x−3)
- In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x...
- In Exercises 1–8, multiply the monomials. (3x²y⁴)(5xy⁷)
- In Exercises 1–8, multiply the monomials. (−3xy²z⁵)(2xy⁷z⁴)
- In Exercises 5–8, find the degree of the polynomial. 3x^2−5x+4
- Perform the indicated operations. (2x^2-x)+(x^2+4x)
- In Exercises 5–8, find the degree of the polynomial. x^2−4x^3+9x−12x^4+63
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain o...
- Perform the indicated operations. -2x^3(x^4-8)
- In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indic...
- Perform the indicated operations. (10m^4-4m^2)/2m
- In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indic...
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain o...
- In Exercises 9–22, multiply the monomial and the polynomial. 4xy(7x+3y)
- In Exercises 15–32, multiply or divide as indicated. (6x+9)/(3x−15) ⋅ (x−5)/(4x+6)
- In Exercises 9–22, multiply the monomial and the polynomial. 3ab² (6a²b³+5ab)
- Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identif...
- In Exercises 15–58, find each product. (2x−3)(x^2−3x+5)
- In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2−4x+4) ⋅ (2x−4)/(x+2)
- Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identif...
- In Exercises 15–58, find each product. (x+7)(x+3)
- Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identif...
- In Exercises 15–58, find each product. (x−1)(x+2)
- In Exercises 15–32, multiply or divide as indicated. (x+5)/7 ÷ (4x+20)/9
- In Exercises 15–58, find each product. (2x−5)(7x+2)
- In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x−2) ÷ (x+2)/(4x−8)
- Add or subtract, as indicated. See Example 2. 3(8p^2-5p) - 5(3p^2-2p+4)
- In Exercises 23–34, find each product using either a horizontal or a vertical format. (a−b)(a²+ab+b²)
- Add or subtract, as indicated. See Example 2. -(8x^3+x-3) + (2x^3+x^2) - (4x^2+3x-1)
- In Exercises 23–34, find each product using either a horizontal or a vertical format. (x²+2x−1)(x²+3x−4)
- In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (−6x³ + ...
- Find each product. See Examples 3–5. (14r-1)(17r+2)
- In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2+3x−10) ÷ (x^2+5x+6)/(x^2+8x+15)
- In Exercises 15–32, multiply or divide as indicated. (x^3−25x)/4x^2 ⋅ (2x^2−2)/(x^2−6x+5) ÷ (x^2+5x)/(7x+7)
- In Exercises 15–58, find each product. (x+5)(x−5)
- Find each product. See Examples 3–5. 2b^3(b^2-4b+3)
- Find each product. See Examples 3–5. (2z-1)(-z^2+3z-4)
- In Exercises 15–58, find each product. (5−7x)(5+7x)
- Find each product. See Examples 3–5. (3w+2)(-w^2+4w-3)
- In Exercises 15–58, find each product. (4x^2+5x)(4x^2−5x)
- In Exercises 33–68, add or subtract as indicated. (4x−10)/(x−2) − (x−4)/(x−2)
- In Exercises 15–58, find each product. (1−y^5)(1+y^5)
- In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (x²ⁿ + 5...
- Find each product. See Examples 3–5. (3y-5)(3y+5)(9y^2-25)
- In Exercises 35–54, use the FOIL method to multiply the binomials. (4x+3)(5x+1)
- Find each product. See Examples 3–5. (x+1)(x+1)(x-1)(x-1)
- In Exercises 35–54, use the FOIL method to multiply the binomials. (3y−4)(2y−1)
- In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (17...
- In Exercises 33–68, add or subtract as indicated. 5/x + 3
- In Exercises 42–46, simplify each algebraic expression. 5x+7x²-4x+2x²
- Find each product. See Examples 5 and 6. (2m+3)(2m-3)
- In Exercises 33–68, add or subtract as indicated. 2/5x − (x+1)/4x
- In Exercises 15–58, find each product. (4x^2−1)^2
- Find each product. See Examples 5 and 6. (a-6b)^2
- In Exercises 35–54, use the FOIL method to multiply the binomials. (3xy−1)(5xy+2)
- Find each product. See Examples 5 and 6. (5r-3t^2)^2
- In Exercises 35–54, use the FOIL method to multiply the binomials. (x−4)(x²−5)
- In Exercises 33–68, add or subtract as indicated. (x+9)/10x^3 + 11/15x^2
- Find each product. See Examples 5 and 6. (2z^4-3y)^2
- In Exercises 15–58, find each product. (9−5x)^2
- In Exercises 15–58, find each product. (x+2)^3
- Subtract −4x³ − x²y + xy² + 3y³ from x³ + 2x²y − y³.
- Add 6x⁴−5x³+2x to the difference between 4x³+3x²−1 and x⁴−2x²+7x−3.
- Find each product. See Examples 5 and 6. [(3a+b)-1]^2
- Find each product. See Examples 5 and 6. [(2m+7)-n]^2
- In Exercises 15–58, find each product. (x−1)^3
- In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)
- Find each product. See Examples 5 and 6. (y+2)^3
- In Exercises 55–68, multiply using one of the rules for the square of a binomial. (2x + y)²
- In Exercises 55–68, multiply using one of the rules for the square of a binomial. (5x − 3y)²
- Perform the indicated operations. See Examples 2–6. (x^4-3x^2+2) - (-2x^4+x^2-3)
- Perform the indicated operations. See Examples 2–6. (7m+2n)^2
- Perform the indicated operations. See Examples 2–6. (3p+5)^2
- In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x^4 y...
- In Exercises 33–68, add or subtract as indicated. (4x^2+x−6)/(x^2+3x+2)−3x/(x+1)+5/(x+2)
- In Exercises 67–82, find each product. (3x−y)(2x+5y)
- Perform the indicated operations. See Examples 2–6. -z^3(9-z) + 4z(2+3z)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (x + 5)(x...
- Find each product. Assume all variables represent positive real numbers. y^5/8(y^3/8-10y^11/8)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (5x + 3)(...
- Find each product. Assume all variables represent positive real numbers. -4k(k^7/3-6k^1/3)
- In Exercises 67–82, find each product. (9x+7y)^2
- In Exercises 67–82, find each product. (x−y)(x^2+xy+y^2)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (1 − y⁵)(...
- Find each product : (4x+5)(4x-5)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (2 − y⁵)(...
- Perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^2-8xy+y^2)+(-8x^2-9xy-4...
- Perform the indicated operations. Indicate the degree of the resulting polynomial. (13x^3y^2-5x^2y-9x^2)-(-11x...
- In Exercises 83–90, perform the indicated operation or operations. (3x+4y)^2−(3x−4y)^2
- Find each product. (x+7y)(3x-5y)
- In Exercises 83–90, perform the indicated operation or operations. (3x+5)(2x−9)−(7x−2)(x−1)
- In Exercises 83–94, find each product. (5x + 7y − 2)(5x + 7y + 2)
- In Exercises 83–94, find each product. [5y + (2x+3)][5y − (2x+3)]
- The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2...
- The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2...
- In Exercises 117–130, simplify each algebraic expression. 7x+5x
- In Exercises 117–130, simplify each algebraic expression. 6x²-x²
- In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let ...
- In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let ...
- In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let ...
- In Exercises 117–130, simplify each algebraic expression. 18x²+4-[6(x²-2)+5]
- Multiply: (2x−5)(x²−3x−6). (Section 5.2, Example 3)
- Replace each boxed question mark with a polynomial that results in the given product. 2x³y² · ? = 12x⁵y⁴