<< Chapter < Page Chapter >> Page >

Find the sum: ( 2 x 2 3 x y 2 y 2 ) + ( 5 x 2 3 x y ) .

7 x 2 6 x y 2 y 2

Got questions? Get instant answers now!

Find the difference: ( p 2 + q 2 ) ( p 2 + 10 p q 2 q 2 ) .

Solution

( p 2 + q 2 ) ( p 2 + 10 p q 2 q 2 ) Distribute. p 2 + q 2 p 2 10 p q + 2 q 2 Rearrange the terms, to put like terms together. p 2 p 2 10 p q + q 2 + 2 q 2 Combine like terms. −10 p q 2 + 3 q 2

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the difference: ( a 2 + b 2 ) ( a 2 + 5 a b 6 b 2 ) .

−5 a b 5 b 2

Got questions? Get instant answers now!

Find the difference: ( m 2 + n 2 ) ( m 2 7 m n 3 n 2 ) .

4 n 2 + 7 m n

Got questions? Get instant answers now!

Simplify: ( a 3 a 2 b ) ( a b 2 + b 3 ) + ( a 2 b + a b 2 ) .

Solution

( a 3 a 2 b ) ( a b 2 + b 3 ) + ( a 2 b + a b 2 ) Distribute. a 3 a 2 b a b 2 b 3 + a 2 b + a b 2 Rearrange the terms, to put like terms together. a 3 a 2 b + a 2 b a b 2 + a b 2 b 3 Combine like terms. a 3 b 3

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: ( x 3 x 2 y ) ( x y 2 + y 3 ) + ( x 2 y + x y 2 ) .

x 3 y 3

Got questions? Get instant answers now!

Simplify: ( p 3 p 2 q ) + ( p q 2 + q 3 ) ( p 2 q + p q 2 ) .

p 3 2 p 2 q + q 3

Got questions? Get instant answers now!

Evaluate a polynomial for a given value

We have already learned how to evaluate expressions. Since polynomials are expressions, we’ll follow the same procedures to evaluate a polynomial    . We will substitute the given value for the variable and then simplify using the order of operations.

Evaluate 5 x 2 8 x + 4 when

  1. x = 4
  2. x = −2
  3. x = 0

Solution

x = 4
5 x squared minus 8 x plus 4.
Substitute 4 for x. 5 times 4 squared minus 8 times 4 plus 4.
Simplify the exponents. 5 times 16 minus 8 times 4 plus 4.
Multiply. 80 minus 32 plus 4.
Simplify. 52.
x = −2
5 x squared minus 8 x plus 4.
Substitute negative 2 for x. 5 times negative 2 squared minus 8 times negative 2 plus 4.
Simplify the exponents. 5 times 4 minus 8 times negative 2 plus 4.
Multiply. 20 plus 16 plus 4.
Simplify. 40.
x = 0
5 x squared minus 8 x plus 4.
Substitute 0 for x. 5 times 0 squared minus 8 times 0 plus 4.
Simplify the exponents. 5 times 0 minus 8 times 0 plus 4.
Multiply. 0 plus 0 plus 4.
Simplify. 4.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Evaluate: 3 x 2 + 2 x 15 when

  1. x = 3
  2. x = −5
  3. x = 0

18 50 −15

Got questions? Get instant answers now!

Evaluate: 5 z 2 z 4 when

  1. z = −2
  2. z = 0
  3. z = 2

18 −4 14

Got questions? Get instant answers now!

The polynomial −16 t 2 + 250 gives the height of a ball t seconds after it is dropped from a 250 foot tall building. Find the height after t = 2 seconds.

Solution

−16 t 2 + 250 Substitute t = 2 . −16 ( 2 ) 2 + 250 Simplify. −16 · 4 + 250 Simplify. −64 + 250 Simplify. 186 After 2 seconds the height of the ball is 186 feet.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

The polynomial −16 t 2 + 250 gives the height of a ball t seconds after it is dropped from a 250-foot tall building. Find the height after t = 0 seconds.

250

Got questions? Get instant answers now!

The polynomial −16 t 2 + 250 gives the height of a ball t seconds after it is dropped from a 250-foot tall building. Find the height after t = 3 seconds.

106

Got questions? Get instant answers now!

The polynomial 6 x 2 + 15 x y gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x = 4 feet and y = 6 feet.

Solution

6 x squared plus 15 x y.
Substitute x equals 4 and y equals 6. 6 times 4 squared plus 15 times 4 times 6.
Simplify. 6 times 16 plus 15 times 4 times 6.
Simplify. 96 plus 360.
Simplify. 456.
The cost of producing the box is $456.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

The polynomial 6 x 2 + 15 x y gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x = 6 feet and y = 4 feet.

$576

Got questions? Get instant answers now!

The polynomial 6 x 2 + 15 x y gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x = 5 feet and y = 8 feet.

$750

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with adding and subtracting polynomials.

Key concepts

  • Monomials
    • A monomial is a term of the form a x m , where a is a constant and m is a whole number
  • Polynomials
    • polynomial —A monomial, or two or more monomials combined by addition or subtraction is a polynomial.
    • monomial —A polynomial with exactly one term is called a monomial.
    • binomial —A polynomial with exactly two terms is called a binomial.
    • trinomial —A polynomial with exactly three terms is called a trinomial.
  • Degree of a Polynomial
    • The degree of a term is the sum of the exponents of its variables.
    • The degree of a constant is 0.
    • The degree of a polynomial is the highest degree of all its terms.
Practice Key Terms 8

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask