Page 354 - Algebra 1

Math Reasoning
Generalize When a polynomial is in standard form, is the leading coefficient always the coefficient of the first term?
b. (x2 +4x-9)-(4x2 -5x+11) SOLUTION
(x2 +4x-9)-(4x2 -5x+11) x2 +4x-9-4x2 +5x-11
x2 -4x2 +4x+5x-9-11 -3x2 + 9x - 20
Removetheparentheses. Arrangeliketermstogether. Combine like terms.
The polynomial -3x2 + 9x - 20 is in standard form. Application: Internet
For the years 1995 through 2001, the number of websites for businesses and education can be represented by the expressions below.
business websites: 0.333t2 - 1.035t + 0.607 education websites: 0.098t2 - 0.121t + 0.296
Write an expression for the total number of business and educational websites.
SOLUTION
0.333t2 - 1.035t + 0.607 + 0.098t2 - 0.121t + 0.296 0.431t2 - 1.156t + 0.903
The expression 0.431t2 - 1.156t + 0.903 represents the total number of websites.
Find the degree of each monomial.
(Ex 1) 2 6 a. 3x yz
b. -23xyz c. 42xy2z3
Write each polynomial in standard form. Then find the leading coefficient.
(Ex 2)
d. 3w2 - 2w4
e. 5ab2 +3a2b2 +8ab-1 f. 2ab-7-5a2b
Add the polynomials. Write each answer in standard form.
(Ex 3)
g. (2x2 +x+8)+(x2 +4)
h. (3n2 +7n-1)+(-2n2 -n+1)
Subtract the polynomials. Write each answer in standard form.
(Ex 4)
i. (12y3 +10)-(18y3 -3y2 +5)
Example
5
Lesson Practice
j. (c2 +6c-2)-(c2 -2c+6)
Lesson 53 339