Problems 1 to 8 : Write each polynomial in standard form. Then, give the leading coefficient.
20y + 4y 3 - 2 + y 2
9x 3 - x + 3 - 7x 4
x - 9 + √ 7x 3 + 6x 2
√2x 2 - (7/2)x 4 + x - 5x 3
y 2 - √5y 3 - 11 - (7/3)y + 9y 4
Problems 9 and 10 : Add the following two polynomials and write the resulting polynomials in standard form.
p(x) = 6x 2 - 7x + 2 and q(x) = 6x 3 - 7x + 15
Problem 10 :
f(x) = 16x 4 - 5x 2 + 9 and g(x) = -6x 3 + 7x - 15
Problems 11 and 12 : Find the difference of the following two polynomials and write the resulting polynomials in standard form.
Problem 11 :
h(x) = 7x 3 - 6x + 1 and f(x) = 7x 2 + 17x - 9
Problem 12 :
h(x) = x - 6x 3 - 5 and f(x) = 1 2x -7x 3 - 5
Problems 1 to 8 : Write each polynomial in standard form. Then, give the leading coefficient.
20y + 4y 3 - 2 + y 2
Find the degree of each term :
Arrange the terms in order from largest degree to smallest degree.
4y 3 + y 2 + 20y - 2
The standard form is (4y 3 + y 2 + 20y - 2) and the leading coefficient is 4.
Find the degree of each term :
Arrange the terms in order from largest degree to smallest degree.
The standard form is ( x 5 + x 3 + 4x) and the leading coefficient is 1.
Find the degree of each term :
-17x 6 : degree 6
Arrange the terms in order from largest degree to smallest degree.
The standard form is ( -17x 6 + 5x) and the leading coefficient is -17.
Find the degree of each term :
Arrange the terms in order from largest degree to smallest degree.
The standard form is ( -6x 4 - 9x 3 - 5x ) and the leading coefficient is -6.
9x 3 - x + 3 - 7x 4
Find the degree of each term :
Arrange the terms in order from largest degree to smallest degree.
-7x 4 + 9x 3 - x + 3
The standard form is ( -7x 4 + 9x 3 - x + 3 ) and the leading coefficient is -7.
x - 9 + √ 7x 3 + 6x 2
Find the degree of each term :
Arrange the terms in order from largest degree to smallest degree.
√ 7x 3 + 6x 2 + x - 9
The standard form is ( √ 7x 3 + 6x 2 + x - 9 ) and the leading coefficient is √ 7 .
√2x 2 - (7/2)x 4 + x - 5x 3
Find the degree of each term :
-(7/2)x 4 : degree 4
Arrange the terms in order from largest degree to smallest degree.
-(7/2)x 4 - 5x 3 + √2x 2 + x
The standard form is ( -(7/2)x 4 - 5x 3 + √2x 2 + x ) and the leading coefficient is - 7/2 .
y 2 - √5y 3 - 11 - (7/3)y + 9y 4
Find the degree of each term :
Arrange the terms in order from largest degree to smallest degree.
9y 4 - √5y 3 + y 2 - (7/3) y - 11
The standard form is ( 9y 4 - √5y 3 + y 2 - (7/3) y - 11 ) and the leading coefficient is 9.
Problems 9 and 10 : Add the following two polynomials and write the resulting polynomials in standard form.
p(x) = 6x 2 - 7x + 2 and q(x) = 6x 3 - 7x + 15
p(x) + q(x) = (6x 2 - 7x + 2) + (6x 3 - 7x + 15)
= 6x 2 - 7x + 2 + 6x 3 - 7x + 15
Arrange the terms in order from largest degree to smallest degree.
= 6x 3 + 6x 2 - 7x - 7x + 2 + 15
Combine the like terms.
= 6x 3 + 6x 2 - 14x + 17
Problem 10 :
f(x) = 16x 4 - 5x 2 + 9 and g(x) = -6x 3 + 7x - 15
f(x) + g(x) = (16x 4 - 5x 2 + 9) + (-6x 3 + 7x - 15)
= 16x 4 - 5x 2 + 9 + -6x 3 + 7x - 15
Arrange the terms in order from largest degree to smallest degree.
= 16x 4 - 6x 3 - 5x 2 + 7x + 9 - 15
Combine the like terms.
= 16x 4 - 6x 3 - 5x 2 + 7x - 6
Problems 11 and 12 : Find the difference of the following two polynomials and write the resulting polynomials in standard form.
Problem 11 :
h(x) = 7x 3 - 6x + 1 and f(x) = 7x 2 + 17x - 9
h(x) - f(x) = ( 7x 3 - 6x + 1 ) - ( 7x 2 + 17x - 9 )
= 7x 3 - 6x + 1 - 7x 2 - 17x + 9
Arrange the terms in order from largest degree to smallest degree.
= 7x 3 - 7x 2 - 6x - 17x + 1 + 9
Combine the like terms.
= 7x 3 - 7x 2 - 23x + 10
Problem 12 :
h(x) = x - 6x 3 - 5 and f(x) = 1 2x -7x 3 - 5
h(x) - f(x) = ( x - 6x 3 - 5 ) - ( 1 2x - 7x 3 - 5 )
= x - 6x 3 - 5 - 1 2x + 7x 3 + 5
Arrange the terms in order from largest degree to smallest degree.
= -6x 3 + 7x 3 + x - 12x -5 + 5
Combine the like terms.
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