Adding Polynomials
Write in standard form:
(3x^2-4x+1)+(x^2)
4x^2-4x+1
Write in standard form:
(2x-4)-(3x+1)
-x-5
Write in standard form:
(x+2)(x-2)
x^2-4
What is standard form of a polynomial?
Terms written in descending order by degree.
What is the degree of this polynomial function?
f(x)=x^4+2x^3-13x^2-14x+24
Write in standard form:
(x+3)(x+7)
2x+10
Write in standard form:
(x-4)-(x^2+2x-1)
-x^2-x-3
Write in standard form:
(3x+2)(x^2-1)
3x^3+2x^2-3x-3
Is the polynomial in standard form? If not, what is it in standard form?
4x^2-3x^4+2
No
-3x^4+4x^2+2
How many terms does the polynomial function have?
f(x)=x^4+2x^3-13x^2-14x+24
5
Write in standard form:
(x+3)+(x^2+3)
x^2+x+6
Write in standard form:
(x^2-2x+7)-(x^2+3x+1)
-5x+6
Write in standard form:
(7a+2)(2a^2-5a+3)
14a^3-31a^2+11a+6
Write the polynomial function in standard form and give the degree of the polynomial.
f(x)=8x^2+10x^7-7x^3-x^4
f(x)=10x^7-x^4-7x^3+8x^2
Degree: 7
What is the leading coefficient of this polynomial function?
f(x)=x^4+2x^3-13x^2-14x+24
1
Write in standard form:
(-2x^2-3x+1)+(-x^2+x-3)
-3x^2-2x-2
Write in standard form:
(x^3-2x^2+3)-(x^2+3)
x^3-3x^2
Write in standard form:
(x-2)(x^2+3x+1)
x^3+x^2-5x-2
Write the polynomial in standard form and give the leading coefficient.
f(x)=-3x^3+2x^5+x+8x^3-6+x^4-3x^2
f(x)=2x^5+x^4+5x^3-3x^2+x-6
Leading coefficient: 2
What is a polynomial?
An expression with multiple terms separated by addition or subtraction.
Write in standard form:
(-3a^3+2a^2-4)+(a^3-3a^2-5a+7)
-2a^3-a^2-5a+3
Write in standard form:
(7x^2y^2-6x^3+xy)-(5x^2y^2-x^3+xy+x)
2x^2y^2-5x^3-x
Write in standard form:
(xy-1)(xy+6)(xy-8)
x^3y^3-3x^2y^2-46xy+48
Write the polynomial function in standard form and find the number of terms and the leading coefficient.
f(x)=-x^3+9x+12-x^4+5x^2
f(x)=-x^4-x^3+5x^2+9x+12
Number of terms: 5
Leading coefficient: -1
Allie said the degree of the polynomial function f(x)=x^5+2x^4+3x^3-2x^6-9x^2-6x+4 is 5 . Explain and correct Allie's error.
The function is not in standard form, but she said the first term had the degree of the polynomial. The degree is 6.