Find Degree of Polynomial Product
Read this topicExplanations 4
- Note: the degree of a polynomial must be a non-negative integer. When we multiply two terms with the same base such as x2x^{2}x2 and x3x^{3}x3, our product is the base raised to…
By Winston Ou, Naomi Burgess, Anusha Rahman
- The degree of a polynomial is guaranteed to be its largest exponent if it contains only one variable. If the polynomial in question contains more than one variable, its degree i…
By Vinitha Ranganeni, Cameron Montag, Moor Xu, Naomi Burgess, Caroline K, Anusha Rahman
- (Video) Find the Degree of a Polynomial Product without Multiplying by Anusha Rahman In this video by Anusha Rahman, you will learn how to find the degree of a polynomial produc…
By Anusha Rahman
- Finding The Degree of a Polynomial Product Now that we've covered the basics of polynomial operations, let's move into the degree. The degree of a polynomial determines both its…
By Anusha Rahman
Problems 27
- Let f(x)=x3−x2+4x−7f(x) = x^3 - x^2 + 4x - 7f(x)=x3−x2+4x−7 and let g(x)=x4−x3+5x2−9x+12g(x) = x^4 - x^3 + 5x^2 - 9x + 12g(x)=x4−x3+5x2−9x+12. What is the degree of f(x)g(x)f(x)…
- What is the degree of the product of the two polynomials 20−16x4220 - 16 x^{42}20−16x42 and 7+x19747 + x^{1974}7+x1974?
- Find the degree of the product of f(x)=3+x+x2f(x) = 3 + x + x^2f(x)=3+x+x2 and g(x)=7−x24g(x) = 7 - x^{24}g(x)=7−x24.
- If we wanted to find the degree of the product of two polynomials, how would we go about it in the easiest or fastest way?
- If the degree of one polynomial H(x)H(x)H(x) is 20 and the degree of another polynomial Q(x)Q(x)Q(x) is 88, what is the degree of the polynomial (Q⋅H)(x)(Q\cdot H)(x)(Q⋅H)(x)?
- What is the degree of (x2+x+1)4(x3−x2+2x−3)3(x^2+x+1)^4 (x^3 -x^2 + 2x -3)^3(x2+x+1)4(x3−x2+2x−3)3?
- The product of x6x^6x6, , and x2+1x2−1x3x^2 + \frac{1}{x^2} - \frac{1}{x^3}x2+x21−x31 is a polynomial P(x)P(x)P(x) (at least when x≠0x\ne0x=0). What is the degree of PPP?
- In terms of mmm and nnn, what is the degree of (xm+xm−1+⋯+x2+x+1)n(x^m + x^{m-1} + \dots + x^2 + x + 1)^n(xm+xm−1+⋯+x2+x+1)n?
- What is the degree of (x2+x+1)5(x5−3x3−2x+1)3(x^2+x+1)^5 (x^5-3x^3-2x+1)^3(x2+x+1)5(x5−3x3−2x+1)3?
- Let fff be a polynomial such that f(0)=1f(0) = 1f(0)=1 and f(1)=f(2)=0f(1) = f(2) = 0f(1)=f(2)=0. Which of the following are possible degrees of fff?
- Let fff be a polynomial such that f(0)=0f(0) = 0f(0)=0 and f(1)=f(2)=f(3)=1f(1) = f(2) = f(3) = 1f(1)=f(2)=f(3)=1. Which of the following are possible degrees of fff?
- In the expression (x3−2x)(2x6−x5−3x2)(x^3 - 2x)(2x^6 - x^5 - 3x^2)(x3−2x)(2x6−x5−3x2), which 222 terms need to be multiplied to find the expression's resulting degree?
- What is the degree of a(3x4−2x2+1)a(3x^4 - 2x^2 + 1)a(3x4−2x2+1) for a≠0a \neq 0a=0?
- What is the resulting degree of (2x−3)(x+1)(\sqrt{2x} - 3)(\sqrt{x} + 1)(2x−3)(x+1)?
- What is the degree in xxx of (3x2y+x)(x−3)(x3+1)(3x^2y + x)(x - 3)(x^3 + 1)(3x2y+x)(x−3)(x3+1)?
- What is the degree in yyy of (y+x)(y2x−2)(y4x2+y)(y + x)(y^2x - 2)(y^4x^2 + y)(y+x)(y2x−2)(y4x2+y)?
- What is the degree of 2(a5b3−a4b5+a2)2(a^5b^3 - a^4b^5 + a^2)2(a5b3−a4b5+a2)?
- What is the name of this expression when simplified? (2x+1)(3x2+x)(2x + 1)(3x^2 + x)(2x+1)(3x2+x)?
- What are the only terms we need to multiply in each polynomial to find the degree of (2x+1)(3x2−x)(4x3)(2x + 1)(3x^2 - x)(4x^3)(2x+1)(3x2−x)(4x3)?
- What is the resulting degree of this expression without multiplying it out completely? (x−8)(3x3−2x2+x−1)(2x2+3x−4)(x - 8)(3x^3 - 2x^2 + x - 1)(2x^2 + 3x - 4)(x−8)(3x3−2x2+x−1)(…
- What is the degree of (xyz+yz3)(x2−y)(xyz + yz^3)(x^2 - y)(xyz+yz3)(x2−y)?
- What is the resulting degree of (2pq−3p)(p2q2−p2q+2pq2+1)(2pq - 3p)(p^2q^2 - p^2q + 2pq^2 + 1)(2pq−3p)(p2q2−p2q+2pq2+1)?
- Can you quickly find the resulting polynomial's degree? (x2+5)(2x+1)(x^2+5)(2x+1)(x2+5)(2x+1)
- Quickly find the polynomial's degree? (x100+x99+⋅⋅⋅+x+1)(x2+x+1)(x^{100}+x^{99}+\cdot\cdot\cdot+x+1)(x^2+x+1)(x100+x99+⋅⋅⋅+x+1)(x2+x+1)
- What is the degree of the resulting polynomial? (x2+4)(x3+8)(x^2+4)(x^3+8)(x2+4)(x3+8)
- What value of aaa should we choose to make a polynomial of degree 777? (xa+4)(2x4−x2+1)(x^a+4)(2x^4-x^2+1)(xa+4)(2x4−x2+1)
- Find the degree of the resulting polynomial. (x3+6x2+11x+6)÷(x+2)(x^3+6x^2+11x+6)\div(x+2)(x3+6x2+11x+6)÷(x+2)