A polynomial is an expression consisting of fractions?dictionary=variables&did=130" onclick="getAsistant(this,event,130,'variables');return false;" style="color:#009000;">variables (or indeterminates) and fractions?dictionary=coefficients&did=400" onclick="getAsistant(this,event,400,'coefficients');return false;" style="color:#009000;">coefficients, that involves only the fractions?dictionary=operations&did=277" onclick="getAsistant(this,event,277,'operations');return false;" style="color:#009000;">operations of fractions?dictionary=addition&did=99" onclick="getAsistant(this,event,99,'addition');return false;" style="color:#009000;">addition, fractions?dictionary=subtraction&did=100" onclick="getAsistant(this,event,100,'subtraction');return false;" style="color:#009000;">subtraction, fractions?dictionary=multiplication&did=103" onclick="getAsistant(this,event,103,'multiplication');return false;" style="color:#009000;">multiplication, and non-negative integer fractions?dictionary=exponents&did=434" onclick="getAsistant(this,event,434,'exponents');return false;" style="color:#009000;">exponents of fractions?dictionary=variables&did=130" onclick="getAsistant(this,event,130,'variables');return false;" style="color:#009000;">variables.
The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 3x^2 + 2x - 5, the degree is 2.
Higher-degree fractions?dictionary=polynomials&did=354" onclick="getAsistant(this,event,354,'polynomials');return false;" style="color:#009000;">polynomials are fractions?dictionary=polynomials&did=354" onclick="getAsistant(this,event,354,'polynomials');return false;" style="color:#009000;">polynomials with a degree fractions?dictionary=greater+than&did=18" onclick="getAsistant(this,event,18,'greater than');return false;" style="color:#009000;">greater than 2. These fractions?dictionary=polynomials&did=354" onclick="getAsistant(this,event,354,'polynomials');return false;" style="color:#009000;">polynomials can have complex fractions?dictionary=shapes&did=36" onclick="getAsistant(this,event,36,'shapes');return false;" style="color:#009000;">shapes and multiple turning fractions?dictionary=points&did=284" onclick="getAsistant(this,event,284,'point');return false;" style="color:#009000;">points when graphed. They can also have multiple real or complex roots.
To solve higher-degree fractions?dictionary=polynomials&did=354" onclick="getAsistant(this,event,354,'polynomials');return false;" style="color:#009000;">polynomials, you can use methods such as fractions?dictionary=factoring&did=280" onclick="getAsistant(this,event,280,'factoring');return false;" style="color:#009000;">factoring, the fractions?dictionary=quadratic+formula&did=346" onclick="getAsistant(this,event,346,'quadratic formula');return false;" style="color:#009000;">quadratic formula, synthetic fractions?dictionary=division&did=104" onclick="getAsistant(this,event,104,'division');return false;" style="color:#009000;">division, or graphing techniques. Understanding the properties of the polynomial, such as the number of real and complex roots, can help in determining the approach to use for solving it.
1. Find the degree of the polynomial: 4x^3 - 2x^2 + 7x - 1
2. Determine the leading coefficient of the polynomial: 2x^4 + 3x^2 - 5x + 1
3. Graph the polynomial y = x^3 - 2x^2 + x - 1
1. The degree of the polynomial 4x^3 - 2x^2 + 7x - 1 is 3.
2. The leading coefficient of the polynomial 2x^4 + 3x^2 - 5x + 1 is 2.
3. The graph of the polynomial y = x^3 - 2x^2 + x - 1 will have a fractions?dictionary=shape&did=231" onclick="getAsistant(this,event,231,'shape');return false;" style="color:#009000;">shape with turning fractions?dictionary=points&did=284" onclick="getAsistant(this,event,284,'point');return false;" style="color:#009000;">points and may intersect the x-axis at various fractions?dictionary=points&did=284" onclick="getAsistant(this,event,284,'point');return false;" style="color:#009000;">points.
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