Polynomials and Their Degrees
Polynomials and Their Degrees
TGM Original
A polynomial has non-negative integer powers of x. Its degree is the highest power with a nonzero coefficient. P(x)=a_nxn+a_n-1xn-1+. s+a_1x+a_0 (a_n 0) A nonzero constant has degree zero. The zero polynomial has no degree under this convention. **Expression** | **Polynomial?** | **Degree** | **Value** P(x)=4x4-5x3-2x+1 | Yes | 4 | P(-1)=12 Q(x)=x6-x3+x+2 | Yes | 6 | Q(2)=60 f(x)=3x2+ x-3x+1 | No | — | f(4)=39 g(x)=10 | Yes | 0 | g(-1)=10 k(x)=3x-2-x-4+5x2-2 | No | — | k(-2)=(299)/(16) Adding and subtracting Collect like powers. When subtracting, change the sign of every term in the second polynomial. (4x5+3x3-12x+7)-(4x3-3x2)=4x5-x3+3x2-12x+7
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Answer:\(P\): polynomial, degree \(4\), \(P(-1)=12\) \(Q\): polynomial, degree \(6\), \(Q(2)=60\) \(f\): non-polynomial, \(f(4)=39\) \(g\): polynomial, degree \(0\), \(g(-1)=10\) \(k\): non-polynomial, \(k(-2)=\frac{299}{16}\)
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