Question

1.the degree of the polynomial 2-x^3+x^2
2.the value of polynomial x-x^3 at x=2
3.the zero of polynomial p(x)=3x+2
4.the remainders when x^3+3x^2+5x+6is divided by x+1​

Answer 1

Answer:

$2. \: \: \: p(x) = x - {x}^{3} \\ \: \: \: \: p(x) = 2 - {2}^{3} \\ \: \: \: p(x) = 2 - 8 \\ \: \: \: p(x) = \underline{ \underline{ - 6}} \\ \\ 3. \: \: \: \: p(x) = 3x + 2 = 0 \\ \: \: \: \: p(x) = 3x = - 2 \\ \: \: \: p(x) = x = \underline{ \underline{ \frac{ - 2}{3} }} \\ \\ 4. \: \: \: \: g(x) = x + 1 = 0 \\ \: \: \: \: g(x) = x = \underline{ \underline{ - 1}} \\ \\ p(x) = {x}^{3} + 3 {x}^{2} + 5x + 6 \\ p( - 1) = {( - 1)}^{3} + 3 {( - 1)}^{2} + 5( - 1) + 6 \\ p( - 1) = - 1 + (3 \times 1) + ( - 5) + 6 \\ p( - 1) = - 1 + 3 - 5 + 6 \\ p( - 1) = \underline{ \underline{ 3}}$