The nth Taylor polynomial Tn(x) for \(f(x)=\ln(1-x)\) based at b=0? Find the smallest value of n such that Taylor's inequality guarantees that \(|\ln(x)-\ln(1-x)|<0.01\) for all x in the interval \(l=[-\frac{1}{2},\frac{1}{2}]\)

Multiply these polynomials: \(12ab(\frac{5}{6a} + \frac{1}{4ab^{2}})\)

Factor the polynomial. \(t^4 - 1\)

Solve, adding the polynomials: \((2.7m – 0.5h) + (-3.2m + 0.2h)\)

For the following polynomial, \(P(x) = x^6 – 2x^2 – 3x^7 + 7\), find: 1) The degree of the polynomial, 2) The leading term of the polynomial, 3) The leading coefficient of the polynomial.

Solve: \(2(7y + z)(3y + 5z)\)

Solve the expression. \((2 – 5w) (2w^2 – 5)\)

Please, multiply: \(3(3m + 4n) (m + 2n)\)

Solve the polynomials: \((1 + x + x^4)(5 + x + x^2 + 3x^2)\)

Tell whether \(5x^{1/2} - 3x^{3}\) is a polynomial.

Find a second-degree polynomial P such that \(P(4)=5\), \(P'(4)=3\), and \(P"(4)=3\)

Add the polynomials: \((t^{2} – 4t + t^{4}) + (3t^{4} + 2t + 6)\)

Please, factor this polynomial: \(x^3 + 1\)

Factor the polynomial \(25t^2 + 90t + 81\)

Please, multiply these polynomials: \((3t – 7)(1 + 3t^2)\)

Solve: \(\displaystyle\frac{1}{{3}}{\left({6}{b}+{4}\right)}\)