*x**4 + 2/3*x**5 + 0*x**2 + 2/3*x**3 + 0*x + 0 = 0.
0, 1
Let t = 6 + -6. Let l(w) be the second derivative of t + 2*w + 5/9*w**3 - 1/6*w**4 - 2/3*w**2. Factor l(d).
-2*(d - 1)*(3*d - 2)/3
Let g(l) be the second derivative of l**5/110 - l**4/22 + 2*l**3/33 + 4*l. Factor g(b).
2*b*(b - 2)*(b - 1)/11
Let k(l) be the second derivative of l**7/42 - 3*l**5/20 - l**4/6 - l. What is w in k(w) = 0?
-1, 0, 2
Let r(q) be the third derivative of 0 + 0*q - 1/90*q**5 + 1/6*q**4 - q**3 - 2*q**2. Determine i, given that r(i) = 0.
3
Let z be 6/4*(-112)/(-12). Let q be (-2 - 1) + z/4. Suppose -1/2*c**2 - 1/2*c + 1/2*c**4 + 0 + q*c**3 = 0. Calculate c.
-1, 0, 1
Let n(d) be the second derivative of 3*d - 1/8*d**2 + 1/20*d**5 - 1/8*d**4 + 1/6*d**3 + 0 - 1/120*d**6. Suppose n(i) = 0. Calculate i.
1
Let t(s) be the third derivative of -2*s**2 + 1/3*s**4 + 4/3*s**3 + 0*s + 1/30*s**5 + 0. Find v, given that t(v) = 0.
-2
Factor 4/3*z + 2 + 2/9*z**2.
2*(z + 3)**2/9
Let q = 13 + -9. Factor -2/7 - 2/7*m**5 + 4/7*m**2 + 4/7*m**3 - 2/7*m**q - 2/7*m.
-2*(m - 1)**2*(m + 1)**3/7
Let c = -7 + 4. Let s be c*1/(-9)*6. Factor 5*t**3 - 2*t**3 - s*t**3.
t**3
Let a(p) = -p**5 - 2*p**4 - p**3 + 2*p**2 + p + 1. Let f be -1*4/2 + 3. Let g(c) = 1 - 40*c**3 + 17*c**3 + 22*c**3. Let m(k) = f*g(k) - a(k). Factor m(h).
h*(h - 1)*(h + 1)**3
Let u(n) = -n**2 - n + 1. Let z(k) = 11*k**2 - 34*k + 30. Let l(j) = 4*u(j) - z(j). Let y(h) = 3*h**2 - 6*h + 5. Let t(o) = 2*l(o) + 11*y(o). Factor t(r).
3*(r - 1)**2
Let c(u) be the third derivative of u**2 + 0*u - 1/660*u**6 + 0*u**4 + 0*u**5 + 0 + 0*u**3 + 1/1155*u**7. Factor c(x).
2*x**3*(x - 1)/11
Let v be (-832)/21 + (-20)/(-70). Let j = v - -40. Factor j*f - 2/3*f**3 - 2/3*f**2 + 2/3*f**4 + 0.
2*f*(f - 1)**2*(f + 1)/3
Factor -20*v**3 - 24*v**3 + 15*v**4 + 54*v + 119*v**2 - 40*v**3 - 20*v**2.
3*v*(v - 3)**2*(5*v + 2)
Determine h so that 5*h - 99*h**2 + 89*h**2 + 10*h**4 - 8*h**5 + 3*h**5 = 0.
-1, 0, 1
Suppose -i**3 - 37*i**4 + 40*i**4 + 4*i**3 = 0. What is i?
-1, 0
Let z(w) be the second derivative of -w**6/45 + w**4/6 - 2*w**3/9 - 4*w - 4. Factor z(m).
-2*m*(m - 1)**2*(m + 2)/3
Let p(c) be the first derivative of 2*c**6/3 - c**4 + 3. What is l in p(l) = 0?
-1, 0, 1
Let d(l) be the second derivative of l**5/5 - 5*l**4/3 - 26*l**3/3 - 14*l**2 - 4*l + 5. Suppose d(o) = 0. What is o?
-1, 7
Let v be (12/5)/(6/20). Factor 7*p**2 + 1 - v*p**2 - 4 - 4*p.
-(p + 1)*(p + 3)
Let m(o) be the first derivative of -3/70*o**5 + 2*o + 2 + 0*o**2 + 1/14*o**4 - 1/21*o**3 + 1/105*o**6. Let w(z) be the first derivative of m(z). Factor w(j).
2*j*(j - 1)**3/7
Let x be 2*(-1)/5*-5. Suppose 4*d + 0 - 12 = 0. Factor 0*i**d + 2*i**5 - 3*i**2 + 2*i**4 + x*i + 0*i - i**2 + 2 - 4*i**3.
2*(i - 1)**2*(i + 1)**3
Let 3*x**3 - x - x**5 - x - 5*x**4 + 4*x**4 + x**2 + 0*x**5 = 0. Calculate x.
-2, -1, 0, 1
Let r be ((-22)/3)/(-2) + 4/12. Let y(u) be the third derivative of -u**2 + 4/3*u**3 + 0*u + 1/10*u**5 - 1/2*u**r + 0 - 1/120*u**6. Let y(k) = 0. What is k?
2
Let g(r) be the first derivative of 5*r**6/4 + 7*r**5/2 + 25*r**4/8 + 5*r**3/6 + 27. Factor g(b).
5*b**2*(b + 1)**2*(3*b + 1)/2
Solve -1/2*c**5 + 0 + 7/2*c**2 - c - 9/2*c**3 + 5/2*c**4 = 0 for c.
0, 1, 2
Let g(u) = u**2 + u + 4. Let a be g(0). Factor 3*f**2 - 2*f + 7 - a*f - 7.
3*f*(f - 2)
Let n = 6734/1405 - -2/281. Factor 0 - 36/5*x**3 + 16/5*x + 2*x**4 + n*x**2.
2*x*(x - 2)**2*(5*x + 2)/5
Let a(q) be the first derivative of -q**6/180 + q**5/60 + q**4/6 - 5*q**3/3 - 1. Let o(c) be the third derivative of a(c). Determine s, given that o(s) = 0.
-1, 2
Let f = -1 + 2. Let z be f - (1 - 0 - 2). Factor 8*c**2 - 2*c**2 - 6*c**3 + z*c - 2*c**3.
-2*c*(c - 1)*(4*c + 1)
Let w be (-2)/(-1)*6/4. Suppose 4*k - 4 = w*f + 20, 3*f = -4*k. Factor -2*n + n**k + 2*n - n**2.
n**2*(n - 1)
Let u(j) be the third derivative of -j**5/60 + j**4/24 + 42*j**2 + 1. Suppose u(b) = 0. Calculate b.
0, 1
Suppose 11 = 3*i + v, 0 = i + 5*v - 8 - 5. Suppose -p = -i*p + 32. Factor p*t**2 + 2/3 - 6*t - 32/3*t**3.
-2*(t - 1)*(4*t - 1)**2/3
Factor 50 + 65*v + 13 - 8*v**2 + 7 + 3*v**2.
-5*(v - 14)*(v + 1)
Let r = -2 - -6. Suppose 0*c - y + 4 = c, c - r*y + 1 = 0. Let -l + 3*l**3 + l**3 - 3*l**c + 0*l = 0. Calculate l.
-1, 0, 1
Suppose 2*f - 6 = 3*f. Let u be (-12)/(-3)*f/(-8). Let -k + 0*k + 2*k**2 + 39*k**3 - 40*k**u = 0. Calculate k.
0, 1
Let u(a) be the first derivative of -a**3/5 + 12*a**2/5 - 48*a/5 - 4. Factor u(r).
-3*(r - 4)**2/5
Suppose 3*b - 12 + 3 = 0. Solve p**4 + 3*p**2 - 5*p + 7*p - 5*p - 4*p**4 + 3*p**b = 0 for p.
-1, 0, 1
Solve 2*l + 2*l**3 - 6*l**3 + 4*l**5 - 2*l**4 + 4*l**5 - 2 + 4*l**2 - 6*l**5 = 0 for l.
-1, 1
Let j = -13 + 35. Let a = -22 + j. Solve 0 + a*l + 1/6*l**2 - 1/6*l**3 = 0 for l.
0, 1
Factor -15 + 4*d**2 - 10 - 5*d**2 + 0*d + 10*d.
-(d - 5)**2
Let p(b) be the second derivative of b**6/120 + b**5/60 - b**4/24 - b**3/6 - 3*b**2/2 + 8*b. Let u(v) be the first derivative of p(v). Factor u(a).
(a - 1)*(a + 1)**2
Let r(c) be the second derivative of -c**6/240 + c**5/40 - c**4/16 + c**3/12 - c**2 + 5*c. Let b(x) be the first derivative of r(x). Factor b(k).
-(k - 1)**3/2
Suppose -2*n = 2*v - 6, -5*v + 5*n + 20 + 5 = 0. Suppose 2*a + 1 = 5. Suppose 8/3*c**2 - 2/3 - a*c**v + 4/3*c**3 - 4/3*c = 0. What is c?
-1, -1/3, 1
Let x(z) = -z**3 + 3*z**2 + z + 5. Let k(c) = 3*c**2 - 5 - 2*c**2 + 4 - 2*c**2. Let p(m) = -4*k(m) - x(m). Determine r, given that p(r) = 0.
-1, 1
Let i(f) be the third derivative of -f**7/5040 - f**6/480 - f**5/120 + f**4/8 + 2*f**2. Let d(w) be the second derivative of i(w). Factor d(n).
-(n + 1)*(n + 2)/2
Suppose -5*h + 10 = -0. Let y(l) be the third derivative of 0 - h*l**2 + 0*l + 0*l**3 + 1/84*l**4 - 1/420*l**6 + 0*l**5. Factor y(r).
-2*r*(r - 1)*(r + 1)/7
Solve 2*y - 14*y + 53 + y**2 - 17 = 0 for y.
6
Let v(c) be the second derivative of c**7/42 - c**5/20 - c**4/6 - 6*c. Let y(r) = -2*r**5 + r**4 + 3*r**3 + 5*r**2. Let m(d) = -10*v(d) - 4*y(d). Factor m(l).
-2*l**3*(l + 1)**2
Let x(s) be the first derivative of -24*s**2 - 8*s - 3 - 30*s**3 - 27/2*s**4. Let x(v) = 0. Calculate v.
-2/3, -1/3
Let z(a) be the first derivative of 169*a**3/9 - 26*a**2/3 + 4*a/3 + 13. Determine g so that z(g) = 0.
2/13
Suppose -2*m + 21 - 3 = 0. Factor 6 - 6*c - 6*c**2 + 7*c - m*c**3 + 8*c.
-3*(c - 1)*(c + 1)*(3*c + 2)
Factor -64 - 12*q**2 + 11*q**2 + 48*q - 11*q**2 + q**3.
(q - 4)**3
Let v(y) = -2*y + 1. Let c be v(-3). Solve w - c*w**2 - 2*w + 6*w**2 = 0.
-1, 0
Suppose 0 = b + 4*b - 4*s + 26, 5*b = 2*s - 28. Let n(u) = -9*u**3 + 3*u**2 - 6*u. Let t(k) = 8*k**3 - 4*k**2 + 6*k. Let v(r) = b*t(r) - 5*n(r). Factor v(w).
-3*w*(w - 2)*(w - 1)
Let h = 2/87 + 38/29. Let j(a) be the first derivative of -1 - h*a - 1/9*a**3 + 2/3*a**2. Factor j(u).
-(u - 2)**2/3
Let q = -649/21 + 95/3. Let f(m) be the first derivative of -9/14*m**4 - q*m**6 + 0*m - 1 + 48/35*m**5 + 2/21*m**3 + 0*m**2. Let f(g) = 0. What is g?
0, 1/4, 1
Let m(b) be the first derivative of -b**6/150 - b**5/150 + b**4/30 + b**3/15 - 2*b**2 + 2. Let y(v) be the second derivative of m(v). Factor y(x).
-2*(x - 1)*(x + 1)*(2*x + 1)/5
Let u be (-38)/(-57)*(-1)/(-2). Let x(p) be the second derivative of p - 1/4*p**2 - u*p**3 - 1/8*p**4 + 0. Factor x(w).
-(w + 1)*(3*w + 1)/2
Suppose 6*d - 18*d = -24. Factor -1/3 + y - 2/3*y**d.
-(y - 1)*(2*y - 1)/3
Suppose 0 = -4*c - v + 4, 7*c - v + 4 = 4*c. Suppose -5*p + q - 2*q = -1, c = 3*q - 3. Factor 0*t + p + 0*t**2 - 1/3*t**4 - 1/3*t**3.
-t**3*(t + 1)/3
Let i(y) be the second derivative of 0*y**3 - 3*y + 0 + 0*y**2 - 1/60*y**5 - 1/36*y**4. Factor i(m).
-m**2*(m + 1)/3
Let a(i) be the third derivative of 1/60*i**5 + 0*i**4 + 0 + 1/420*i**7 + 0*i + 3*i**2 + 1/90*i**6 - 1/36*i**3. Factor a(v).
(v + 1)**3*(3*v - 1)/6
Let y(b) be the first derivative of 1 - 1/12*b**3 + 0*b**2 + 0*b + 1/16*b**4. Factor y(v).
v**2*(v - 1)/4
Let b(c) be the third derivative of c**7/210 + c**6/120 - c**5/20 - 5*c**4/24 - c**3/3 + 26*c**2. Suppose b(p) = 0. What is p?
-1, 2
Let v(n) = n**2 + 11*n - 10. Let s be v(-12). Find d, given that d**3 + 0 - 3/2*d**s - d + 3/2*d**4 = 0.
-1, -2/3, 0, 1
Let k(f) be the first derivative of -10/27*f**3 + 0*f - 1/9*f**2 - 1 - 2/9*f**4. Factor k(s).
-2*s*(s + 1)*(4*s + 1)/9
Suppose 2*j - 6 = -0*j. Factor -2*h**2 + 2 + 3*h - 6 + j*h.
-2*(h - 2)*