**4 + 3*k**3 - 6*k**3 - 3*k**3 - k**4.
2*k**2*(k - 4)*(k + 1)
Suppose 2*b + 3*r + 6 = 0, -5*r - 10 = -2*b + 4*b. Determine z so that b + 1/2*z - 7/2*z**2 + 4*z**3 + 8*z**4 = 0.
-1, 0, 1/4
Let b(a) be the first derivative of -a**7/588 - a**6/180 - a**5/210 - a**3 + 6. Let x(l) be the third derivative of b(l). Find c, given that x(c) = 0.
-1, -2/5, 0
Let c(h) = 29*h**4 - 57*h**3 + 37*h**2 - 11*h + 2. Let s(z) = 19*z**4 - 38*z**3 + 25*z**2 - 7*z + 1. Let p(t) = 5*c(t) - 8*s(t). Factor p(n).
-(n - 1)**3*(7*n + 2)
Let c(w) be the second derivative of w**4/12 + w**3/6 - 3*w**2 + 3*w. Let q(s) = 1. Let l(r) = c(r) + 6*q(r). Factor l(j).
j*(j + 1)
Suppose 3*l - 8*l + 4*d + 15 = 0, 4*d = 2*l - 6. Factor 4*k**4 + 4*k**5 - 5 - 4*k**2 + 0*k - 20*k**l + 32*k - 3 - 8.
4*(k - 1)**3*(k + 2)**2
Let f(u) = u**5 - 7*u**4 + 7*u**3 + 3*u**2 + 4*u. Let k(w) = 6*w**4 - 6*w**3 - 3*w**2 - 3*w. Let v(z) = 3*f(z) + 4*k(z). Determine t so that v(t) = 0.
-1, 0, 1
Let h(k) be the first derivative of -k**7/840 - k**6/360 + k**5/120 + k**4/24 + k**3/3 - 1. Let z(v) be the third derivative of h(v). Factor z(j).
-(j - 1)*(j + 1)**2
Let y be (2 - (0 + 1))*3. Suppose -y*p + 4 = -p. Let 2*c**2 - p*c**4 + c - c = 0. What is c?
-1, 0, 1
Factor -1/4*z**3 + 1/2*z**4 + 0 + 0*z - 1/4*z**2.
z**2*(z - 1)*(2*z + 1)/4
Let t(n) be the third derivative of n**8/1008 - 4*n**7/315 + 5*n**6/72 - 19*n**5/90 + 7*n**4/18 - 4*n**3/9 - 10*n**2. Find j such that t(j) = 0.
1, 2
Let h(s) be the third derivative of -s**8/11200 - s**7/6300 - s**4/6 + 2*s**2. Let m(x) be the second derivative of h(x). Factor m(f).
-f**2*(3*f + 2)/5
Let d(b) be the first derivative of 0*b**2 - 2 + 1/3*b**4 + 1/3*b**3 + 1/10*b**5 - 2*b. Let w(o) be the first derivative of d(o). Factor w(g).
2*g*(g + 1)**2
Let j = 8 + -4. Factor n**2 + 2 + j*n + 1 - 3*n - 5.
(n - 1)*(n + 2)
Let g(u) be the first derivative of u**5/15 - u**3/18 - 2*u - 3. Let n(t) be the first derivative of g(t). Find h, given that n(h) = 0.
-1/2, 0, 1/2
Let h = 1/5 + 13/35. Determine z so that 2/7*z**2 + h - 6/7*z = 0.
1, 2
Let z = -21802/2553 - -196/23. Let j = z + 236/777. Factor j*c**4 + 0 + 4/7*c**3 + 0*c + 2/7*c**2.
2*c**2*(c + 1)**2/7
Let b(v) be the third derivative of 4*v**7/35 + 3*v**6/20 - 19*v**5/20 + 3*v**4/8 + v**3 - 20*v**2. Determine f so that b(f) = 0.
-2, -1/4, 1/2, 1
Suppose 12 = 4*y - 36. Suppose -3*j - y = 4*b - 6*j, 0 = 3*b + 2*j - 8. Suppose 0 + 0*t + 2/3*t**4 + b*t**3 - 2/3*t**2 = 0. What is t?
-1, 0, 1
Suppose z - 5*z = -20. Let m(o) = -6*o**4 + 8*o**3 - 8*o**2 + 6*o. Let u(k) = 2*k**4 - 3*k**3 + 3*k**2 - 2*k. Let l(s) = z*m(s) + 14*u(s). Factor l(i).
-2*i*(i - 1)*(i + 1)**2
Let t(b) be the first derivative of -b + 1 + 0*b**2 - 1/3*b**3. Let o(j) = j. Let p(v) = -2*o(v) - t(v). Solve p(f) = 0 for f.
1
Let n = 37 - 31. Let p(h) be the second derivative of -1/63*h**7 + 0 + 0*h**2 - 1/30*h**5 + 2/45*h**n + 0*h**3 + h + 0*h**4. Let p(d) = 0. Calculate d.
0, 1
Let c(k) be the second derivative of 1/21*k**3 - 3/7*k**2 + 0 - 5*k + 1/21*k**4. Let c(v) = 0. Calculate v.
-3/2, 1
What is q in 15*q**2 + 13*q**2 - 43*q**2 + 11*q**2 - 4*q = 0?
-1, 0
Let a(v) be the second derivative of v**6/15 + 3*v**5/10 + v**4/2 + v**3/3 - 3*v. Factor a(w).
2*w*(w + 1)**3
Let p = -21 - -9. Let o be (-16)/p*(-1 + 4). Factor -4*g**2 - 15*g - o - 2*g**2 + g.
-2*(g + 2)*(3*g + 1)
Let k(l) be the second derivative of 0*l**2 + 1/66*l**4 + 2/33*l**3 + 0 + l. Factor k(o).
2*o*(o + 2)/11
Let s be (9/3 + -1)/1. Let o(y) = 2*y**2 - 2*y + 1. Let i be o(s). Determine t so that -t**5 - 7*t**i + 7*t**5 - t**4 = 0.
-1, 0
Let w = 9 - 5. Suppose -5*m - 4*s = 5, -m + 2*s + 9 = -w. Factor 2/3*p**m + 0*p + 0 - 2/9*p**5 + 4/9*p**2 + 0*p**4.
-2*p**2*(p - 2)*(p + 1)**2/9
Let z(w) = 2*w + 3. Let g be z(0). Let s(k) be the first derivative of 2*k**2 + 0*k + g - 2/3*k**3. Factor s(t).
-2*t*(t - 2)
Let q(d) = -8*d**2 + 60*d - 16. Let z(u) = 9*u**2 - 60*u + 16. Let o(p) = 5*q(p) + 6*z(p). Let o(i) = 0. What is i?
2/7, 4
Let h(o) = -2*o - 9. Let i be h(-6). Factor -s**2 - 2*s**2 - i - 8*s + s**2 - 5.
-2*(s + 2)**2
Let u(o) be the second derivative of -o**6/135 + o**5/45 + o**4/18 - 4*o**3/27 - 4*o**2/9 - o. Find v such that u(v) = 0.
-1, 2
Find l such that -1/5*l**3 + 1/5*l**2 - 1/5*l**4 + 0 + 1/5*l**5 + 0*l = 0.
-1, 0, 1
Let y(p) be the second derivative of -2*p**6/15 + 2*p**5/5 - 4*p**3/3 + 2*p**2 + 4*p. Factor y(j).
-4*(j - 1)**3*(j + 1)
Let f(y) be the second derivative of -y**6/135 + y**5/30 - y**4/54 - y**3/9 + 2*y**2/9 - y. Let f(p) = 0. Calculate p.
-1, 1, 2
Let h(x) = -3*x**5 - 2*x**4 + 6*x**3 + x**2 + 1. Let n(u) = -9*u**5 - 5*u**4 + 18*u**3 + 2*u**2 - u + 3. Let i(q) = -8*h(q) + 3*n(q). Solve i(p) = 0 for p.
-1, 1/3, 1
Let g be (14/21)/((-4)/(-18)). Solve g*s**5 - 3*s**4 + 2*s**4 + 6*s**2 - 3*s - s**4 - 4*s**4 = 0 for s.
-1, 0, 1
Solve 6*p**3 + 310*p**4 - 3 - 313*p**4 + 6 - 6*p = 0 for p.
-1, 1
Suppose 0*m - 2*m = -2*g + 14, 2*g = 5*m + 29. Find w, given that 2/3*w + 1/3*w**g + 0 = 0.
-2, 0
Factor -2*x - 2/5*x**4 + 2/5*x**3 + 4/5 + 6/5*x**2.
-2*(x - 1)**3*(x + 2)/5
Factor -36*j**2 - 208/5*j**3 - 47/5*j - 4/5 + 64/5*j**4.
(j - 4)*(4*j + 1)**3/5
Let v(r) be the second derivative of r**4/54 - 2*r**3/27 - 11*r. Solve v(g) = 0 for g.
0, 2
Let h = -14378/15 + 959. Let i(s) be the second derivative of -3/50*s**5 + 0 + 2/5*s**2 - h*s**3 - 3*s + 4/15*s**4. Factor i(c).
-2*(c - 1)**2*(3*c - 2)/5
Let a(b) be the second derivative of b**5/140 - b**4/42 - b**3/14 + 14*b. Factor a(u).
u*(u - 3)*(u + 1)/7
Let a(f) be the second derivative of f**4/3 + 4*f**3/3 - 13*f. Determine u, given that a(u) = 0.
-2, 0
Let k(l) be the first derivative of l**4/42 - 2*l**3/21 + 3*l + 2. Let y(b) be the first derivative of k(b). Find r, given that y(r) = 0.
0, 2
Let t(v) = 4*v - 86. Let b be t(22). Let 2/7 + 2/7*o - 4/7*o**b = 0. Calculate o.
-1/2, 1
Let y(u) be the first derivative of 2 + 0*u - 1/9*u**3 - 1/18*u**4 - 1/2*u**2 - 1/90*u**5. Let q(b) be the second derivative of y(b). Factor q(m).
-2*(m + 1)**2/3
Let t be (-4)/40*2*-3. Let 0 - t*q**3 - 6/5*q**2 - 3/5*q = 0. Calculate q.
-1, 0
Let f(l) be the second derivative of -l**7/14 + 9*l**5/20 + l**4/2 - 30*l. Factor f(w).
-3*w**2*(w - 2)*(w + 1)**2
Let m(k) be the third derivative of -k**8/196 - 4*k**7/735 + 13*k**6/210 + 8*k**5/105 - 2*k**4/21 + 19*k**2. Solve m(s) = 0 for s.
-2, -1, 0, 1/3, 2
Suppose -5 = 7*c - 2*c - 5*q, -2*q + 10 = 2*c. Factor -3*z - 4*z - 5*z**2 - 2 - 2*z + c*z.
-(z + 1)*(5*z + 2)
Factor 0 + c**2 - 5/2*c**3 + 0*c + 2*c**4 - 1/2*c**5.
-c**2*(c - 2)*(c - 1)**2/2
Let h = -876 - -2644/3. Factor 8/3*q + 0 + 10/3*q**3 + 2/3*q**4 + h*q**2.
2*q*(q + 1)*(q + 2)**2/3
Let s(n) be the first derivative of 2*n**5/55 - 5*n**4/22 - 4*n**3/11 - 25. Factor s(l).
2*l**2*(l - 6)*(l + 1)/11
Let q be (-3 - -2) + 9/3. Factor -6*l**q + 4*l**2 + l + 0*l - l**5 + 2*l**4.
-l*(l - 1)**3*(l + 1)
Let p(a) = 5*a**2 - 5*a. Let v(h) = 3*h**2 - 3*h. Let z(w) = -2*p(w) + 5*v(w). Factor z(x).
5*x*(x - 1)
Let r(b) be the first derivative of 2/25*b**5 + 0*b - 1 + 3/10*b**4 + 1/5*b**2 + 2/5*b**3. Factor r(o).
2*o*(o + 1)**3/5
Let v(t) be the first derivative of 1/5*t + 3/10*t**2 + 1/5*t**3 + 1/20*t**4 - 1. Factor v(l).
(l + 1)**3/5
Solve -5*h + 15*h + 14*h**2 - 2 - 22*h**2 = 0.
1/4, 1
Let m(j) = -2*j - 6. Let f be m(-4). Factor 4*r**f - r**3 + 5 - 6 + 0*r**2 - 3*r - 7*r**2.
-(r + 1)**3
Let z(f) = 2*f**5 + 8*f**4 - 12*f**3 + 10*f - 4. Let q(m) = 2*m**5 + 7*m**4 - 11*m**3 - m**2 + 9*m - 3. Let y(i) = 4*q(i) - 3*z(i). Factor y(o).
2*o*(o - 1)**2*(o + 1)*(o + 3)
Let s(g) be the second derivative of -g**4/22 + g**3/11 + 10*g. Solve s(l) = 0 for l.
0, 1
Let t(j) be the second derivative of j**5/30 - j**4/12 + 4*j**2 + j. Let h(k) be the first derivative of t(k). Solve h(i) = 0.
0, 1
Let c be ((-30)/(-24))/(3*2/24). Solve -2/5*w**c + 0*w**3 + 0*w + 0*w**2 - 2/5*w**4 + 0 = 0.
-1, 0
Let v(l) be the first derivative of l**4/4 - l**3 + 3*l**2/2 - l + 3. Let w(s) = 2*s**3 - 4*s**2 + 2*s. Let a(f) = 4*v(f) - 3*w(f). Let a(c) = 0. Calculate c.
-2, 1
Let w = -265 - -2123/8. Let a = w + -1/24. Factor a*g**2 + 0*g - 1/3.
(g - 1)*(g + 1)/3
Let o(x) = -7*x + x**2 - 4 - 5*x**2 + 12*x + x**3. Let t be o(3). Factor -r**t + 2 + 1 - 2.
-(r - 1)*(r + 1)
Let j be (-4)/6*(0 - 3). Let x = -5 - -9. 