 - c*k**3 + 0*k**2 + 0*k + 0 + 0*k**4.
2*k**3*(k - 1)*(k + 1)/5
Let a(r) = -r**2 + 0 - 13*r + 1 - 7. Let v be a(-12). Suppose 4*h**2 + 2*h**5 - 4*h**5 + v*h**3 - 4*h**5 - 4*h**4 + 0*h**2 = 0. Calculate h.
-1, -2/3, 0, 1
Let k(c) be the second derivative of -c**5/80 - c**4/8 - 3*c**3/8 + 6*c. Factor k(u).
-u*(u + 3)**2/4
Let q = -3/29 - -143/261. Suppose 0 + 0*n + q*n**4 - 2/9*n**3 + 0*n**2 - 2/9*n**5 = 0. Calculate n.
0, 1
Let n(i) be the first derivative of i**4/6 - 4*i**2/3 - 9. Factor n(j).
2*j*(j - 2)*(j + 2)/3
Let b be (8/30)/((-2)/(-5)). Let j be ((-46)/(-12) - 4)*-2. Determine k so that -1/3*k + 0 - j*k**3 - b*k**2 = 0.
-1, 0
Factor 133/2*s**2 + 2 + 147/2*s**3 + 20*s.
(3*s + 1)*(7*s + 2)**2/2
Suppose -24 = -27*x + 21*x. Determine m, given that 0*m**3 + 0*m**2 + 0*m + 0 + 2/7*m**5 - 2/7*m**x = 0.
0, 1
Suppose 41 = -4*n + 57. Determine s so that -10/9*s**2 + 0 + 14/9*s**3 + 2/9*s - 2/3*s**n = 0.
0, 1/3, 1
Let d(t) = 16*t**2 - 21*t + 11. Let g(u) = 3*u**2 - 4*u + 2. Let c(x) = -4*d(x) + 22*g(x). What is s in c(s) = 0?
0, 2
Let l(t) = t**2 + 2*t. Let r(f) = 2*f**2 + f. Let y(h) = 3*l(h) - 2*r(h). Let k be y(4). Factor 1/2*u**3 - 1/2*u + 0 + k*u**2.
u*(u - 1)*(u + 1)/2
Let r(m) be the third derivative of 0 + 1/120*m**4 - 1/30*m**3 - 1/1050*m**7 + 1/150*m**5 + 0*m - 1/300*m**6 - 5*m**2 + 1/1680*m**8. Factor r(x).
(x - 1)**3*(x + 1)**2/5
Find q, given that -2/5 - 9/5*q**2 + 7/5*q - 1/5*q**4 + q**3 = 0.
1, 2
Let y(h) be the first derivative of h**4/4 + 3*h**3 + 27*h**2/2 + 27*h - 10. Suppose y(m) = 0. What is m?
-3
Let k = 5/126 - -8/63. Factor 1/6*a - 1/6 + k*a**2 - 1/6*a**3.
-(a - 1)**2*(a + 1)/6
Find l such that -34/9*l**3 + 68/9*l**2 - 56/9*l + 2/3*l**4 + 16/9 = 0.
2/3, 1, 2
Let o(c) be the third derivative of -1/330*c**5 + 0*c + 1/33*c**3 + 0*c**4 + 2*c**2 + 0. Factor o(m).
-2*(m - 1)*(m + 1)/11
Let a = 18 - 23. Let k be a/10 - (-2)/4. Suppose -1/4*c**2 + 1/4*c**4 + 1/4*c**3 - 1/4*c + k = 0. What is c?
-1, 0, 1
Let p(u) be the first derivative of 9 + 1/12*u**4 + 1/15*u**5 - 1/18*u**6 - 1/9*u**3 + 0*u + 0*u**2. Suppose p(z) = 0. Calculate z.
-1, 0, 1
Let o(u) be the second derivative of -u**6/360 + u**5/75 + u**4/30 - 3*u**3/2 - 5*u. Let x(n) be the second derivative of o(n). Factor x(d).
-(d - 2)*(5*d + 2)/5
Let o(p) = p**2 + p. Let v(f) = 2*f**2 - 18*f - 6. Let h(t) = 3*o(t) + 3*v(t). Factor h(n).
3*(n - 6)*(3*n + 1)
Let r(z) be the first derivative of 2*z**3/45 - 8*z**2/15 + 32*z/15 + 9. Suppose r(u) = 0. What is u?
4
Let k(o) be the first derivative of o**6/21 + 2*o**5/35 - o**4/14 - 2*o**3/21 + 14. Find b, given that k(b) = 0.
-1, 0, 1
Let y = 134 - 400/3. Let c(h) be the first derivative of -8/3*h**2 + 3/2*h**4 - 4 - y*h**3 + 8/3*h. Factor c(l).
2*(l + 1)*(3*l - 2)**2/3
Let p(z) be the first derivative of -z**3/5 + 3*z**2/5 - 69. Solve p(r) = 0.
0, 2
Suppose x + 9 + 15 = 0. Let q be (-23)/(-4) + (-6)/x. Factor -l**2 - 5*l**3 + 3*l**2 - l**4 - q*l**4.
-l**2*(l + 1)*(7*l - 2)
Let h(b) = b**3 - b**2 + 1. Let o be h(9). What is c in -282*c**3 + o*c**4 - 64*c**2 - 49*c**3 - 320*c**5 - 8 + 60*c + 23*c**4 - 9*c**3 = 0?
-2/5, 1/4, 1
Let m(x) be the second derivative of x**4/12 + 2*x**3/5 + 2*x**2/5 - 7*x. Find a such that m(a) = 0.
-2, -2/5
Let g(i) be the second derivative of i**8/33600 - i**7/6300 + i**6/3600 + 3*i**4/4 + 2*i. Let k(h) be the third derivative of g(h). Factor k(a).
a*(a - 1)**2/5
Let k(h) be the first derivative of -2*h**3/57 - 2*h**2/19 + 6*h/19 - 9. Find b, given that k(b) = 0.
-3, 1
Let c(q) = q**3 - 9*q**2 + 9*q + 38. Let g be c(7). Let k(l) be the first derivative of 4/3*l**g - 1/3*l**6 + 3*l**2 - l**4 + 1 + 2*l - 6/5*l**5. Factor k(j).
-2*(j - 1)*(j + 1)**4
Suppose -3*v + 0*v**4 + 5*v**3 - 3*v**4 + 3*v**2 - 2*v**3 = 0. Calculate v.
-1, 0, 1
Let q be 1/(-2)*(-6 + 8). Let c be q/(0 - 2/8). Factor -4*x**2 + 0*x**3 + 2*x - c*x - 2*x**3.
-2*x*(x + 1)**2
Let x be 4*1*3/6. Let g be ((-3)/27)/(4/(-12)). Suppose -1/3*r**3 - r - r**x - g = 0. Calculate r.
-1
Let o(c) be the first derivative of 4/5*c**5 + 5/3*c**2 - 1 - 11/6*c**4 + 4/9*c**3 - 4/3*c. Determine b, given that o(b) = 0.
-2/3, 1/2, 1
Let k(b) = b. Let u(w) be the second derivative of w**4/12 + 5*w**3/6 - 4*w. Let a(q) = -4*k(q) + u(q). Suppose a(y) = 0. Calculate y.
-1, 0
Let v(w) be the first derivative of -3/2*w - 27/2*w**3 + 81/8*w**4 + 27/4*w**2 - 10. Solve v(j) = 0.
1/3
Let v be (-1)/(-1)*(14 - 7). Let h(j) be the third derivative of 0*j**6 - j**2 + 0 + 1/50*j**5 + 1/30*j**4 + 0*j + 0*j**3 - 1/525*j**v. What is q in h(q) = 0?
-1, 0, 2
Let c(w) be the first derivative of -3*w**4/4 + 3*w**3 - 12*w - 23. Factor c(d).
-3*(d - 2)**2*(d + 1)
Let h = -54 - -56. Factor 2/3*m**h + 4/3*m + 2/3.
2*(m + 1)**2/3
Let n be (-54)/(-10) + (-4)/10. Let t(b) = b - 2. Let u be t(1). Let w(m) = -1. Let f(c) = c**3 - c - 5. Let p(s) = n*w(s) + u*f(s). Factor p(z).
-z*(z - 1)*(z + 1)
Suppose 3*h = -3*z + 3, -h + 5*h + z - 7 = 0. Factor 0*u**2 + u**3 - u**2 + u**h - u**2.
u**2*(u - 1)
Let j(m) = -m**2 - 5*m + 3. Let u(t) = t**3 - 5. Let v be u(0). Let o be j(v). Factor 3*s**2 - 4 + o*s**2 - 4*s + 6*s.
2*(s + 1)*(3*s - 2)
Let b(j) be the third derivative of 0 + 1/6*j**3 + 0*j + 1/12*j**4 + 6*j**2 + 1/60*j**5. Find i, given that b(i) = 0.
-1
Let c(m) = 95*m**3 - 145*m**2 + 155*m - 35. Let j(n) = -8*n**3 + 12*n**2 - 13*n + 3. Let s(q) = -3*c(q) - 35*j(q). Factor s(v).
-5*v*(v - 2)*(v - 1)
Let m(i) = i**3 - 9*i**2 + 15*i - 4. Let f be m(7). Let s(g) be the first derivative of -3 + 2/3*g**f + 0*g - g**2. Factor s(u).
2*u*(u - 1)
Let w(b) be the third derivative of b**5/30 + b**4/8 + b**3/6 - 3*b**2. Let p(m) = -4*m**2 - 7*m - 3. Let a(q) = -3*p(q) - 7*w(q). Factor a(i).
-2*(i - 1)*(i + 1)
Suppose 1/3*g + 1/3*g**2 + 0 = 0. What is g?
-1, 0
Let f be (-1)/3*-9*(-4)/(-24). What is w in -1/2*w**2 + 1/4*w**4 + f*w**3 - 1/4*w - 1/4*w**5 + 1/4 = 0?
-1, 1
Let m = -3 + 6. Let l(k) = -11*k - 2*k**3 + m*k**3 + 24*k**2 + 17 + 41*k. Let a(o) = 12*o**2 + 15*o + 9. Let r(d) = 5*a(d) - 3*l(d). Factor r(n).
-3*(n + 1)**2*(n + 2)
Let y be 2 - 3 - 86/(-78). Let a = y - -22/39. Let n**4 + n - a*n**3 - 1/3*n**5 - 1/3 - 2/3*n**2 = 0. What is n?
-1, 1
Suppose -2*s + s = 0. Let l = -2 - -2. Suppose -2 + l + s + 16*r - 32*r**2 = 0. What is r?
1/4
Let p(t) = -t**3 + 2*t**2 + 3*t + 2. Let i be p(3). Factor -1 + i*o**2 - 3*o**2 - 2*o + 0*o**2.
-(o + 1)**2
Let v(x) = -75*x**5 - 290*x**4 - 422*x**3 - 291*x**2 - 96*x - 7. Let l(j) = j**4 + j**3 - 1. Let p(h) = -5*l(h) - v(h). Factor p(o).
3*(o + 1)**3*(5*o + 2)**2
Let j be 2/(-6)*-3*2. Suppose 0 = j*x - 5*x + 12. Factor -18*w - 10*w**2 - 4 + 14*w**3 - x*w**3 + 14*w**4 + 8*w**3.
2*(w - 1)*(w + 1)**2*(7*w + 2)
Let p(l) = 3*l - l**3 - 2*l - 2*l. Let i be p(-1). Factor j**3 - j**5 - j**i + 3*j**2 - j**2 - j**4.
-j**2*(j - 1)*(j + 1)**2
Find k such that 0*k**2 + 0 + 1/4*k - 1/4*k**3 = 0.
-1, 0, 1
Let o be 2/4 - (-231)/154. Factor 12*u - 8*u**o - 9/2.
-(4*u - 3)**2/2
Let j(t) be the first derivative of 3*t**4/8 + t**3/2 - 15*t**2/4 + 9*t/2 + 24. Factor j(y).
3*(y - 1)**2*(y + 3)/2
Let x be ((-80)/(-25))/(-4) + 1. Determine i so that -3/5*i**2 + 2/5*i + x = 0.
-1/3, 1
Let f be (-4)/(-34) - (-1302)/1071. Let l = 2 + 2. Solve -4/3*r**2 - 2/3 + 2*r - f*r**3 + 2*r**l - 2/3*r**5 = 0.
-1, 1
Let r(k) = 2*k - 14. Let n be r(9). Let -y**n + 0*y + 4/3*y**3 - 1/3*y**2 + 0 = 0. What is y?
0, 1/3, 1
Let x(t) be the third derivative of 0*t**3 + 0 + 0*t + 1/105*t**7 - 7*t**2 + 1/30*t**5 - 1/30*t**6 + 0*t**4. Factor x(u).
2*u**2*(u - 1)**2
Let i(y) = y**3 - 6*y**2 + 2. Let f be i(6). Factor -6*b**2 + f - 3*b**3 - 3*b**5 + 8*b**4 - b**3 + 7*b - 4.
-(b - 1)**3*(b + 1)*(3*b - 2)
Let b(g) be the third derivative of -1/12*g**5 + 1/40*g**6 + 0*g - 2*g**2 + 0 + 1/12*g**4 + 0*g**3. Suppose b(y) = 0. Calculate y.
0, 2/3, 1
Suppose -g = -1 - 5. Let a = 6 - g. Suppose -1/5 + a*x**2 - 2/5*x**3 + 1/5*x**4 + 2/5*x = 0. What is x?
-1, 1
Let a(x) be the third derivative of -x**7/2520 + x**6/180 - x**5/30 - x**4/12 - 3*x**2. Let y(t) be the second derivative of a(t). Find l such that y(l) = 0.
2
Let v(k) be the third derivative of -1/2*k**3 - 1/8*k**4 + 1/20*k**5 + 1/40*k**6 + 2*k**2 + 0 + 0*k. Factor v(s).
3*(s - 1)*(s + 1)**2
Suppose 4*n = 4 + 12. Suppose 5*m + 4*z - 8 - 2 = 0, 0 = -n*m + 3*z + 8. Factor 