*f(t). Suppose a(u) = 0. What is u?
0, 1
Let z(i) be the first derivative of i**5/10 - 5*i**3/6 + 2*i + 4. Find v such that z(v) = 0.
-2, -1, 1, 2
Let p be (-1032)/(-32)*3/9. Let m = 11 - p. Determine f so that m*f - 1/4*f**3 - 1/4*f**2 + 1/4 = 0.
-1, 1
Suppose p + 2*p**2 - 7*p - 40 + 40 = 0. Calculate p.
0, 3
Let z(g) = -g**3 + 6*g**2 + 8*g - 7. Let y = -6 + 13. Let h be z(y). What is m in 20/9*m**5 + 2*m**4 - 16/9*m**3 + h - 2*m**2 - 4/9*m = 0?
-1, -1/2, -2/5, 0, 1
Let q(r) = 37*r - 32. Let b be q(1). Determine n so that 26*n**2 - 33*n**3 + 49/2*n**b - 77/2*n**4 - 4*n + 0 = 0.
-1, 0, 2/7, 2
Let p(z) be the first derivative of -z**6/1800 + z**5/600 - 4*z**3/3 - 4. Let y(d) be the third derivative of p(d). Factor y(j).
-j*(j - 1)/5
Factor 1/2*y**2 + y + 1/2.
(y + 1)**2/2
Let o(f) = -f**2. Let s(q) = q**3 + 4*q. Let k(g) = -5*o(g) + s(g). Factor k(u).
u*(u + 1)*(u + 4)
Suppose -g + 6 = g. Factor -1 - r**2 - 5*r + 0 + g*r.
-(r + 1)**2
Suppose t - 6 = -2. Suppose -d + 11 = t*o, 5*o = -0*o - 5*d + 25. Suppose 1/2*p**4 + 2*p**3 + 3*p**o + 2*p + 1/2 = 0. What is p?
-1
Suppose 0 = -5*l - 1 + 11. Let 0*s**3 - 32 - 64*s - 8*s**4 - 16*s**3 - 48*s**l + 6*s**4 = 0. Calculate s.
-2
Let x(r) be the second derivative of r**8/1680 + r**7/210 + r**6/120 - r**5/30 - r**4/6 + r**3/6 + 3*r. Let m(w) be the second derivative of x(w). Factor m(i).
(i - 1)*(i + 1)*(i + 2)**2
Let c = -135/7 + 703/35. Solve -2/5*t**2 - 2/5 - c*t = 0 for t.
-1
Let p(d) be the second derivative of -7*d**7/12 + 7*d**6/6 + 101*d**5/40 - 31*d**4/12 - 13*d**3/3 - 2*d**2 + 14*d. Suppose p(y) = 0. Calculate y.
-1, -2/7, 1, 2
Suppose 0 = -5*o + h + 17, 2*h - 7 = o + 7*h. Suppose -o*x + 15 = 2*x. Let 1/4*f + f**2 + 1/2*f**x + 0 - 3/4*f**5 - f**4 = 0. What is f?
-1, -1/3, 0, 1
Solve -6*c**2 - 4*c + 3*c**2 + 2*c**2 - c**2 = 0.
-2, 0
Let c be ((-1)/((-21)/(-6)))/((-3)/7). Let n(m) be the third derivative of c*m**4 - 1/12*m**5 + m**2 - 2/3*m**3 + 0*m - 7/120*m**6 + 0. Factor n(x).
-(x - 1)*(x + 2)*(7*x - 2)
Let k be (-3)/(-5)*(5 - 0). Let o = 13/10 + 1/5. Factor 0 - 15/2*y**2 + 6*y**3 - o*y**4 + k*y.
-3*y*(y - 2)*(y - 1)**2/2
Let y be 77/30 - 23/(-230). Factor -4/3 - y*w**2 - 10/3*w - 2/3*w**3.
-2*(w + 1)**2*(w + 2)/3
Suppose 0 = 4*a + 1 + 3. Let x = a - -2. Factor 3*z**2 - 4*z**3 + 2*z - 4*z**2 + x + 0*z + 2*z**3.
-(z - 1)*(z + 1)*(2*z + 1)
Let p(t) be the second derivative of 2*t**6/15 - 2*t**4/3 + 2*t**2 + 26*t. Factor p(g).
4*(g - 1)**2*(g + 1)**2
Let c(a) be the first derivative of 2/3*a**3 + 0*a**4 + 2 + 1/1080*a**6 + 0*a + 0*a**2 + 1/180*a**5. Let t(h) be the third derivative of c(h). Solve t(s) = 0.
-2, 0
Suppose -5*o - 3 + 13 = 0. Let a(x) be the first derivative of 2 + 3/2*x**o + 3/2*x**3 - 3/2*x. Factor a(k).
3*(k + 1)*(3*k - 1)/2
Let c(s) = -s**2 - 1. Let r(y) = 4*y**2 + 2*y + 2. Let x(n) = -2*c(n) - r(n). What is d in x(d) = 0?
-1, 0
Let g(l) be the first derivative of 0*l**3 - 1/150*l**6 + 0*l**5 + 0*l**2 - 3 + 2*l + 1/60*l**4. Let h(c) be the first derivative of g(c). Solve h(t) = 0 for t.
-1, 0, 1
Let s(a) = 31*a**2 + 11*a - 3. Let u(r) = -30*r**2 - 10*r + 2. Let n(h) = 2*s(h) + 3*u(h). Let n(o) = 0. Calculate o.
-2/7, 0
Suppose 3*n - 2*f = 76, 0*n - 2*n - 4*f = -40. Solve p**3 - p + n - 26 - p**2 + 3*p**2 = 0 for p.
-2, -1, 1
Suppose -2*y - 40 = -50. Let t(c) be the third derivative of 5*c**2 + 0 + 1/24*c**4 + 1/60*c**6 + 0*c + 1/12*c**y - 1/3*c**3. Solve t(k) = 0.
-2, -1, 1/2
Let q(d) be the first derivative of 4*d**3/3 + 4*d**2 - 12*d - 9. Determine t so that q(t) = 0.
-3, 1
Let f be ((-1 - -1)/(-4))/1. Let g(k) be the second derivative of 0*k**4 + 0*k**2 + f*k**3 + 0 + 1/80*k**5 + 1/120*k**6 + 2*k. Factor g(p).
p**3*(p + 1)/4
Let z = 3 - 1. Suppose -m**2 + 9*m**z + 5*m + 1 - 4*m**2 = 0. Calculate m.
-1, -1/4
Factor -1/2*h**4 + 3*h**3 - 2 + 6*h - 13/2*h**2.
-(h - 2)**2*(h - 1)**2/2
Let y(q) be the third derivative of q**5/120 + q**4/16 + q**3/6 - 14*q**2. Factor y(x).
(x + 1)*(x + 2)/2
Let u(h) be the second derivative of 3/10*h**4 + 3*h + 0*h**2 + 1/15*h**6 - 2/15*h**3 + 0 - 6/25*h**5. Find k such that u(k) = 0.
0, 2/5, 1
Suppose 0 = 3*t - 2*t - 2. Factor -4*j - 5*j**3 + 6*j**t + 8*j**3 - 5*j**3.
-2*j*(j - 2)*(j - 1)
Suppose -v - 5 = -2*v. Suppose -5*w = -v*z, w = z - 3*z + 9. Factor -2*x**3 - 1 - 4*x + w - 4 + 1 - 5*x**2.
-(x + 1)**2*(2*x + 1)
Let a(w) be the third derivative of w**5/24 + 3*w**4/16 - w**3/6 + 19*w**2. Suppose a(o) = 0. Calculate o.
-2, 1/5
Let g(k) = -4*k**3 + k. Let w be g(-1). Let b = 327/196 + 4/49. Factor -b*z**w + 5/4*z**2 + 1/2*z + 0.
-z*(z - 1)*(7*z + 2)/4
Let f(o) be the third derivative of 0 - o**2 + 1/1050*o**7 + 0*o + 0*o**3 - 1/300*o**6 + 1/300*o**5 + 0*o**4. Factor f(t).
t**2*(t - 1)**2/5
Suppose -q + 220 = 5*m, 0 = -2*m + m - q + 40. Suppose -j + m = 2*j. Let 15*r - 2*r**2 + r**3 - j*r = 0. Calculate r.
0, 2
Let f(b) be the first derivative of -2*b**5/5 - 9*b**4/2 - 16*b**3 - 16*b**2 + 10. Let f(g) = 0. What is g?
-4, -1, 0
Let t = -67 - -70. Let g(a) be the second derivative of -a + 0 - 1/6*a**4 - 1/20*a**5 + 0*a**2 - 1/6*a**t. Factor g(n).
-n*(n + 1)**2
Solve -4/7 + 2/7*h**3 - 8/7*h**2 + 10/7*h = 0 for h.
1, 2
Let u(y) be the second derivative of 2/7*y**2 + 0 - 5*y + 1/21*y**3 - 1/70*y**5 - 1/21*y**4. Factor u(o).
-2*(o - 1)*(o + 1)*(o + 2)/7
Let b(a) = a**2 + a - 12. Let o be b(-13). Determine k so that o*k**4 + 60*k**3 - 285*k**5 - 9*k**2 + 3*k - 6*k + 93*k**5 = 0.
-1/4, 0, 1/4, 1
Let l(h) be the third derivative of 41*h**5/240 + 43*h**4/96 + h**3/12 + 30*h**2 + 2. Factor l(b).
(b + 1)*(41*b + 2)/4
Let q = 58 - 58. Let o(y) be the second derivative of 1/4*y**2 + 1/6*y**3 + 3*y + 0 + q*y**4 - 1/20*y**5 - 1/60*y**6. Factor o(f).
-(f - 1)*(f + 1)**3/2
Let m(t) be the third derivative of -t**7/120 - t**6/40 - t**5/80 + t**4/48 + 15*t**2. Suppose m(o) = 0. Calculate o.
-1, 0, 2/7
Factor 2/15*o**4 + 0 + 0*o + 2/3*o**3 + 0*o**2.
2*o**3*(o + 5)/15
Let s(a) = a**5 - 3*a**4 - 3*a**3 - a**2 + 2*a + 2. Let v(f) = -f**5 + 4*f**4 + 3*f**3 + 2*f**2 - 2*f - 3. Let r(h) = 6*s(h) + 4*v(h). Factor r(n).
2*n*(n - 2)*(n - 1)*(n + 1)**2
Factor -5*d**2 - 4*d + 2*d**3 - 2*d**3 + 0*d**3 + 4 + 3*d**3.
(d - 2)*(d + 1)*(3*d - 2)
Suppose 6*p + 3*s + 6 = 7*p, -2*p + 3*s = -9. Find q such that 0*q - 3/4*q**p + 0 - 1/4*q**2 - 1/2*q**4 = 0.
-1, -1/2, 0
Let x be (-2)/28*(-60)/15. Factor 4/7*b**2 + 0 - 2/7*b - x*b**3.
-2*b*(b - 1)**2/7
Let l(d) = -72*d**4 + 82*d**3 + 50*d**2 - 70*d - 2. Let c(k) = 29*k**4 - 33*k**3 - 20*k**2 + 28*k + 1. Let p(j) = 12*c(j) + 5*l(j). Find y such that p(y) = 0.
-1, 1/6, 1
Factor -2/3 - 15*n**3 - 16*n**2 - 17/3*n.
-(3*n + 1)**2*(5*n + 2)/3
Let y = 4 + -4. Let l(h) be the third derivative of -1/45*h**5 - 2*h**2 + 1/180*h**6 + y*h + 0 + 1/36*h**4 + 0*h**3. Factor l(f).
2*f*(f - 1)**2/3
Factor -12/5*s**2 - 9/5*s + 0 - 3/5*s**3.
-3*s*(s + 1)*(s + 3)/5
Suppose -15 = 60*t - 63*t. Let h(p) be the second derivative of 0*p**2 + 0 - 2*p - 1/70*p**t - 1/42*p**4 + 0*p**3. Find s such that h(s) = 0.
-1, 0
Let d(w) be the first derivative of -w**3/3 + 5*w**2/2 + 6*w - 4. Let g be d(6). Factor 1/2*k**4 + 1/2*k**3 + g - 1/2*k**2 - 1/2*k.
k*(k - 1)*(k + 1)**2/2
Let z be (2 + 18/(-4))*(-260)/325. Find l, given that 0 - 2/13*l**5 - 6/13*l**4 + 6/13*l**z + 4/13*l - 2/13*l**3 = 0.
-2, -1, 0, 1
Let u be (-24)/2*2/(-6). Let t be (-15)/(-7) - u/4. Factor 2/7*r**2 + 8/7 - t*r.
2*(r - 2)**2/7
Let i(z) be the first derivative of z**5/5 - z**4/2 - z**3/3 + z**2 + 5. Factor i(n).
n*(n - 2)*(n - 1)*(n + 1)
Let q = -19/2 - -10. Factor -3/2*x + 2 - q*x**2.
-(x - 1)*(x + 4)/2
Let o = -73 + 78. Let x(d) be the third derivative of 1/21*d**3 + d**2 + 0*d + 0 + 1/420*d**6 + 1/70*d**o + 1/28*d**4. Find y such that x(y) = 0.
-1
Let b(l) be the second derivative of -l**3 + 7/2*l**2 - 2*l - 2/3*l**4 + 0. Let s(g) = g**2 + g - 1. Let d(n) = -3*b(n) - 21*s(n). Suppose d(i) = 0. What is i?
0, 1
Suppose 9*n - 13 = 5. Let j(m) be the first derivative of -1/2*m**n - 1/6*m**3 - 1 - 1/2*m. Factor j(o).
-(o + 1)**2/2
Let x(t) = 3*t**2 - 37*t - 40. Let y(z) = 8*z**2 - 92*z - 100. Let w(u) = 12*x(u) - 5*y(u). Suppose w(p) = 0. What is p?
-1, 5
Suppose -14*s = -16*s + 4. Find k, given that -5/3*k - 1/3 - 4/3*k**s = 0.
-1, -1/4
Let t = -1/1485 + 40097/2970. Suppose t*l + 1/2*l**3 + 27/2 + 9/2*l**