
Let v = 124 - 1239/10. Let m(s) be the second derivative of 0 + 1/5*s**5 - 1/6*s**4 - 1/2*s**2 - 2/3*s**3 + s + v*s**6. Determine k, given that m(k) = 0.
-1, -1/3, 1
Let u(t) be the second derivative of 7*t - 1/3*t**2 + 1/36*t**4 + 1/18*t**3 + 0. Solve u(h) = 0 for h.
-2, 1
Factor 0 - k**4 - 39*k**3 + 1 + 2*k + 20*k**3 + 17*k**3.
-(k - 1)*(k + 1)**3
Let y = -8 + 9. Let t be 0 + y + (4 - 3). Let 4*p**3 + 2*p**3 - 9*p**4 + 3 - 9*p + 3*p**5 + 6*p**2 + 0*p**t = 0. What is p?
-1, 1
Let o be (-357)/(-30)*(0 + 16). Let s = 191 - o. Factor 0 + 3/5*x**2 - 1/5*x + 1/5*x**4 - s*x**3.
x*(x - 1)**3/5
Let q(f) = -4*f + 20. Let x(y) = 9*y - 41. Let l(u) = 13*q(u) + 6*x(u). Let d be l(-6). What is t in 7/3*t**3 - 5/3*t**5 + t**4 - t**d + 0 - 2/3*t = 0?
-1, -2/5, 0, 1
Let c = 569/95 + -110/19. Suppose -1/5 - c*r**3 + 1/5*r**2 + 1/5*r = 0. What is r?
-1, 1
Let j = 27/17 + -3709/34. Let v = j - -110. Solve 5/2*p**3 - v*p**5 + p**4 + 0*p + 0 - p**2 = 0.
-1, 0, 2/5, 1
Let s be 6/(-27) + (-47)/(-9). Factor 4*u**5 + 2*u - 2*u**s - 4*u**3 - 2*u**5 + 2*u**5.
2*u*(u - 1)**2*(u + 1)**2
Let x(a) be the third derivative of a**6/45 - a**4/12 - a**3/9 - 15*a**2. Find j, given that x(j) = 0.
-1/2, 1
Let n = -153 - -479/3. Let h = 55 + -53. Solve 10/3*o**4 + 10/3*o + n*o**h + 2/3 + 2/3*o**5 + 20/3*o**3 = 0.
-1
Let p be (3 - 0)*(-4)/(-2). Suppose p*r + w - 6 = r, 5*r - 3 = 2*w. Factor -n**4 - 2*n**3 + 2*n + r + 0*n**2 + 0*n**2.
-(n - 1)*(n + 1)**3
Let b be 3/2*(-32)/(-30). Suppose 187 = 8*m + 171. Factor -b + 8/5*o - 2/5*o**m.
-2*(o - 2)**2/5
Let l(k) be the first derivative of 3*k**5/35 + 3*k**4/28 - 3. Determine y, given that l(y) = 0.
-1, 0
Suppose 3*z + 2 = 3*w - w, -2 = -5*z + 2*w. Let v = 3302/5 + -660. Factor 0*t + 2/5*t**z - v.
2*(t - 1)*(t + 1)/5
Factor -6/11 + 2/11*t**3 + 14/11*t - 10/11*t**2.
2*(t - 3)*(t - 1)**2/11
Let f(h) = -h**3 - h**2 + 4*h - 6. Let a be f(-3). Factor -i**2 + a + 1/3*i.
-i*(3*i - 1)/3
Let g be 77/(-198) - (-10)/12. Factor g*a + 0 + 2*a**4 + 40/9*a**3 + 26/9*a**2.
2*a*(a + 1)**2*(9*a + 2)/9
Find t such that 8*t**5 - 21*t**5 + 4*t**5 + 6*t**5 + 9*t**4 - 6*t**3 = 0.
0, 1, 2
Let p(j) be the third derivative of 0*j - 7/36*j**4 + 0 + 2/9*j**3 + 1/10*j**5 - 1/36*j**6 + 4*j**2 + 1/315*j**7. What is s in p(s) = 0?
1, 2
Let p(h) = -4*h**3 + 5*h**2 - h - 3. Let t(j) = 36*j**3 - 44*j**2 + 8*j + 28. Let q(a) = -28*p(a) - 3*t(a). Factor q(u).
4*u*(u - 1)**2
Let n(y) be the third derivative of y**7/4620 + y**6/660 - y**4/33 + y**3/6 + 4*y**2. Let u(p) be the first derivative of n(p). Determine h so that u(h) = 0.
-2, 1
Let k(x) = x**2 - 8*x + 16. Let s be k(4). Determine b, given that 4/7*b + 10/7*b**3 - 18/7*b**2 + 18/7*b**4 - 2*b**5 + s = 0.
-1, 0, 2/7, 1
Factor 48*t**2 + 47*t**2 + 10*t - 100*t**2 - 5*t**3.
-5*t*(t - 1)*(t + 2)
Let z = 33 + -24. Let 6*g**3 + 0*g**3 + z*g**2 + 6*g - 2*g**3 - g**3 = 0. Calculate g.
-2, -1, 0
Let l = -36 - -109/3. Let 0*z**2 + 4/3*z + l*z**4 + 0 - z**3 = 0. Calculate z.
-1, 0, 2
Let b(n) = 10*n**4 + 30*n**3 + 30*n**2 - 15*n - 35. Let s(i) = 11*i**4 + 31*i**3 + 30*i**2 - 14*i - 34. Let j(r) = 6*b(r) - 5*s(r). Let j(q) = 0. What is q?
-2, 1
Suppose -5*r - v + 21 = -2*v, -3*r = -4*v + 1. Let -5*d**5 + 0*d**r + 0*d**5 + 3*d**5 = 0. Calculate d.
0
Let x(n) be the second derivative of -3*n**5/20 + 3*n**4/4 + 8*n. Solve x(p) = 0.
0, 3
Let u be 0/1*1/(-2). Let d(c) be the first derivative of 4/3*c**3 + c**2 + u*c + 1/2*c**4 - 1. Let d(m) = 0. Calculate m.
-1, 0
Let x(a) be the third derivative of -1/280*a**7 + 0*a**3 + 0 + 0*a**4 + 1/80*a**6 - 6*a**2 + 0*a - 1/80*a**5. Solve x(o) = 0.
0, 1
Let o(w) = -w**3 + w**2 - w + 3. Let a be o(0). Suppose -1 + 19 = a*n. Factor h**2 - 3*h**5 - h**4 - 7*h**3 + 4*h**5 + n*h**3.
h**2*(h - 1)**2*(h + 1)
Suppose 0 + 0*c - 6/13*c**3 - 4/13*c**2 - 2/13*c**4 = 0. What is c?
-2, -1, 0
Suppose -4 = -3*l + 2*l. Suppose w + 3 - l + 1 - w**2 = 0. What is w?
0, 1
Let k(y) be the third derivative of y**8/1512 - 4*y**7/945 + y**6/180 + 2*y**5/135 - y**4/27 + y**2. Solve k(n) = 0 for n.
-1, 0, 1, 2
Let f(z) be the second derivative of -z**4/3 - 12*z**3 - 162*z**2 - 21*z. Factor f(p).
-4*(p + 9)**2
Suppose d - 3 = -1. Solve 4/3*y + 1/3*y**d + 1 = 0.
-3, -1
Let x = 49 - 195/4. Suppose q + x*q**2 + 1 = 0. What is q?
-2
Let q(s) = -2*s**3 + 7*s**3 - 4*s**2 + 0*s + 4*s**4 - 5*s**2 - 13*s + 13. Let k(m) = -m**4 - m**3 + 2*m**2 + 3*m - 3. Let j(i) = 26*k(i) + 6*q(i). Factor j(u).
-2*u**2*(u - 1)**2
Let o be 273/6 - 2/4. Let h be (o/70)/((-6)/(-8)). Suppose 6/7*c**2 - 2/7*c**3 - h*c + 2/7 = 0. What is c?
1
Let b(l) be the third derivative of -l**7/525 + l**6/100 - l**5/75 + 14*l**2. Let b(x) = 0. Calculate x.
0, 1, 2
Suppose 2 = -3*d - 4*q, 0 = 5*d - 5*q - 18 - 2. Factor -19*l**d + 0*l + 16*l**2 + 3*l.
-3*l*(l - 1)
What is g in -1/3*g**3 + g**2 - g**4 - 1/3*g**5 + 0 + 2/3*g = 0?
-2, -1, 0, 1
Let u(y) = y**3 - y**2 - y + 1. Let s(k) = -24*k**3 - 11*k**2 + 9*k - 4. Let j(c) = -s(c) - 4*u(c). Factor j(o).
5*o*(o + 1)*(4*o - 1)
Let r(j) be the first derivative of j**6/6 + 2*j**5/5 - 2*j**3/3 - j**2/2 - 15. Factor r(u).
u*(u - 1)*(u + 1)**3
What is z in -3/2*z + 3/2*z**3 - 3/2 + 3/2*z**2 = 0?
-1, 1
Let l(o) be the first derivative of -o**6/600 + o**4/40 + o**3/15 - o**2 + 3. Let w(z) be the second derivative of l(z). Solve w(k) = 0.
-1, 2
Let b be (-1 - 3/(-1)) + 0. Factor 3*y**b + 21*y - 5*y**2 - 19*y.
-2*y*(y - 1)
Let j(k) be the third derivative of k**6/360 - k**5/180 - 8*k**2. What is w in j(w) = 0?
0, 1
Let v = -245/18 + 124/9. Find y such that y - v*y**2 - 3/2 = 0.
3
Let p(w) be the second derivative of w**9/378 - w**8/1680 - w**7/315 - w**4/4 + 4*w. Let k(u) be the third derivative of p(u). What is d in k(d) = 0?
-2/5, 0, 1/2
Let t = -1 + 5. Let 0*g**2 - 2*g**2 - 2*g + t*g**2 + 0*g = 0. What is g?
0, 1
Factor -75*m**2 + 51*m**2 - 18*m**4 - 19*m**3 - 3*m**5 - 9*m**3 - 8*m**3.
-3*m**2*(m + 2)**3
Let s = -31 - -31. Suppose -5*n + 40 - 15 = s. Find v such that 0*v + 1/3*v**n + 0 + 1/3*v**2 + v**3 + v**4 = 0.
-1, 0
Let b be -3*1/(-2)*116/87. Determine t so that 2/3*t + 0 - 1/3*t**b - 1/3*t**3 = 0.
-2, 0, 1
Factor 6/7*c + 6/7*c**2 + 2/7 + 2/7*c**3.
2*(c + 1)**3/7
Let i(q) = -q**3 + 5*q**2 + 6*q + 2. Let n be i(6). Let c = -148/11 + 752/33. Let -20/3*g**4 + 29/3*g**3 - 2/3 - c*g**5 - 1/3*g + 22/3*g**n = 0. What is g?
-1, -1/2, 2/7, 1
Let d(p) = 7*p**3 + p**2 - p - 7. Let c(o) = 6*o**3 + 2*o**2 - 2*o - 6. Let w(m) = -3*c(m) + 2*d(m). Factor w(l).
-4*(l - 1)*(l + 1)**2
Let f = -455 + 457. Factor 0 - 4/5*a + 2/5*a**f.
2*a*(a - 2)/5
Determine a, given that -10*a**4 + 3*a**2 - 9*a - a**4 + 9*a**3 + 8*a**4 + 0*a**2 = 0.
-1, 0, 1, 3
Let w(t) be the second derivative of -t**4/3 - 2*t**3/3 + 4*t**2 + 2*t. Let w(s) = 0. Calculate s.
-2, 1
Let u(k) be the second derivative of -k**5/20 + k**4/6 + 5*k**3/6 - 3*k**2 - 16*k. Determine b so that u(b) = 0.
-2, 1, 3
Let u be ((-3 - -8)*4/10)/6. Suppose 1/6*h + u - 1/6*h**2 = 0. Calculate h.
-1, 2
Let v(j) be the third derivative of -2*j**7/525 + j**6/50 - 2*j**5/75 - 29*j**2. Factor v(o).
-4*o**2*(o - 2)*(o - 1)/5
Let k = -2/189 - -164/189. Factor -2/7 - k*y**2 - 6/7*y - 2/7*y**3.
-2*(y + 1)**3/7
Let h(r) be the third derivative of 0*r**3 - 1/60*r**4 + 0*r + r**2 + 0 + 1/300*r**6 + 0*r**5. Let h(p) = 0. Calculate p.
-1, 0, 1
Let o(r) be the first derivative of -2*r**3/27 + 2*r**2/9 + 2*r/3 + 5. Suppose o(a) = 0. What is a?
-1, 3
Factor 2/5*n**2 + 0 + 1/5*n.
n*(2*n + 1)/5
Let s(y) be the second derivative of 1/5*y**5 + 1/30*y**6 + 3*y + 1/2*y**2 + 2/3*y**3 + 0 + 1/2*y**4. Determine n so that s(n) = 0.
-1
Let x(u) = -8*u**4 + 4*u**3 + 2*u**2 - 10*u + 6. Let o(z) = z**4 + z - 1. Let p(s) = -6*o(s) - x(s). Factor p(k).
2*k*(k - 2)*(k - 1)*(k + 1)
Let g(c) = 89*c**5 + 42*c**4 - 57*c**3 + 8*c**2 + 9. Let h(n) = -n**5 - n**3 + 1. Let f(v) = -2*g(v) + 18*h(v). Factor f(i).
-4*i**2*(i + 1)*(7*i - 2)**2
Let w(x) be the third derivative of -x**5/240 - 5*x**4/96 - 46*x**2. Factor w(d).
-d*(d + 5)/4
Factor 3/5*l**2 + 18/5*l + 3.
3*(l + 1)*(l + 5)/5
Factor -2*k**4 + 12*k**2 + 17*k**3 + 5*k + k**3 - 2*k + 14*k**4 + 3*k**5.
3*k*(k + 1)**4
Suppose -7 = 5*f - 22. Factor -f + 4*d + 1 + 4 + 2*d**2.
2*(d + 1)**2
Let u(j) be the second derivative of 5*j - 1/70*j**7 + 0*j**2 - 27/100*j**5 + 1/10*j**6 + 0 - 1/5