. Solve 1/2*q - 1/6*q**s + 1/3 - 1/2*q**3 - 1/6*q**2 = 0.
-2, -1, 1
Let t(b) be the first derivative of -6/5*b**2 - 3/20*b**4 + 4/5*b**3 + 0*b + 28. Factor t(k).
-3*k*(k - 2)**2/5
Let m(n) be the third derivative of -n**8/84 - 4*n**7/35 - 7*n**6/15 - 16*n**5/15 - 3*n**4/2 - 4*n**3/3 - 36*n**2. Suppose m(d) = 0. What is d?
-2, -1
Let g be (5/6)/((-1520)/(-456)). Suppose g*m**2 + 2*m + 4 = 0. Calculate m.
-4
Find x, given that -1/2*x**3 + 15/2*x**2 + 17/2 + 33/2*x = 0.
-1, 17
Suppose -7*l - 1 - 27 = 0. Let w be 16/42*(-3)/l. Determine j, given that 0 + w*j**2 - 2/7*j**4 + 2/7*j - 2/7*j**3 = 0.
-1, 0, 1
Let c(z) be the second derivative of -3*z**5/40 - z**4/2 - 5*z**3/4 - 3*z**2/2 - 119*z. Factor c(h).
-3*(h + 1)**2*(h + 2)/2
Let q(c) be the first derivative of -14*c**6/27 - 148*c**5/45 + 67*c**4/9 + 1012*c**3/27 + 128*c**2/3 + 16*c + 263. Suppose q(n) = 0. What is n?
-6, -1, -2/7, 3
Let d(f) be the second derivative of f**6/300 + f**5/75 + f**4/60 - f**2 - 9*f. Let v(k) be the first derivative of d(k). Find l, given that v(l) = 0.
-1, 0
Suppose 0 = -4*x + j + 20, 2*x - 51*j = -50*j + 12. Factor -1/2*d**3 + 0 + 1/4*d**x + 0*d + 1/4*d**2.
d**2*(d - 1)**2/4
Let k be (-88)/(-16) - 3/12*-2. Suppose 30 = k*i + 9*i. Let 2/13*r**i - 6/13*r + 4/13 = 0. Calculate r.
1, 2
Let f(y) be the first derivative of y**6/210 + y**5/70 + y**4/84 - 3*y + 15. Let k(v) be the first derivative of f(v). Factor k(j).
j**2*(j + 1)**2/7
Let a = 256 - 254. Let j(s) be the third derivative of 0*s**3 - 1/12*s**4 + 1/10*s**5 + 2*s**a + 0*s + 0 - 1/30*s**6. Factor j(l).
-2*l*(l - 1)*(2*l - 1)
Let -64*c - 50 - 20*c**2 + 15*c**3 - 13*c - 21*c + 13*c = 0. Calculate c.
-1, 10/3
Suppose 77*h + 88*h + 40*h**2 - 165*h + 4*h**4 + 44*h**3 = 0. Calculate h.
-10, -1, 0
Let f(a) = -a**2 + a - 1. Let b(g) = 25*g**3 - 61*g**3 - 17 - 80*g**2 - 44*g - 3*g. Let w(v) = 3*b(v) - 15*f(v). Factor w(l).
-3*(3*l + 2)**2*(4*l + 3)
Let j(h) be the second derivative of 9*h + 1/30*h**5 + 0*h**2 + 0*h**4 + 0 + 0*h**3 - 5/126*h**7 + 1/30*h**6. Factor j(g).
-g**3*(g - 1)*(5*g + 2)/3
Let b(c) be the third derivative of c**6/1620 - c**5/135 + c**4/27 - c**3/2 - 8*c**2. Let p(j) be the first derivative of b(j). Suppose p(q) = 0. Calculate q.
2
Let c(f) = f**2 + 3*f - 6. Let p be c(-5). Suppose 0 = -2*u - p + 10. Factor 2*n**3 - 109*n**2 + 1 - 6*n + u + 109*n**2.
2*(n - 1)**2*(n + 2)
What is n in -1/2*n**5 - 4 + 11*n + 5/2*n**4 - 1/2*n**3 - 17/2*n**2 = 0?
-2, 1, 4
Let k be (-20)/(-50) + 19/(-35) + 22/77. Determine g so that -2/7*g**3 - k*g**2 + 1/7*g**4 + 2/7*g + 0 = 0.
-1, 0, 1, 2
Factor 0 - 9*m**2 - 17/2*m - 1/2*m**3.
-m*(m + 1)*(m + 17)/2
Let z(h) = -2*h**3 + 80*h**2 - 732*h + 648. Let i(x) = 4*x**3 - 159*x**2 + 1462*x - 1296. Let f(s) = 6*i(s) + 11*z(s). Solve f(k) = 0.
1, 18
Solve -d - d**3 - 29*d**2 + 53*d**2 - 22*d**2 = 0 for d.
0, 1
Suppose -46/9*h**2 - 22/9*h**3 - 2/9*h**4 + 70/9*h + 0 = 0. Calculate h.
-7, -5, 0, 1
Let z(u) = -10*u**2 - 212*u - 988. Suppose 8*t = -32 - 8. Let n(p) = 4*p**2 + 85*p + 395. Let h(g) = t*z(g) - 12*n(g). Find y, given that h(y) = 0.
-10
Let s = -417 - -2921/7. Factor -6/7*p + 0 + s*p**2.
2*p*(p - 3)/7
Let q = -6701/5 - -1341. Factor 0*x**2 - 4/5*x**3 + q*x - 2/5 + 2/5*x**4.
2*(x - 1)**3*(x + 1)/5
Let x = -1/4138 - -106558/18621. Let r = -38/9 + x. Factor 3/2 - 9/2*q + 9/2*q**2 - r*q**3.
-3*(q - 1)**3/2
Let p = 16 + -8. Factor l**5 + l**5 - 6*l**3 - 4*l - 10*l**4 + 10*l**2 + 0*l + p*l**4.
2*l*(l - 1)**3*(l + 2)
Let x(o) be the second derivative of -o**9/10584 + o**7/2940 - 7*o**3/6 + 9*o. Let w(h) be the second derivative of x(h). Factor w(q).
-2*q**3*(q - 1)*(q + 1)/7
Suppose 25*j = 19*j - 18. Let w be ((-30)/(-4) + j)*(-4)/(-42). Factor 6/7*y**2 + 0 + 3/7*y + w*y**3.
3*y*(y + 1)**2/7
Let c be (9/6*-2)/(15/(-10)). Let o be ((-44)/21 + c)/((-8)/48). Factor 0*a**2 + 4/7*a - o*a**3 + 2/7 - 2/7*a**4.
-2*(a - 1)*(a + 1)**3/7
Suppose -3/2*q**2 - 27/2*q - 27 = 0. Calculate q.
-6, -3
Factor 5/2*j**2 + 4*j - 2.
(j + 2)*(5*j - 2)/2
Determine q so that -118*q**3 - 19*q**2 + 26082*q**4 - 20*q**5 + 6*q**2 - 26351*q**4 = 0.
-13, -1/4, -1/5, 0
Let u(x) = -x - 1. Let k be u(-3). Suppose -d + k*f + 8 = 0, 3*f + 2*f + 26 = 4*d. Find c such that -9*c + 12*c**2 + d*c + 13*c - 3*c**4 - c**4 = 0.
-1, 0, 2
Let z be 6*10/35*7/28. Find g, given that 5/7*g**4 + g**3 + 1/7*g**5 + 0*g + z*g**2 + 0 = 0.
-3, -1, 0
Factor -148*t**2 + 11*t + 146*t**2 - 61*t.
-2*t*(t + 25)
Let u(x) be the first derivative of x**6/30 + x**5/5 + x**4/3 + 13*x**2/2 - 7. Let y(s) be the second derivative of u(s). Find j, given that y(j) = 0.
-2, -1, 0
Let o be (-18)/(-8)*(261/(-54) - (-10 + 5)). Factor o*x + 0 - 1/8*x**2.
-x*(x - 3)/8
Let h(q) be the first derivative of q**4/48 - q**3/8 + q**2/4 - 4*q - 6. Let p(t) be the first derivative of h(t). What is s in p(s) = 0?
1, 2
Let p(l) be the second derivative of l**6/180 - l**5/30 + l**4/18 - 11*l**2 - 37*l. Let u(c) be the first derivative of p(c). Factor u(z).
2*z*(z - 2)*(z - 1)/3
Factor -103 + 75 - 24*l + 11*l**2 - 7*l**2.
4*(l - 7)*(l + 1)
Let o(y) be the first derivative of -y**3/6 - 5*y**2 + 21*y/2 + 39. Solve o(p) = 0.
-21, 1
Let j be (-26)/65*(-20)/26. Solve 0 + 2/13*n - j*n**2 + 2/13*n**3 = 0.
0, 1
Let h(f) be the second derivative of f**7/21 + 7*f**6/15 + 19*f**5/10 + 25*f**4/6 + 16*f**3/3 + 4*f**2 - 88*f. Find x, given that h(x) = 0.
-2, -1
Let t(g) be the third derivative of -g**5/30 - 2*g**4/3 - 16*g**3/3 - 459*g**2. Factor t(a).
-2*(a + 4)**2
Let z(w) = -w**2 + 2*w. Let m(b) = -8*b**2 + 30*b - 64. Let h(c) = 2*m(c) - 18*z(c). Factor h(g).
2*(g - 4)*(g + 16)
Let c(f) be the first derivative of -5*f**5 - 85*f**4/2 - 120*f**3 - 155*f**2 - 95*f + 243. Factor c(x).
-5*(x + 1)**3*(5*x + 19)
Let v(j) = 39*j**2 + 2*j + 0*j + 1 - 4*j. Let p be v(1). Solve -r**2 + p*r**4 - 5*r**5 - 7*r**2 - 25*r**5 + 0*r**2 = 0 for r.
-2/5, 0, 2/3, 1
Let b(u) be the second derivative of 0 + 28/9*u**3 - 4/3*u**2 - 49/18*u**4 + 12*u. Let b(w) = 0. What is w?
2/7
Suppose 75/7 + 3/7*z**2 + 30/7*z = 0. What is z?
-5
Let p(v) be the second derivative of 18*v + 0 - 2/9*v**2 + 5/27*v**3 - 2/27*v**4 + 1/90*v**5. Solve p(g) = 0 for g.
1, 2
Let b(j) be the first derivative of -5*j**3/3 + 11*j**2/2 + 19. Let h(c) = -55*c**2 + 120*c. Let y(m) = 45*b(m) - 4*h(m). Determine d, given that y(d) = 0.
0, 3
Let w = 250 - 240. Suppose -2*g = 0, -2*g + 9 = w*l - 7*l. What is s in -4/9*s**l + 0*s - 2/9*s**4 + 0 - 2/9*s**2 = 0?
-1, 0
Let t(r) be the first derivative of 9*r**5/80 + r**4/4 - 5*r**3/8 - 3*r**2/4 + 8*r + 6. Let p(h) be the first derivative of t(h). Let p(c) = 0. Calculate c.
-2, -1/3, 1
Let g = -31888 + 223234/7. Factor -2/7*o**2 + g + 16/7*o.
-2*(o - 9)*(o + 1)/7
Let m(c) be the third derivative of -c**5/420 - c**4/42 - c**3/14 - 62*c**2. Factor m(r).
-(r + 1)*(r + 3)/7
What is y in 0*y**3 + 4 + 12*y**4 + 4*y**2 - 4 - 8*y**3 - 16*y**4 + 8*y = 0?
-2, -1, 0, 1
Suppose -84*y**3 - 10/3 + 79*y + 1213/3*y**2 = 0. Calculate y.
-2/9, 1/28, 5
Let n = 9 - 7. Let z be -2*1*6/(-6). Determine r so that 3 + 1/3*r**z - n*r = 0.
3
Suppose -16 = -y - o, -2*y + 4*o - 22 = -3*y. Let r = 18 - y. Factor 0 - 2/9*i**r - 2/3*i**2 + 2/9*i + 2/3*i**3.
-2*i*(i - 1)**3/9
Let x(j) be the first derivative of -2/27*j**3 - 8/9*j**2 - 8 + 8/3*j + 1/18*j**4. Factor x(w).
2*(w - 2)**2*(w + 3)/9
Suppose 2 + 7 = 3*b. Suppose -b*q = -0*j - j, 0 = -5*j + 2*q + 13. Factor j*x**2 - 4 + 27*x**3 - 2 + 33*x**2 + 3*x.
3*(x + 1)*(3*x - 1)*(3*x + 2)
Let q(u) be the second derivative of 0 - u + 2/9*u**3 - 1/2*u**2 - 1/36*u**4. What is x in q(x) = 0?
1, 3
Let a(c) be the first derivative of 0*c**2 + 0*c**4 - 1/40*c**5 - 3*c + 0*c**3 + 5. Let g(o) be the first derivative of a(o). Find v such that g(v) = 0.
0
Let m = -50 + 59. Let q be 0/7*((-9)/3)/m. Factor -12/7*k**3 + 0*k + q + 4/7*k**4 + 8/7*k**2.
4*k**2*(k - 2)*(k - 1)/7
What is v in 4*v**3 + 11*v**4 + 4*v**3 + 15*v**4 - 24*v**4 = 0?
-4, 0
Suppose -112*k - 3*k**3 + 799 - 194*k + 737 + 72*k**2 - 270*k = 0. Calculate k.
8
Let h(x) be the third derivative of x**6/75 - 2*x**5/75 + x**4/60 + 3*x**2 - 41. Determine s so that h(s) = 0.
0, 1/2
Let x(w) = -w**3 - w - 1. Let n(f) = 10*f**3 + 37*f**2 + 55*f + 15. Suppose 0 = -5*p + 3*p + 12. Let t(h) = p*x(h) + 2*n(h). Factor t(r).
2*(r + 2)*(r + 3)*(