*4 - 2/5*v**5 = 0.
0, 1, 2
Let g(b) be the first derivative of 2*b**3/27 - 59*b**2/9 - 840. Determine x, given that g(x) = 0.
0, 59
Determine i so that 9 - 1/2*i**3 - 21/2*i + 4*i**2 = 0.
2, 3
Let b(u) = 8*u. Let y(w) = w**3 - 26*w**2 + 26*w - 25. Let g be y(25). Let k be b(g). Suppose 3*d**2 + 0 + 3/2*d**5 + k*d**3 - 3/2*d - 3*d**4 = 0. Calculate d.
-1, 0, 1
Let k(q) = -3*q**3 - 16*q**2 - 27*q - 12. Let y(a) = -a**2. Let z(p) = k(p) + 2*y(p). Factor z(m).
-3*(m + 1)**2*(m + 4)
Let c(a) = 8*a**3 + 395*a**2 + 771*a + 389. Let q(m) = 52*m**3 + 2568*m**2 + 5012*m + 2528. Let x(n) = 32*c(n) - 5*q(n). Find f such that x(f) = 0.
-48, -1
Let r(p) be the first derivative of -p**3/3 - 33*p**2 - 92. Factor r(k).
-k*(k + 66)
Let r(x) be the second derivative of 1/18*x**3 + 1/126*x**7 + 1/45*x**6 + 1/3*x**2 + 0 - 1/9*x**4 - 1/30*x**5 + 36*x. Solve r(u) = 0 for u.
-2, -1, 1
Let t(y) be the first derivative of 1/12*y**2 + 5 - 1/3*y + 1/18*y**3. Factor t(b).
(b - 1)*(b + 2)/6
Factor -211 + 2*n**2 - 5*n**2 - 36*n + 130.
-3*(n + 3)*(n + 9)
Let b = 49 - 54. Let c(t) = 22*t**4 + 113*t**3 + 68*t**2 - 25*t. Let k(r) = -45*r**4 - 225*r**3 - 135*r**2 + 50*r. Let w(m) = b*c(m) - 2*k(m). Factor w(n).
-5*n*(n + 1)*(n + 5)*(4*n - 1)
Let b = 35501/30 + -7993/6. Let c = 150 + b. Factor -2/5*o**2 + c*o + 8/5.
-2*(o - 4)*(o + 1)/5
Let w be 7 + (30/(-3))/5. Let h(v) = -15*v**2 + 45*v - 42. Let u(k) = -6*k**2 + 18*k - 17. Let y(j) = w*h(j) - 12*u(j). Determine n, given that y(n) = 0.
1, 2
Let z(o) be the third derivative of o**4/12 - o**3 + 2*o**2. Let y be z(4). Factor -2*s**5 - 5*s**y + 4*s**4 + 4*s**3 + s**2 - 2*s**5.
-4*s**2*(s - 1)**2*(s + 1)
Let a(p) be the third derivative of -p**8/6048 + p**7/3780 + p**6/648 - p**5/180 + 7*p**4/24 + 19*p**2. Let r(m) be the second derivative of a(m). Factor r(i).
-2*(i - 1)*(i + 1)*(5*i - 3)/9
Let o(j) be the first derivative of 3*j**4 + 11*j**3 + 15*j**2 + 9*j + 632. Suppose o(y) = 0. Calculate y.
-1, -3/4
Let 10/3*n**4 + 20/3*n**3 - 40/3*n**2 + 16/3*n - 2*n**5 + 0 = 0. What is n?
-2, 0, 2/3, 1, 2
Let f(w) = w**3 - 6*w**2 + 5*w + 9. Let j be f(5). Factor -j*x**3 + 0*x + 18*x - 6*x + 7*x**4 - 3*x - 5*x**2 - 2.
(x - 1)**2*(x + 1)*(7*x - 2)
Let i(b) be the first derivative of b**4/10 - 112*b**3/15 + 145*b**2 + 3364*b/5 + 310. Factor i(k).
2*(k - 29)**2*(k + 2)/5
Find z such that -20*z**2 - 6*z - 4*z**5 - 22*z**4 - 6*z**2 - 17*z**3 - 21*z**3 = 0.
-3, -1, -1/2, 0
Let m(f) be the third derivative of -f**7/210 + f**6/10 - 7*f**5/10 + 5*f**4/6 + 25*f**3/2 + 51*f**2. Factor m(c).
-(c - 5)**2*(c - 3)*(c + 1)
Let c be (4 - 0/4)*15/20. Let t(n) be the first derivative of -9/2*n + c*n**2 - 4 - 1/2*n**3. Solve t(u) = 0.
1, 3
Let y(b) be the first derivative of -b**6/3 + 22*b**5/5 - 5*b**4 - 212*b**3/3 - 133*b**2 - 98*b + 161. Let y(q) = 0. What is q?
-1, 7
Let q(f) = 6*f**3 + 2*f**2 - 2*f. Let s(b) = b**3 + b**2 - b. Let z(a) = q(a) - 5*s(a). Let o be z(2). Factor 0*t + 2/15*t**o - 8/15.
2*(t - 2)*(t + 2)/15
Factor 2/9*f**2 - 8/9*f + 0.
2*f*(f - 4)/9
Suppose -37*b = -13*b - 48. Let s(v) be the first derivative of 1/13*v**b + 0*v - 7 + 2/39*v**3. Solve s(n) = 0.
-1, 0
Suppose 0 = -3*w + b - 3, -353 = -3*w - 4*b - 341. Factor w + 32/5*j + 24/5*j**2 + 4/5*j**3.
4*j*(j + 2)*(j + 4)/5
Let q be ((-1)/(-5))/(14*(-24)/(-720)). Factor -q*a - 1/7*a**2 + 0.
-a*(a + 3)/7
Let j(d) = -d**2 + 23*d + 40. Suppose 4*p - 2*t = -3*t - 23, p + 11 = -2*t. Let h(m) = m**2 + m. Let c(w) = p*h(w) - j(w). Factor c(l).
-4*(l + 2)*(l + 5)
Let t = 68423/51315 - 1/17105. Find k, given that -4/3*k + 2/3*k**2 - 2/3*k**4 + 0 + t*k**3 = 0.
-1, 0, 1, 2
Let x(w) be the third derivative of w**7/42 - w**6/6 + 5*w**5/12 - 5*w**4/12 + 76*w**2. Factor x(s).
5*s*(s - 2)*(s - 1)**2
Let g(u) be the first derivative of 9*u**2/2 - 16*u - 28. Let m be g(2). Factor -1/2*d**m + d - 1/2.
-(d - 1)**2/2
Let o be ((-12)/14)/(3/(-5 + 0 - -2)). Suppose -o*c**2 + 0*c - 2/7*c**3 + 0 = 0. Calculate c.
-3, 0
Factor 4/5*y**3 - 4/5*y + 1/5 + y**4 - 6/5*y**2.
(y - 1)*(y + 1)**2*(5*y - 1)/5
Suppose -4*l + 3*l + 40 = 2*b, 0 = -5*l + 2*b + 212. Suppose -6*c**2 + 84 - l - 42 - 3*c**3 = 0. Calculate c.
-2, 0
Let w(o) be the third derivative of 6*o**2 + 1/160*o**5 - 1/960*o**6 + 1/48*o**4 + 0 + 0*o**3 + 0*o. Determine r so that w(r) = 0.
-1, 0, 4
Suppose 19*p + 7981 = 8019. Factor 0 + 2*w + 17/2*w**3 - 5/2*w**4 - 8*w**p.
-w*(w - 2)*(w - 1)*(5*w - 2)/2
Suppose 0 = 3*y - 110 - 70. Let -y + 5*h**4 + 10*h**3 - 95*h**2 - 65*h + 43*h + 162*h = 0. Calculate h.
-6, 1, 2
Let n be (6 - 2) + 1 - -1. Let s be 228/30 + n/15. Find l, given that -5*l**2 + 2 - l + s*l**2 - 4*l**2 = 0.
-2, 1
Suppose -76*z + 111*z**2 - 332*z**4 - 56*z**3 + 0*z + 665*z**4 - 324*z**4 + 12 = 0. What is z?
2/9, 1, 2, 3
Let y be (3/((-9)/(-30)))/1. Factor y*w - 25 - 5*w**2 + 25.
-5*w*(w - 2)
Let q(l) be the second derivative of l**5/20 + l**4/8 - 3*l**2 - 9*l. Let b(k) be the first derivative of q(k). Let b(h) = 0. What is h?
-1, 0
Suppose 2*r = -5*b - 8, r + r - 4*b - 28 = 0. Let i be (r/4)/((-7)/(-14)). Find j such that -6*j**2 - 324*j**4 - 14*j**2 - 144*j**i + 4*j**2 = 0.
-2/9, 0
Find a such that 46/15*a + 2/15*a**2 + 44/15 = 0.
-22, -1
Let j(s) be the third derivative of 5*s**8/84 + 76*s**7/105 + 59*s**6/30 - 14*s**5/3 - 32*s**4/3 + 64*s**3/3 - 9*s**2 + 5. Determine k, given that j(k) = 0.
-4, -1, 2/5, 1
Let c(r) be the first derivative of 2*r**5/55 - r**4/22 - 79. Factor c(l).
2*l**3*(l - 1)/11
Suppose -2612*a**2 + 23*a**4 - 40*a**3 + 2687*a**2 - 18*a**4 = 0. What is a?
0, 3, 5
Solve 16*r**4 - 9*r**4 + 5*r**2 + 25*r**3 - 25*r - 12*r**4 = 0 for r.
-1, 0, 1, 5
Let -29*g - 996*g**2 + 45*g**4 - 1017*g**2 - 225*g**3 - 11*g + 2203*g**2 = 0. What is g?
0, 1/3, 2/3, 4
Let g = -4/669 + 7594/2007. Factor g*w - 4/3 - 14/9*w**3 + 32/9*w**2.
-2*(w - 3)*(w + 1)*(7*w - 2)/9
Let v(d) = -23*d**2 + 556*d - 233. Let k(l) = 8*l**2 - 188*l + 78. Let r(c) = -7*k(c) - 2*v(c). Suppose r(g) = 0. What is g?
2/5, 20
Let t(k) be the first derivative of 2*k**3 + 0*k**5 + 16 + 1/2*k**6 + 0*k + 0*k**2 - 9/4*k**4. Factor t(r).
3*r**2*(r - 1)**2*(r + 2)
Let o(i) = i**3 + 8*i**2 + 11*i - 4. Suppose 16 = -9*w - 38. Let c be o(w). Let x**c + 2 + 11/3*x = 0. Calculate x.
-3, -2/3
Let f(p) = 3*p**2 - 26*p - 8. Let n be f(-4). Let l = n + -141. Solve 0*y**2 + 0*y - l*y**4 + 0 - 3/2*y**5 - 3/2*y**3 = 0.
-1, 0
Suppose -2*f - 13 = -8*b + 5*b, 0 = -4*b + 4*f + 20. Let u(l) be the first derivative of -4/3*l**2 + 2/9*l**b + 8/3*l + 2. Solve u(t) = 0.
2
Let r(f) be the third derivative of f**8/16128 + f**7/4032 - f**5/30 + 4*f**2. Let m(o) be the third derivative of r(o). Let m(j) = 0. What is j?
-1, 0
Let t(z) be the second derivative of 0*z**2 - 12*z + 2/39*z**3 + 0 - 1/78*z**4. Suppose t(o) = 0. Calculate o.
0, 2
Let z(q) = q**2 + 9*q - 20. Let c be z(2). Let u(f) be the first derivative of 1/8*f**2 - c + 0*f + 1/24*f**6 + 0*f**5 + 0*f**3 - 1/8*f**4. Factor u(v).
v*(v - 1)**2*(v + 1)**2/4
Suppose -5*m - 5*r + 55 = 0, 0 = 12*m - 13*m - 2*r + 17. Determine f, given that -2/11*f**m - 4/11*f**4 + 4/11*f**2 + 0 + 8/11*f**3 - 6/11*f = 0.
-3, -1, 0, 1
Factor -4*w**4 + 88*w**3 - 162*w**2 - 56*w - 32*w - 112*w**2 - 206*w**2 + 484.
-4*(w - 11)**2*(w - 1)*(w + 1)
Let c(y) be the third derivative of -y**8/131040 - y**7/10920 - y**5/4 + 8*y**2. Let g(p) be the third derivative of c(p). Let g(x) = 0. Calculate x.
-3, 0
Let u be (6/27)/(-9 + 1360/144). Determine n so that 3/2 + 5/2*n - 1/2*n**3 + u*n**2 = 0.
-1, 3
Let t = -44 - -47. Let f(l) be the first derivative of -6 + 2/5*l**5 + l**4 - 2*l + 0*l**t - 2*l**2. Factor f(y).
2*(y - 1)*(y + 1)**3
Let i(s) be the first derivative of 7*s**4 - 100*s**3/3 + 52*s**2 - 32*s - 101. Determine x, given that i(x) = 0.
4/7, 1, 2
Let x(w) be the second derivative of -w**7/105 - 2*w**6/15 - w**5/2 - 71*w. Find t such that x(t) = 0.
-5, 0
Let i(d) be the second derivative of 5/18*d**6 - 7*d - 11/36*d**4 + 0 - 2/3*d**3 + 1/2*d**5 + 2/3*d**2. Factor i(z).
(z + 1)**2*(5*z - 2)**2/3
Suppose 9/4*z**3 - 21/4*z**2 + 3/2*z**4 - 9/4*z + 15/4 = 0. What is z?
-5/2, -1, 1
Let b = -83 + 85. Factor -5*o**2 - 10*o**2 - 4*o**4 - o**4 + b*o - 7*o - 15*o**3.
-5*o*(o + 1)**3
Suppose -274*w - 165*w = -567 - 311. Suppose -l**3 - 4*l**4 + 1/2 + 7/2*l**w + 11/4*l - 7/4*l**5 = 0. Calcula