/2
Let n be -2 + (-32)/(-6) + (-7)/21. Factor 0*f**2 - 1/2*f**n + 0 + 0*f - 1/4*f**4.
-f**3*(f + 2)/4
Let d be (-6)/4 + (-363)/(-110). Let b(h) be the first derivative of 3/2*h**4 - 5/2*h**6 + 0*h**2 + 0*h**3 + 0*h - d*h**5 - 3. Solve b(u) = 0.
-1, 0, 2/5
Let u(d) = 2*d**3 + 6*d**2 + 5*d - 7. Let m be u(-3). Let h be 2/m + 115/55. Factor -2 + 8/3*k - 2/3*k**h.
-2*(k - 3)*(k - 1)/3
Find j, given that -6 + 75/4*j - 81/4*j**2 + 33/4*j**3 - 3/4*j**4 = 0.
1, 8
Let s(b) be the first derivative of -1/12*b**3 - 9/4*b - 15 - 3/4*b**2. Factor s(m).
-(m + 3)**2/4
Suppose -2*f = 2*f + 4*a - 40, -2*a = -f + 7. Let p be (-3)/(f/(-15)) - 3. Solve 3 - 8 - 5 - 3*x**p - 12*x + 1 = 0.
-3, -1
Let s be (-50)/(-20)*12/5. Let w(c) = 16*c**2 - c + 11. Let k(q) = -3*q**2 - 2. Let g(p) = s*w(p) + 33*k(p). Solve g(z) = 0.
-2, 0
Let u be (5/(-15) - 1)/(8/(-2)). Suppose w - 1 = -0*w. Factor u*x**2 - 4/3*x + w.
(x - 3)*(x - 1)/3
Let r(h) = h**3 + h - 1. Suppose 0 = -27*b + 22*b + 25. Let p(j) = 16*j**3 - 20*j**2 + 12*j - 3. Let f(l) = b*r(l) - p(l). Let f(q) = 0. What is q?
-2/11, 1
Let n(z) be the second derivative of 8/15*z**3 - 1/20*z**4 + 0 - 3*z + 2/5*z**2 + 2/75*z**6 - 11/100*z**5. Find b such that n(b) = 0.
-1, -1/4, 2
Determine t so that -36/7*t**2 - 48/7 - 80/7*t - 4/7*t**3 = 0.
-6, -2, -1
Let j(x) = 2*x**3 - 4*x**2 + 7*x. Let h(q) = -q**2 - 11*q + 5. Let k be h(-11). Let c(b) = 2*b**3 - 4*b**2 + 8*b. Let t(w) = k*c(w) - 6*j(w). Factor t(o).
-2*o*(o - 1)**2
Let j(b) be the second derivative of -b**6/6 + 17*b**5/2 - 1265*b**4/12 - 510*b**3 - 810*b**2 + b + 6. Suppose j(c) = 0. Calculate c.
-1, 18
Let x(d) = 4*d**2 - 1. Let y be x(-1). Suppose -y = -3*h + 3. Factor -2*c**2 + 8 - 5 - 3 + h*c.
-2*c*(c - 1)
Let v be (530/(-583) - (-1 + 0))/(6/12). Solve -4/11 + 2/11*g**2 + 6/11*g**3 - 6/11*g + v*g**4 = 0 for g.
-2, -1, 1
Let l be (-476)/(-49) - (-2)/7. Determine u so that -u**4 - 132 + 137 - l*u**2 + 6*u**4 = 0.
-1, 1
Let b be (47/(-42) + (-10)/60)*(-1)/9. Let 1/7*c + 0 - b*c**2 = 0. What is c?
0, 1
Suppose -a - 2*n - 3*n = -3, 2*n = -2*a + 22. Let g = -9 + a. Let g*c**4 - 3*c**4 + c**4 + 4*c**3 + 2*c**2 = 0. What is c?
-1, 0
Factor 0*j**2 + 0*j - 1/3*j**5 + 16/3*j**4 + 0 - 64/3*j**3.
-j**3*(j - 8)**2/3
Let f = -1 + 1. Let z be 9/(-4)*(-140)/210. Factor 0 + 3*g**2 + f*g**3 + z*g**5 - 3*g**4 - 3/2*g.
3*g*(g - 1)**3*(g + 1)/2
Factor -8*u + 5*u**3 - 7*u**3 - 62*u**3 - 44*u**2 - 28*u**4.
-4*u*(u + 1)**2*(7*u + 2)
Let b(h) = -h**2 - 22*h - 31. Let k(p) = -24*p - 32. Let d(m) = 4*b(m) - 5*k(m). Factor d(c).
-4*(c - 9)*(c + 1)
Suppose 52*d - 1 = -1. Let g(n) be the first derivative of 10*n**2 + 20/3*n**3 - 15/4*n**4 + d*n - 5. Suppose g(o) = 0. What is o?
-2/3, 0, 2
Solve 9/8*w**3 + 1/4*w + 5/8*w**4 + 7/8*w**2 + 1/8*w**5 + 0 = 0.
-2, -1, 0
Let s = -34 - -2857/84. Let f(j) be the third derivative of 1/735*j**7 + 1/420*j**6 - 1/210*j**5 + 0 + 0*j - s*j**4 + 0*j**3 + 7*j**2. Factor f(y).
2*y*(y - 1)*(y + 1)**2/7
Let u(x) be the third derivative of -x**7/1365 - x**6/65 - 2*x**5/39 - 20*x**2 - 3. Determine m, given that u(m) = 0.
-10, -2, 0
Let l = -39/14 - -20/7. Let y(h) be the second derivative of 1/4*h**4 + 3/10*h**6 - 9*h + 0*h**3 + 0*h**2 + 0 - l*h**7 - 9/20*h**5. Factor y(k).
-3*k**2*(k - 1)**3
Let s(c) be the third derivative of c**8/11200 - c**7/600 + c**6/80 - 9*c**5/200 - c**4/2 + 3*c**2. Let h(v) be the second derivative of s(v). Factor h(j).
3*(j - 3)**2*(j - 1)/5
Let 132/7*j + 1452/7 + 3/7*j**2 = 0. What is j?
-22
Let d(j) be the first derivative of j**5/15 - j**3/9 - 100. Find n such that d(n) = 0.
-1, 0, 1
Let z = 51 + -41. Let z*c - 10*c + 5*c**2 = 0. Calculate c.
0
Let q = -193 - -136. Let x be -4 + 1 - q/3. Let 21*r - 8 + 28 + 3*r + 4*r**2 + x = 0. What is r?
-3
Let 32*k - 336/5 + 4/5*k**2 = 0. Calculate k.
-42, 2
Suppose 0 = -84*u + 9*u + 300. Solve 1/9*z**3 + 0 - 1/9*z + 1/9*z**u - 1/9*z**2 = 0.
-1, 0, 1
Suppose 3*k - k = -40. Let c be (-3)/(-8)*k/(-30). Factor 9*w**2 + 27/2*w + 27/4 + 5/2*w**3 + c*w**4.
(w + 1)*(w + 3)**3/4
Let t be -1 - -27 - (-2)/(-2). Suppose -3 = -2*q + y + t, 0 = 3*q - y - 43. Factor q*b**2 + 0*b**3 + 12 + 2*b**3 + b**3 + 21*b + 3*b.
3*(b + 1)*(b + 2)**2
Let a(g) = g**3 - 3*g**2 - 4*g + 1. Suppose 5*s - 5*i + i + 13 = 0, 3*i = -9. Let p(u) = -1. Let j(r) = s*p(r) - 5*a(r). Factor j(m).
-5*m*(m - 4)*(m + 1)
Let s(u) = 51*u - 24*u - 5*u**2 - 25*u - 3. Let g(c) = 4*c**2 - 2*c + 3. Let r(x) = 6*g(x) + 5*s(x). Factor r(f).
-(f - 1)*(f + 3)
Factor -153/4*i**2 - 9 - 21/4*i**3 - 42*i.
-3*(i + 1)*(i + 6)*(7*i + 2)/4
Let w(k) be the third derivative of 1/35*k**5 + 0 + k**2 + 1/70*k**6 + 0*k - 1/6*k**4 - 2/735*k**7 - 4/7*k**3. Suppose w(n) = 0. What is n?
-1, 2, 3
Let i(g) be the second derivative of -g**6/60 - g**5/8 - 5*g**4/24 + 5*g**3/12 + 3*g**2/2 + 33*g. Let i(a) = 0. What is a?
-3, -2, -1, 1
Let j(h) be the first derivative of h**4/22 + 10*h**3/33 - 6*h**2/11 - 345. Let j(f) = 0. What is f?
-6, 0, 1
Factor 520*h + h**2 + 4*h**2 + 205 - 730*h.
5*(h - 41)*(h - 1)
Let g be -2 + (-10)/(-15)*21. Suppose 24 = 12*h - g. Suppose -3/2*k**2 - 3/2*k**h + 3/2 + 3/2*k = 0. What is k?
-1, 1
Let i(a) be the second derivative of 5/9*a**3 + 1/9*a**4 - a**2 + 0 - 29*a. Let i(q) = 0. Calculate q.
-3, 1/2
Let o(r) be the third derivative of -r**5/300 - 3*r**4/40 - 7*r**3/15 + 2*r**2 - 18*r. Let o(a) = 0. What is a?
-7, -2
Let t be 59 + 9/(-15) + 48/30. Suppose -17*a + 2*a = -t. Find x such that -18/11*x - a*x**3 + 16/11*x**4 + 48/11*x**2 - 2/11*x**5 + 0 = 0.
0, 1, 3
Let v(r) be the first derivative of r**9/16632 - r**7/2310 + r**5/660 - 14*r**3/3 - 6. Let f(u) be the third derivative of v(u). Factor f(p).
2*p*(p - 1)**2*(p + 1)**2/11
Let k(c) = -c**3 - 229*c + 0*c**3 + 234*c + 4. Let z(d) = -d - 1. Let h(g) = k(g) + 2*z(g). Factor h(r).
-(r - 2)*(r + 1)**2
Let v(a) be the third derivative of -a**7/126 - 7*a**6/360 - a**5/90 + a**2 + 49. Factor v(i).
-i**2*(i + 1)*(5*i + 2)/3
Suppose q = 4*z - 3*q - 8, 2 = 2*q. Factor -192*p**2 - p**5 + p**z + 192*p**2.
-p**3*(p - 1)*(p + 1)
Let q be 6/4 - 2/4. Suppose -2*k - q + 0*k - 2*k + 2*k - k**2 = 0. What is k?
-1
Let u(i) be the first derivative of i**5/10 + 2*i**4 - i**3/6 - 4*i**2 + 114. Find o, given that u(o) = 0.
-16, -1, 0, 1
Let w(r) = -16*r + 5. Let o be w(-4). Let v = -69 + o. Factor v*d**2 + 0 + 3/4*d - 3/4*d**3.
-3*d*(d - 1)*(d + 1)/4
Suppose 0 = 2*i - 3*i + 3. Suppose i*h + 4 = 5*h. Solve -3*q + h*q**2 + 6 - 4 + q - 2*q = 0 for q.
1
Let a be (26/39)/(64/24). Let t be (-28)/16*4/(-14). Factor t*p**2 + 1/4*p**3 + a*p + 0.
p*(p + 1)**2/4
Let c(i) be the third derivative of i**8/336 - i**7/105 - i**6/40 + i**5/15 + i**4/6 + 2*i**2 + 2*i. Suppose c(v) = 0. What is v?
-1, 0, 2
Let i(u) be the second derivative of -2*u**6/45 + 4*u**5/45 + u**4/27 - 4*u**3/27 + 366*u. Factor i(n).
-4*n*(n - 1)**2*(3*n + 2)/9
Find c, given that 144/5*c + 2592/5 + 2/5*c**2 = 0.
-36
Let y(j) = 6*j**4 - 16*j**3 - 2*j**2 - 4*j. Let p(q) = q**4 - q**3 + q**2. Suppose g + 3*r = -2*r + 23, 2 = g - 2*r. Let h(n) = g*p(n) - y(n). Factor h(v).
2*v*(v + 1)**2*(v + 2)
Let l(h) be the second derivative of -h**5/4 + 25*h**4/6 - 115*h**3/6 + 35*h**2 - 22*h - 1. Factor l(u).
-5*(u - 7)*(u - 2)*(u - 1)
Suppose 11*q - 15*q + 20 = 0. Let d(t) be the third derivative of 1/100*t**q + 0*t - 3*t**2 + 0 + 0*t**4 + 0*t**3. Suppose d(f) = 0. What is f?
0
Let p(f) = 14*f**4 - 110*f**3 + 531*f**2 + 155*f. Let k(l) = -l**4 - 2*l**3 + l. Let u(x) = -14*k(x) - 2*p(x). Factor u(c).
-2*c*(c - 9)**2*(7*c + 2)
Let n(d) be the third derivative of d**8/672 + d**7/20 + 97*d**6/240 - 11*d**5/8 - 121*d**4/24 + 449*d**2. Suppose n(l) = 0. Calculate l.
-11, -1, 0, 2
Let c(x) be the first derivative of -5*x**4/4 - 25*x**3/3 + 71. Factor c(a).
-5*a**2*(a + 5)
Let b(m) be the second derivative of 25*m**4/42 - 7*m**3/3 - 2*m**2/7 + 63*m. Factor b(w).
2*(w - 2)*(25*w + 1)/7
Factor 2*w**3 - 5*w**3 - 7*w**3 - 3*w**4 + 12*w + 15 - 6*w**2 - 2*w**3 - 6.
-3*(w - 1)*(w + 1)**2*(w + 3)
Solve -66*o**2 - o**4 - 76*o**2 + 197*o**2 - 14*o**3 - 68*o**2 = 0 for o.
-13, -1, 0
Factor 7*v + 8*v + 22*v**2 - 9*v**2 - 7*v - 12*v**2.
v*(v + 8)
Factor -2/21*b**3 + 2 + 22/21*b**2 - 62/21*b.
-2*(b - 7)*(b - 3)*(b - 1)/21
Let m = -26/3 - -290/33. Let h(k) be the first derivative of -4/11*k - 3/11*k**