1, 2
Solve -386*t**3 - 3*t**4 - 60*t**2 + 351*t**3 - 2*t**4 = 0 for t.
-4, -3, 0
Let p(r) be the second derivative of r**6/6 - r**5 - 5*r**4/6 + 10*r**3 + 45*r**2/2 + 13*r + 2. Factor p(a).
5*(a - 3)**2*(a + 1)**2
Let g be (-195)/(-3)*1/63 + (-3)/21. Factor 2/9*i**2 + 2/3*i - g.
2*(i - 1)*(i + 4)/9
Let w(o) = -3*o**3 + 23*o**2 - 20*o - 4. Let k(z) = 5*z**3 - 24*z**2 + 19*z + 6. Let v(g) = -2*k(g) - 3*w(g). What is l in v(l) = 0?
-22, 0, 1
Let c(u) be the third derivative of u**9/1512 + u**8/420 - u**7/420 - u**6/90 + 8*u**3/3 - 11*u**2. Let f(p) be the first derivative of c(p). Factor f(w).
2*w**2*(w - 1)*(w + 1)*(w + 2)
Let y(p) be the third derivative of -p**7/3570 + p**6/3060 + p**3/3 + 15*p**2. Let g(q) be the first derivative of y(q). Factor g(d).
-2*d**2*(2*d - 1)/17
Let g = -2 + 2. Suppose -240 = -172*j + 92*j. Find a such that g*a + 2/9*a**4 + 0 + 2/9*a**2 + 4/9*a**j = 0.
-1, 0
Let d(o) be the first derivative of -21*o**4/4 - 15*o**3 - 108*o**2/7 - 48*o/7 - 8. Factor d(v).
-3*(v + 1)*(7*v + 4)**2/7
Let g(m) be the first derivative of -2*m**2 + 1/12*m**4 + 2/3*m**3 + 3*m - 7 - 1/20*m**5. Let i(j) be the first derivative of g(j). Solve i(s) = 0 for s.
-2, 1, 2
Let k(z) = 24*z**2 - 130*z. Let f(w) = 9*w**2 - 26*w - 4. Let t(p) = 8*p**2 - 26*p - 3. Let o(a) = -3*f(a) + 4*t(a). Let b(v) = -6*k(v) + 28*o(v). Factor b(m).
-4*m*(m - 13)
Let 2*v**3 + 14/5*v - 4/5 - 2/5*v**4 - 18/5*v**2 = 0. What is v?
1, 2
Let c(q) = -q**3 - 4*q**2 - q - 1. Let s(f) = f**3 - 8*f**2 + 6*f + 3. Let j be s(7). Let i be c(j). Factor -r + 3 - 2*r - 3*r**2 + i*r.
-3*(r - 1)*(r + 1)
Suppose -4/9*t**2 + 0*t - 8/9*t**4 - 10/9*t**3 + 0 - 2/9*t**5 = 0. Calculate t.
-2, -1, 0
Let t(p) be the third derivative of -p**6/15 - 3*p**5/10 - p**4/2 - p**3/3 + p**2 - 39. Suppose t(q) = 0. Calculate q.
-1, -1/4
Determine r, given that -1 + 4/3*r - 1/3*r**2 = 0.
1, 3
Suppose 0 = -16*q + 7*q + 27. Suppose -3*b**q - 3*b**5 + 12*b + 6*b**4 - 11*b - b = 0. Calculate b.
0, 1
Let u(x) be the third derivative of x**8/2520 - x**7/420 - x**6/90 - x**5/20 + 7*x**2. Let b(g) be the third derivative of u(g). Solve b(k) = 0 for k.
-1/2, 2
Let w be 212/(-70) - (-6)/14. Let q = 31/10 + w. Solve 0*j**3 + 0 - j - q*j**4 + 3/2*j**2 = 0 for j.
-2, 0, 1
Let v(g) = -g**3 + 4*g**2 + 2*g. Let s be v(4). What is l in -2*l - s*l**2 + l + l**4 + 7*l**2 + l**3 = 0?
-1, 0, 1
Let g(a) = a**2 + a - 72. Let t be g(8). Factor 2/13*l**3 + 0 + t*l + 2/13*l**4 - 4/13*l**2.
2*l**2*(l - 1)*(l + 2)/13
Suppose -79*d = 45*d. Find k, given that 0 + d*k**2 - 4/7*k**4 - 8/7*k**3 + 0*k = 0.
-2, 0
Factor 67/4 - 69/8*v + 1/8*v**2.
(v - 67)*(v - 2)/8
Factor -2/15 + 2/15*u**2 + 0*u.
2*(u - 1)*(u + 1)/15
Let t(y) be the second derivative of -19/15*y**4 + 4/15*y**3 + 0 + 10*y - 27/50*y**6 + 0*y**2 + 99/50*y**5. Let t(x) = 0. What is x?
0, 2/9, 2
Let j(q) be the second derivative of -q**4/54 - 58*q**3/27 - 841*q**2/9 - 3*q + 5. Factor j(b).
-2*(b + 29)**2/9
Let a(v) be the second derivative of 15/4*v**2 + 0 + 16*v + 3/2*v**3 + 1/8*v**4. Factor a(z).
3*(z + 1)*(z + 5)/2
Let u(v) = -3*v**3 + 2*v**2 - 2 + 11*v**2 + 2*v - 4*v**2 + v**3. Let p(c) = c**3 - 4*c**2 - c + 1. Let r(x) = 7*p(x) + 3*u(x). What is t in r(t) = 0?
-1, 1
Let i = 531 + -258. Let k = -189 + i. Suppose 86*w**2 - 5*w**3 + 3*w**3 - k*w**2 = 0. What is w?
0, 1
Factor 3*f**4 - 4*f**2 + 79 + 18*f**3 - 18*f - 106 + 28*f**2.
3*(f - 1)*(f + 1)*(f + 3)**2
Let r(b) be the second derivative of 0*b**2 + 5/6*b**4 + 0*b**3 - 5/42*b**7 - 5/4*b**5 + 2/3*b**6 + 0 + 5*b. Factor r(k).
-5*k**2*(k - 2)*(k - 1)**2
Suppose 3*z - 5 = 1. Let u be (z + 16/(-12))*3. Factor -10*q**4 + 15*q**4 - 6*q**4 - 3*q**3 - u*q + 5*q**2 + q**5.
q*(q - 1)**3*(q + 2)
Let k(c) = c**2 + 3*c. Let g be k(-4). Suppose -g*f - 5 + 17 = 0. Factor -27 + 12*b**2 + b + 3*b**2 + 3*b**f + 8*b.
3*(b - 1)*(b + 3)**2
Let v = -3165 + 3168. Let b(j) be the third derivative of 3*j**v + 9*j**2 + 0*j + 0 + 1/45*j**6 + 1/945*j**7 + 1/5*j**5 + j**4. Suppose b(d) = 0. What is d?
-3
Let i(m) be the first derivative of -3*m**8/2800 - m**7/140 - m**6/200 - 9*m**3 + 32. Let q(l) be the third derivative of i(l). Let q(d) = 0. Calculate d.
-3, -1/3, 0
Let t(f) be the third derivative of -3*f**6/2 + 15*f**5/4 - 5*f**4/3 - 5*f**3/6 + 79*f**2. What is l in t(l) = 0?
-1/12, 1/3, 1
Let q(n) be the first derivative of 3*n**5/20 + 3*n**4/8 - n**3/4 - 3*n**2/4 + 116. Factor q(g).
3*g*(g - 1)*(g + 1)*(g + 2)/4
Let i = 6 - 18. Let s = 15 + i. Factor -2*q**3 + 0*q**s - 4*q**3 + 3*q**2 + 5*q**3.
-q**2*(q - 3)
Find n such that -20*n**2 - 5626*n**4 - 5617*n**4 + 11239*n**4 + 21*n**3 + 8*n - 5*n**3 = 0.
0, 1, 2
Let t be (-4)/10*42/(-30). Let r(z) be the first derivative of -1/2*z**4 + 0*z + 0*z**2 - t*z**5 - 1 + 4/15*z**3. Factor r(b).
-2*b**2*(b + 1)*(7*b - 2)/5
Let 7*v**3 + 8*v**2 - 84 + 84 - 3*v**3 - 4*v**4 = 0. Calculate v.
-1, 0, 2
Let p be (-18)/(-81)*(-12)/(-2). Let n = 9 + -25/3. Factor 0*z**2 - 2/3 - p*z + 4/3*z**3 + n*z**4.
2*(z - 1)*(z + 1)**3/3
Factor 0 + 2/7*o**5 + 60/7*o**3 + 48/7*o + 88/7*o**2 + 18/7*o**4.
2*o*(o + 2)**3*(o + 3)/7
Let j(w) = -5*w**2 + 14*w - 9. Let x(r) = -24*r**2 + 70*r - 46. Suppose -5*t + f + 20 = 0, 3*t - t + f - 1 = 0. Let i(c) = t*x(c) - 16*j(c). Factor i(b).
2*(b - 1)*(4*b - 3)
Let l = -3/1090 - -657/1090. Let i be ((-2)/20)/(2/(-12)). Factor -3/5*w**3 + 0 + i*w**4 - l*w**2 + 3/5*w.
3*w*(w - 1)**2*(w + 1)/5
Let m(k) = 5*k**4 + 104*k**3 + 502*k**2. Let r(d) = 15*d**4 + 314*d**3 + 1507*d**2. Let i(c) = -7*m(c) + 2*r(c). Factor i(j).
-5*j**2*(j + 10)**2
Let c(d) = -d**2 - 5*d + 2. Let y(s) = -6*s**2 - 29*s + 13. Let i be (-53 + -1)/(-6)*13/(-3). Let t(x) = i*c(x) + 6*y(x). Let t(p) = 0. What is p?
-7, 0
Let a be (-370)/(-111) - 7/((-63)/6). Factor 3/4*o**3 + 3/4*o**2 + 1/4*o**a + 1/4*o + 0.
o*(o + 1)**3/4
Suppose -2*a + 54 - 48 = 0. Suppose 1/5 + 0*p**2 - 2/5*p**a + 2/5*p - 1/5*p**4 = 0. What is p?
-1, 1
Let h be (-1)/(16/(-20) + (-4)/(-6)). Factor 12*m + 3/2*m**4 + 3/2*m**5 - h*m**3 - 3/2*m**2 - 6.
3*(m - 1)**3*(m + 2)**2/2
Let s(m) be the third derivative of m**7/7560 + m**6/108 + 5*m**5/18 - 7*m**4/24 + 17*m**2. Let q(d) be the second derivative of s(d). Factor q(p).
(p + 10)**2/3
Let n be (-3)/((-27)/(-8)) + (221 - 220). Let h(l) be the first derivative of -2 + 0*l + n*l**2 - 2/27*l**3. Find q, given that h(q) = 0.
0, 1
Determine r, given that 1617/2 + 3/2*r**3 - 315/2*r - 9/2*r**2 = 0.
-11, 7
Suppose 27 = -3*x + 6. Let h = x - -9. Solve 3*l**4 + l**2 - 4*l**h + 6*l**3 + 6*l**2 = 0 for l.
-1, 0
Find b such that 8/11*b + 2/11*b**2 + 8/11 = 0.
-2
Let r(z) = z**3 - 39*z - 18. Let h be r(-6). Let k(w) be the second derivative of 0 - 6*w - 3/80*w**5 + 1/8*w**3 + h*w**2 - 1/40*w**6 + 1/16*w**4. Factor k(p).
-3*p*(p - 1)*(p + 1)**2/4
Suppose -5*j + 16 = -14. Suppose 2*c - 4*c = 4*f + 6, f + 2*c = -j. Factor -1/2*n + f + 5/4*n**3 - 3/4*n**2.
n*(n - 1)*(5*n + 2)/4
Let i(c) = -60*c**2 + 505*c + 115. Let a(w) = -w**2 + w - 1. Let t(u) = -25*a(u) + i(u). Factor t(o).
-5*(o - 14)*(7*o + 2)
Let p be 29/(1131/(-330))*(-1)/16. Let h = p + -2/13. Let -h*o**5 - 9/8*o**3 + 0*o**2 + 0 + 3/2*o**4 + 0*o = 0. Calculate o.
0, 1, 3
Let i be -7*(-95)/(-25) + 4/(-10). Let m = -53/2 - i. Factor 5/2*p**2 + 2*p**3 + 0 + m*p.
p*(p + 1)*(4*p + 1)/2
Let r(y) be the third derivative of y**10/50400 + y**9/20160 - y**5/30 + 14*y**2. Let p(i) be the third derivative of r(i). What is q in p(q) = 0?
-1, 0
Let n = -18 - -36. Let y = -18 + n. Find o, given that y + 17*o - 3 + 0 - 5*o**2 - 3 = 0.
2/5, 3
Let d(k) = 81*k**3 + 6*k**2 - 60*k - 12. Suppose w + 3*w = -4. Let g(m) = -m**2. Let b(i) = w*d(i) - 15*g(i). Suppose b(z) = 0. Calculate z.
-2/3, -2/9, 1
Let g(o) be the first derivative of o**6/9 - 6*o**5/35 - 5*o**4/42 + 2*o**3/7 - 2*o**2/21 - 82. Find p such that g(p) = 0.
-1, 0, 2/7, 1
Suppose 2*c = -5 + 13. Suppose c*r = 12*r - 72. Factor 63/2*s**3 + r*s + 109/4*s**2 + 49/4*s**4 + 1.
(s + 1)**2*(7*s + 2)**2/4
Let a = -879062/9 + 97418. Let d = a + 256. Factor 2/9*n**2 + d*n + 0.
2*n*(n + 2)/9
Factor -3*w**2 + 219 + 36*w - 587 + 209 + 198.
-3*(w - 13)*(w + 1)
Suppose -3*o + 5*c = -100, 10*o - 136 = 6*o + 4*c. Suppose 5*s - o = -25. Suppose 0 + 1/2*u**s + u = 0. What is u?
-2, 0
Let f = -257/15 - -2093/60. Factor f*b**3 - 45/4*b**2 + 1 - 43/4*b**4 