
Suppose 23*w + 8644 - 3124 = 0. Let d = -240 - w. Factor -1/4*a**2 + 0*a + 0 + 1/4*a**4 + d*a**3.
a**2*(a - 1)*(a + 1)/4
Find g, given that 3/2 - 95/2*g + 368*g**2 + 128*g**3 = 0.
-3, 1/16
Let t = -6/283 - -463/8490. Let r(s) be the second derivative of 1/18*s**4 + 11*s + 0*s**3 + 0 + 0*s**2 + t*s**5. Determine p, given that r(p) = 0.
-1, 0
Factor 1/2*s**3 - 66*s**2 - 42592 + 2904*s.
(s - 44)**3/2
Suppose -o + 10 = 3*z, 4*o = 2*z - 2 - 0. Suppose -3*q = -5*l - 21, 5 = 2*q - l - 2. What is n in 0*n**2 + 6*n**q - 2*n**4 - 9 + 13 - 10*n + 2*n**z = 0?
-2, 1
Let j(r) be the first derivative of -r**6/60 - r**5/40 + r**4/12 - 8*r - 20. Let a(x) be the first derivative of j(x). Factor a(d).
-d**2*(d - 1)*(d + 2)/2
Let l be 2/(30/12 - 2). Let u(b) be the first derivative of -22/15*b**3 + 13/10*b**l - 4 + 2/5*b**2 - 8/25*b**5 + 0*b. Suppose u(p) = 0. What is p?
0, 1/4, 1, 2
Let r = -27 + 29. Factor r*j**2 + 0*j**3 - 2*j + 2*j**3 - 2 + 0*j**3.
2*(j - 1)*(j + 1)**2
Let o(v) be the third derivative of 0 + 0*v - 1/15*v**5 + 1/2*v**3 + 11/24*v**4 - 6*v**2. Factor o(p).
-(p - 3)*(4*p + 1)
Suppose -8*g + 5*g = -78. Suppose 20 = -3*r + g. Suppose -3/2*a**5 + 15*a**r + 3/2 - 15/2*a - 15*a**3 + 15/2*a**4 = 0. Calculate a.
1
Let g(b) be the second derivative of 0 - 4/21*b**3 + 7*b - 3/35*b**6 + 4/21*b**4 + 3/70*b**5 + 0*b**2. Factor g(c).
-2*c*(c + 1)*(3*c - 2)**2/7
Let i = 24 - 14. Let c be ((-8)/i)/((-8)/20). Factor -h**2 + h**2 - 2*h + c*h**2.
2*h*(h - 1)
Let u(z) be the third derivative of -z**6/360 - z**5/45 + 5*z**4/72 + 4*z**2. Let u(f) = 0. Calculate f.
-5, 0, 1
Suppose z + 5*r = -85, 5*z + 7*r - 2*r + 525 = 0. Let v be z/(-90) + -3 + 2. Factor 0 - v*w**5 - 2/9*w**2 - 2/3*w**4 + 0*w - 2/3*w**3.
-2*w**2*(w + 1)**3/9
Let n = 16 - 9. Suppose 0 = 4*o + n - 7. Factor -2/5*j**3 + o*j**2 + 1/5 - 1/5*j**4 + 2/5*j.
-(j - 1)*(j + 1)**3/5
Let g(k) = 9*k**3 + 44*k**2 - 119*k + 54. Let i(j) = 10*j**3 + 45*j**2 - 125*j + 55. Let r(y) = 5*g(y) - 4*i(y). Determine b so that r(b) = 0.
-10, 1
Let m(z) be the second derivative of 7/30*z**3 + 1/150*z**6 + 0 + 1/5*z**2 + 1/20*z**5 - 19*z + 3/20*z**4. Let m(a) = 0. Calculate a.
-2, -1
Let r(y) be the third derivative of 125*y**5/84 + 25*y**4/14 + 6*y**3/7 + y**2 + 26. Factor r(k).
(25*k + 6)**2/7
Let b(l) be the second derivative of -l**4/6 + 53*l**3/3 + 110*l**2 - 74*l + 1. What is p in b(p) = 0?
-2, 55
Let w(d) = d + 8. Let c be w(-3). Find j such that 144*j - 3 + 27*j**4 + 47 + 0*j**5 + 168*j**2 + 96*j**3 + 3*j**c + 4 = 0.
-2, -1
Let s = -186 + 186. Let z(o) be the third derivative of s*o**3 + 0*o - 1/132*o**4 - 1/1155*o**7 - 5*o**2 + 1/330*o**5 + 0 + 1/660*o**6. What is k in z(k) = 0?
-1, 0, 1
Let q(l) be the third derivative of -l**7/420 - l**6/80 - l**5/60 - 7*l**2 - 7*l. Factor q(n).
-n**2*(n + 1)*(n + 2)/2
Let c(k) be the third derivative of -k**10/5040 - k**9/1008 - k**8/560 - k**7/840 + 19*k**4/24 - 6*k**2. Let q(x) be the second derivative of c(x). Factor q(w).
-3*w**2*(w + 1)**2*(2*w + 1)
Let k be 0/((42/1)/7). Let m(h) be the third derivative of -5*h**2 + 1/504*h**8 + k + 1/180*h**6 + 0*h**3 + 0*h**5 + 0*h**4 - 2/315*h**7 + 0*h. Factor m(w).
2*w**3*(w - 1)**2/3
Factor 86*b + 116*b**2 + 2*b**5 + 20*b**4 + 891 - 867 + 14*b**3 + 58*b**3.
2*(b + 1)**3*(b + 3)*(b + 4)
Let d(t) be the second derivative of 13*t + 0 - 2/15*t**3 - 1/100*t**5 + 1/15*t**4 + 0*t**2. Suppose d(m) = 0. Calculate m.
0, 2
Let t = 11 - 2. Suppose -11 = -3*x - 5. Find w such that t*w**5 + 3*w**3 + 9*w**4 - 4*w**3 - w**2 + 2*w**3 - x*w**3 = 0.
-1, -1/3, 0, 1/3
Suppose r = -5*b + 22, -9*b = -6*b + 2*r - 16. Let q(f) be the second derivative of 1/2*f**2 + 0 + 3*f - 1/2*f**3 + 3/16*f**b. Suppose q(j) = 0. What is j?
2/3
Factor 1/7*y**3 + 0 - 18/7*y + 15/7*y**2 - 2/7*y**4.
-y*(y - 2)*(y + 3)*(2*y - 3)/7
Let a(r) be the first derivative of -5/3*r**3 + 0*r**2 - 15/2*r**4 - 7 + 0*r - 10/3*r**6 - 9*r**5. Factor a(h).
-5*h**2*(h + 1)**2*(4*h + 1)
Let b = 119 + -97. What is u in -9*u**5 + 4*u**5 - 19*u**4 - 15*u**3 + 17*u**2 - b*u**2 + 4*u**4 = 0?
-1, 0
Let t be (-18)/(-9) + (0 - -3). Suppose -13 = -t*k + 12. Factor k*z**5 + 3*z**4 - 2*z**5 - 2*z**3 - 8*z**2 - 7*z**2 - 6*z - 7*z**3.
3*z*(z - 2)*(z + 1)**3
Find a, given that -4/5*a**2 + 8/5*a**3 + 2/5*a**5 - 2*a - 4/5 + 8/5*a**4 = 0.
-2, -1, 1
Let b(s) be the first derivative of s**7/840 + s**6/480 - s**5/240 - s**4/96 - s**2/2 + 7. Let p(c) be the second derivative of b(c). Solve p(w) = 0.
-1, 0, 1
Let w be 15/(-20)*((-8)/(-45))/(-4). Let f(d) be the second derivative of 0 + 1/5*d**2 + 6*d - w*d**3 - 1/60*d**4. Let f(k) = 0. What is k?
-2, 1
Let y(v) = -9*v**2 + 255*v + 990. Let x(w) = -2*w**2 + 51*w + 198. Let r(s) = -24*x(s) + 5*y(s). Solve r(j) = 0 for j.
-11, -6
Let a(v) = -v**2 + 5*v + 4. Let q be a(5). Suppose 9 = -6*w + 33. Factor 2*l**3 - l**5 - 4*l**2 - l - 5*l**w + 6*l**q + l**4 + 2.
-(l - 2)*(l - 1)**2*(l + 1)**2
Factor 0 + 2*h**2 - 1/2*h**3 + 1/2*h**5 - 2*h**4 + 0*h.
h**2*(h - 4)*(h - 1)*(h + 1)/2
Let u(f) be the first derivative of 79*f**4 + 728/5*f**5 - 232*f**3 - 98*f**6 - 32*f + 20 + 136*f**2. Determine i so that u(i) = 0.
-1, 2/7, 2/3, 1
Suppose 2*i + 40 = -5*v, -4*i + 3*i = -5*v + 50. Let q = i + 32. Factor 2/3*d + 2/3*d**3 + 0 - 4/3*d**q.
2*d*(d - 1)**2/3
Determine j so that -9*j**4 + 225 + 36*j**3 + 315*j + 34*j**3 - 385*j - 220*j**2 + 4*j**4 = 0.
-1, 1, 5, 9
Let t(n) = n**3 + n + 1. Let f(s) = -s**4 + 11*s**3 - 22*s**2 + 27*s - 6. Let k be 5/10 - (-22)/4. Let w(j) = k*t(j) - 2*f(j). Let w(l) = 0. Calculate l.
1, 3
Let y be 1/((17 - 5) + -10). Suppose -2 - 3/2*g**2 - 4*g + g**3 + y*g**4 = 0. What is g?
-2, -1, 2
Let a(s) be the third derivative of -1/10*s**6 + 0 - 1/15*s**5 - 1/84*s**8 + 0*s + 0*s**4 + 22*s**2 + 0*s**3 - 2/35*s**7. Suppose a(z) = 0. Calculate z.
-1, 0
Let g(n) = 17*n**2 - 65*n + 17. Let l(a) be the second derivative of -3*a**4/4 + 11*a**3/2 - 4*a**2 - a - 5. Let j(i) = 2*g(i) + 5*l(i). Factor j(r).
-(r - 3)*(11*r - 2)
Let o(p) = -9*p**2 - 25*p + 26. Let b(s) = 16*s**2 + 51*s - 53. Let t(u) = -4*b(u) - 7*o(u). Let t(f) = 0. Calculate f.
-30, 1
Let -1/2*w**5 - 15/2 + 7/2*w + 11*w**2 - 7/2*w**4 - 3*w**3 = 0. Calculate w.
-5, -3, -1, 1
Determine z, given that -8*z - 65*z**2 + 43*z**2 + 23*z**2 = 0.
0, 8
Let a(k) be the second derivative of 2*k**7/49 - 46*k**6/105 + 41*k**5/35 + k**4/7 - 88*k**3/21 + 40*k**2/7 - 375*k. Determine d, given that a(d) = 0.
-1, 2/3, 1, 2, 5
Let n be ((-35)/20 - -4)/6. Let k(o) be the third derivative of 0*o + 0 - 1/2*o**3 + 10*o**2 - n*o**4 - 3/20*o**5 - 1/40*o**6. Factor k(r).
-3*(r + 1)**3
Determine c, given that 89*c**2 - 33*c - 177*c**2 - 54 + 85*c**2 = 0.
-9, -2
Factor 9*y - 6 + 3/4*y**4 - 9/4*y**3 - 3/2*y**2.
3*(y - 2)**2*(y - 1)*(y + 2)/4
Determine h, given that -3*h**3 + 12*h - 3*h**2 + 0 + 3/4*h**4 = 0.
-2, 0, 2, 4
Let y(j) be the third derivative of 0*j**4 + 0*j**3 - 1/672*j**8 + 1/840*j**7 + 0 + 1/240*j**6 - 1/240*j**5 + 0*j - 27*j**2. Determine r, given that y(r) = 0.
-1, 0, 1/2, 1
Let y(q) be the second derivative of -1/30*q**5 + 1/18*q**4 + 0*q**3 + 0 - 8*q + 0*q**2. Solve y(g) = 0 for g.
0, 1
Let t = -107/78 + 20/13. Let b(z) be the first derivative of t*z**4 + 1/6*z + 1/3*z**3 + 1/3*z**2 + 1 + 1/30*z**5. Suppose b(h) = 0. Calculate h.
-1
Let z(f) = -3*f - 98. Let x be z(-33). Let b be (-42)/(-10) + x + (-13 - -9). Solve 3*l**4 - b*l**3 + 0 + 6/5*l - 3*l**2 = 0 for l.
-1, 0, 2/5, 1
Let s be 395/158 + (-6)/(-4). Let h(b) be the second derivative of 5/27*b**3 - 2/9*b**2 + 13*b - 1/27*b**s + 0. Factor h(f).
-2*(f - 2)*(2*f - 1)/9
Let g(o) be the first derivative of -o**6/180 - o**5/30 + o**4/4 - 2*o**3 - 7. Let c(t) be the third derivative of g(t). Factor c(k).
-2*(k - 1)*(k + 3)
Find y, given that -2/5*y**3 + 16/5*y**2 - 28/5 - 2*y = 0.
-1, 2, 7
Let g be ((-136)/(-22))/4 + (4 + -2)/(-2). Suppose -2/11*x**5 + 0*x**4 + 0*x + 0 + g*x**3 + 4/11*x**2 = 0. Calculate x.
-1, 0, 2
Let m(u) = -2*u**3 - 9*u**2 - 9*u - 3. Let d be m(-3). Let o be (d/(-7))/(3 + 52/(-28)). Factor -o*r**3 + 1/8*r**2 + 3/8*r - 1/4 + 1/8*r**4.
(r - 2)*(r - 1)**2*(r + 1)/8
Let q(r) = 2*r**3 + 4*r**2 + 2*r - 6. Let o(s) = -4*s**3 - 8*s**2 - 4*s + 10. Let b(n) = 3*o(n) + 5*q(n). Solve b(m) = 0.
-1, 0
Let y(j) = j**2 - 2. Let l(r) = -r**3 - 7*r**2 + 4*r + 9. Let u be l