 Find i, given that -4*i**3 + 12*i**2 - m*i**2 - 2 + 5*i - i**3 + 0 = 0.
-1, 2/5, 1
Let w be ((-247)/273 - -3) + 6/(-63). Solve -w*l - 1/4*l**2 - 4 = 0 for l.
-4
Suppose -25 = -8*u + 3*u. Let m(s) = 32*s**3 - 92*s**2 + 80*s - 20. Let c(v) = -33*v**3 + 92*v**2 - 80*v + 21. Let g(b) = u*m(b) + 4*c(b). Factor g(t).
4*(t - 2)*(t - 1)*(7*t - 2)
Let j(y) be the first derivative of -1 - 2/5*y**3 - 2/5*y**2 + 2/5*y. Factor j(d).
-2*(d + 1)*(3*d - 1)/5
Let w be -36 + 40 + ((-62)/6 - -7). Factor -8/3 + w*t**2 + 0*t.
2*(t - 2)*(t + 2)/3
Let d be 5/(12 - 121/11). Let o(b) be the third derivative of 2/105*b**7 + 0*b + 0 + 12*b**2 + 4/3*b**4 - 4/15*b**6 - 32/3*b**3 + b**d. What is l in o(l) = 0?
-1, 1, 4
Suppose 2*f = -9*f + 22. Let s be 8/10*28/56. Suppose s*m + 0 + 4/5*m**f + 2/5*m**3 = 0. Calculate m.
-1, 0
Let a = -4/1077 - -730/3231. Suppose -2/9*o**2 - a - 4/9*o = 0. Calculate o.
-1
Let l(z) be the third derivative of -z**8/42 - 2*z**7/21 - z**6/30 + 2*z**5/15 + 2*z**2 - 16*z. Solve l(h) = 0 for h.
-2, -1, 0, 1/2
Suppose -3*k - 29 = -2*k. Let d be k/(-9) - 6/27. Determine i so that -3*i**5 - 16 + 3*i**4 + 16 - 3*i**2 + d*i**3 = 0.
-1, 0, 1
Let a(q) = q**3 - 3*q**2 + 3*q + 1. Let g be a(3). Suppose -g = -3*s - 1. Factor 3*i - 3*i**3 - 3*i**4 - 1 + s*i**2 + 4 - 3.
-3*i*(i - 1)*(i + 1)**2
Let k(d) be the second derivative of -d**6/480 + d**4/96 + 2*d**2 + 4*d. Let u(g) be the first derivative of k(g). Factor u(i).
-i*(i - 1)*(i + 1)/4
Let t = -2368 + 30786/13. Factor -8/13*q**2 - 2/13*q + t*q**3 + 8/13.
2*(q - 4)*(q - 1)*(q + 1)/13
Let q(z) be the first derivative of 1/9*z**3 + 2/3*z**2 + 4/3*z + 8. Determine r so that q(r) = 0.
-2
Let m be 3 - 292*(-7)/(-700). Let b(i) be the first derivative of 0*i**4 + 2/15*i**3 - 1/10*i**2 + 4 + 1/30*i**6 + 0*i - m*i**5. Factor b(u).
u*(u - 1)**3*(u + 1)/5
Let -3*u**2 - 9/2*u - 3/2 = 0. What is u?
-1, -1/2
Let u(v) = v**3 - 2*v**2 - 5*v. Let a be u(4). Suppose 3*t = -3*t + a. Factor -1 - 5*q**t - 2*q + 6*q**2 + q + q**3.
(q - 1)*(q + 1)**2
Let p(y) be the second derivative of -y**5/4 - 7*y**4/9 - 11*y**3/18 + y**2/3 + 151*y. Determine q so that p(q) = 0.
-1, 2/15
Suppose -2*m - 3*c = -248, -m + 39 = 3*c - 82. Let x = -125 + m. Determine h, given that 0*h**3 + 2/3*h**4 + 0*h**x + 2/3*h**5 + 0 + 0*h = 0.
-1, 0
Solve 0 - 5*w - 1/2*w**3 - 7/2*w**2 = 0 for w.
-5, -2, 0
Factor 794/3*p**2 - 616*p + 968/3 + 2/3*p**4 + 28*p**3.
2*(p - 1)**2*(p + 22)**2/3
Suppose -2*u = -u. Let i = u + 5. Let a(l) = 7*l**2 - 3*l + 13. Let g(s) = -20*s**2 + 10*s - 38. Let w(f) = i*g(f) + 14*a(f). Factor w(v).
-2*(v - 2)**2
Suppose -22 = -5*c + 3. Let a be (c + 4)*(-1)/(-2). Solve 0*s + a*s**5 - 3/2*s**4 + 0 - 5/2*s**3 - 1/2*s**2 = 0 for s.
-1/3, 0, 1
Let q(o) be the first derivative of o**3/3 - 6*o**2 + 20*o - 9. Factor q(r).
(r - 10)*(r - 2)
Suppose 24*r = -2*g + 21*r + 31, 2*r = g + 2. Let n(j) be the first derivative of g + j**4 + 4*j - 1/5*j**5 - j**3 - 2*j**2. Solve n(z) = 0.
-1, 1, 2
Let o(q) be the first derivative of 3*q**6/14 - 6*q**5/5 - 51*q**4/28 + 8*q**3 + 30*q**2/7 - 7. Let o(c) = 0. What is c?
-2, -1/3, 0, 2, 5
Let p(c) = 55*c**2 + 5295*c - 5805. Let z(h) = 5*h**2 + 481*h - 528. Let l(j) = 6*p(j) - 65*z(j). Factor l(n).
5*(n - 1)*(n + 102)
Let a(r) = -21*r - 3*r**2 - 4*r**2 - 15 + 2*r**2 + 4*r**2. Let o be a(-20). Factor 18 + 8*q**2 - o*q**3 - 60*q + 22 - 3*q**2 + 25*q**2.
-5*(q - 2)**3
Let m(s) be the second derivative of 0 - 1/6*s**2 + 8*s + 0*s**3 + 1/36*s**4. Factor m(j).
(j - 1)*(j + 1)/3
What is i in 0*i**2 + 0*i + 1/7*i**4 + 0 + 2/7*i**3 = 0?
-2, 0
Factor -5*i**4 - 75*i**2 + 2*i**4 + 7*i**4 + 8*i**3 - 32*i + 59*i**2.
4*i*(i - 2)*(i + 2)**2
Let b(l) = -l**3 - 3*l**2 + 10*l - 10. Let c be b(-8). Let m = c + -230. What is x in 2*x**3 + 2/3*x**4 + m + 2*x**2 + 2/3*x = 0?
-1, 0
Let l be (0 + 4)/(-1 + (-20)/(-25)). Let k be (-13 - l) + 3/(-1). What is j in -11/2*j**2 - 9/2*j**5 + 7/2*j**3 + j + 11/2*j**k + 0 = 0?
-1, 0, 2/9, 1
Let r = -1126 + 1126. Factor r - 1/5*s**2 - 3/5*s.
-s*(s + 3)/5
Let a(g) be the second derivative of 5*g**3 - 3*g. Let o be a(1). Factor 15*q**3 - 27*q**5 - 99*q**3 - 90*q**4 + o*q**2 - 54*q**2.
-3*q**2*(q + 2)*(3*q + 2)**2
Let f(w) be the second derivative of 0*w**2 - 1/4*w**4 - 3/5*w**5 - 3*w - 1/10*w**6 + 0 + 3*w**3. Factor f(c).
-3*c*(c - 1)*(c + 2)*(c + 3)
Let w be (-2 - (-50)/20)/1. Solve -3/2*q + 3/2*q**4 + q**3 + 1/2*q**5 - w - q**2 = 0.
-1, 1
Suppose -2*o - 4*c - 6 = -0, -3 = c. Factor 6*f**o - 9 + f**3 - 2*f**3 - 3*f**2 - 2*f**3 - 15*f.
3*(f - 3)*(f + 1)**2
Suppose 0 = 4*l - 24 - 12. Suppose l = -3*s + 18. Factor -w**2 + 7*w**2 + 15*w**3 + 12*w - 12 - s*w**2 + 36*w**2.
3*(w + 1)*(w + 2)*(5*w - 2)
Solve -74*u**3 - 98*u**3 - 4*u**4 + 76*u**3 - u + u = 0 for u.
-24, 0
Suppose -4*o + 20 = 3*t, 37*o + 3*t - 22 = 32*o. Factor -o*x - 1/2*x**2 - 2.
-(x + 2)**2/2
Let -1/3*m**2 - 4 + 8/3*m = 0. What is m?
2, 6
Let t(j) be the first derivative of 2*j**5/55 - 5*j**4/11 + 24*j**3/11 - 56*j**2/11 + 64*j/11 - 112. Determine z, given that t(z) = 0.
2, 4
Let n(z) be the first derivative of 5*z**6/6 + 21*z**5 + 775*z**4/4 + 2195*z**3/3 + 420*z**2 - 3920*z - 502. What is v in n(v) = 0?
-7, -4, 1
Let d(w) be the second derivative of -w**5/150 - 103*w**4/90 - 520*w**3/9 + 2704*w**2/15 - 77*w - 2. Factor d(b).
-2*(b - 1)*(b + 52)**2/15
Let 24/7*r**4 + 0*r + 0 - 50/7*r**3 + 2*r**5 + 12/7*r**2 = 0. What is r?
-3, 0, 2/7, 1
Find n, given that -501*n**2 - 33*n**3 + 209*n**4 + 118*n**3 + 210*n**4 + 520*n - 423*n**4 - 100 = 0.
1/4, 1, 10
Let f = 29 + -27. Suppose 3*h**f - 14 - 5*h**2 - 4 - 12*h = 0. What is h?
-3
Let f(d) be the second derivative of -d**7/42 - d**6/30 + 3*d**5/4 - 23*d**4/12 + 5*d**3/3 + 26*d - 3. Find k, given that f(k) = 0.
-5, 0, 1, 2
Let t(g) be the third derivative of 0 - 4*g**2 + 1/50*g**5 + 0*g**3 - 1/30*g**4 - 1/300*g**6 + 0*g. Find d such that t(d) = 0.
0, 1, 2
Let w = -3/263 - -685/13939. Let y = 49/106 + w. Factor 0 + 1/2*p**3 - y*p + 0*p**2.
p*(p - 1)*(p + 1)/2
Let v(z) be the third derivative of -z**7/210 + z**5/10 - z**4/3 + 11*z**3/3 - 5*z**2. Let h(r) be the first derivative of v(r). Factor h(s).
-4*(s - 1)**2*(s + 2)
Let g(j) be the third derivative of 0*j - 1/75*j**5 + 0*j**6 + 0 + 1/525*j**7 + 14*j**2 + 1/15*j**3 + 0*j**4. Suppose g(d) = 0. What is d?
-1, 1
Let u(i) = 44*i**2 + 88*i + 20. Let q(l) = -132*l**2 - 266*l - 59. Let x(s) = 4*q(s) + 11*u(s). Find t, given that x(t) = 0.
-2, -2/11
Factor -1/2*f**2 + 32*f - 512.
-(f - 32)**2/2
Let v(b) be the third derivative of b**7/8820 + b**6/360 + 7*b**4/12 - 23*b**2. Let u(x) be the second derivative of v(x). Determine z, given that u(z) = 0.
-7, 0
Let b(y) = 4*y**3 + 35*y**2 - 54*y + 7. Let o(u) = -4*u**3 - 36*u**2 + 54*u - 8. Let h(i) = -3*b(i) - 4*o(i). Suppose h(l) = 0. Calculate l.
-11, 1/4, 1
Determine h, given that 16/3 - 1/6*h**3 + 0*h - h**2 = 0.
-4, 2
Let w be ((-3)/(-46))/(18/(-24)). Let z = w - -211/46. Let 1/2*r**2 + 3*r + z = 0. Calculate r.
-3
Suppose 30 = 5*a + 2*x, 6*a + 11 = 5*a + 3*x. Suppose -l + 5*j - 1 = -16, -15 = a*l + 5*j. Solve 0 + 5/2*p**3 - 10*p + l*p**2 = 0 for p.
-2, 0, 2
Let k be ((-36)/64 - -1)/((-22)/(-24)). Let q = k - 5/22. What is d in 1/2*d**3 + 0 - q*d - 1/4*d**5 + 0*d**2 + 0*d**4 = 0?
-1, 0, 1
Let v(m) be the second derivative of -1/300*m**6 - 1/5*m**4 + 8/15*m**3 + 0 + 5*m + 1/25*m**5 - 3*m**2. Let b(i) be the first derivative of v(i). Factor b(n).
-2*(n - 2)**3/5
Suppose 0 = -5*n + 5*d - 20, d - 8 = -d. Let t be n/(-1 - (0 - 4)). Solve -4/15*y**3 + 0*y**2 - 2/5*y**4 - 2/15*y**5 + t*y + 0 = 0 for y.
-2, -1, 0
Let a = -259 + 261. Let v(z) be the first derivative of 0*z + 3/20*z**4 - 3/25*z**5 - 1/10*z**6 + 1/5*z**3 + 5 + 0*z**a. Factor v(h).
-3*h**2*(h - 1)*(h + 1)**2/5
Find f, given that 0 - 2/15*f**4 + 2/5*f**3 - 4/15*f + 2/15*f**2 - 2/15*f**5 = 0.
-2, -1, 0, 1
Let f(y) be the second derivative of -y**7/1120 + 29*y**6/2880 - y**5/80 - 7*y**4/6 + 33*y. Let n(i) be the third derivative of f(i). Factor n(c).
-(c - 3)*(9*c - 2)/4
Let u(w) be the first derivative of -w**7/560 + w**6/40 - w**5/16 + 19*w**3/3 + 13. Let a(x) be the third derivative of u(x). Suppose a(v) = 0. Calculate v.
0, 1, 5
Let s(m) be the third derivative of 1/96*m**5 + 0 + 1/960*m**6 + 26*m**2 + 0*m + 1/16*m**3 + 7/192*m**4. Determ