r -x*a**2 + z - 28*a**4 - 12*a**5 - 64/3*a**3 + 0*a.
-4*a**2*(a + 1)*(3*a + 2)**2/3
Let c(q) = q**5 + q**3 - q**2 + q. Let s(y) = -26*y**5 + 8*y**3 + 2*y**2 - 24*y + 4. Let f(o) = 36*c(o) + 2*s(o). Find k such that f(k) = 0.
-2, -1/2, 1/2, 1
Let f = 1215 + -10927/9. Suppose 0 = 2*d + 2*d - 8. Find u such that -f*u**3 + 2/9*u**d + 0 + 0*u = 0.
0, 1/4
Let z be -46 - 1708/(-36) - 20/18. Determine o, given that 0 - 5/3*o - 2*o**2 - z*o**3 = 0.
-5, -1, 0
Let b(n) be the first derivative of -15/2*n**2 - 8 - 5/3*n**3 + 0*n. Let b(c) = 0. What is c?
-3, 0
Let z(k) = -6*k**3 + 3*k**2 + 3*k. Let u(t) = -t**4 + 13*t**3 - 5*t**2 - 7*t. Let b(y) = 3*u(y) + 7*z(y). Solve b(n) = 0.
-2, 0, 1
Let t = -6257/6 + 1043. Let d(i) be the first derivative of 0*i + t*i**3 + 4 - 1/2*i**2 + 1/8*i**4. Suppose d(a) = 0. Calculate a.
-2, 0, 1
Let f(l) be the third derivative of 0*l**3 - 8*l**2 + 0*l**4 + 1/570*l**5 + 0*l + 0. Determine j, given that f(j) = 0.
0
Let w = 79887/7 + -11412. Factor -9/7*n - 6/7 - w*n**2.
-3*(n + 1)*(n + 2)/7
Let o(y) = -38*y**2 + 25*y - 23. Let t(k) = 4*k**2 - k - 1. Let p(x) = 2*o(x) + 18*t(x). Factor p(f).
-4*(f - 4)**2
Factor -9/7*h + 0 + 3/7*h**3 - 6/7*h**2.
3*h*(h - 3)*(h + 1)/7
Factor -541*d - 231*d + 14357*d**2 - 96 - 14381*d**2 + 192*d.
-4*(d + 24)*(6*d + 1)
Let g(r) be the second derivative of r**9/15120 - r**8/3360 + r**7/2520 + r**4/3 - 10*r. Let y(p) be the third derivative of g(p). Find v, given that y(v) = 0.
0, 1
Let p = 2354/5 + -470. Find n, given that p*n**3 + 0 - 2/5*n**2 - 2/5*n = 0.
-1/2, 0, 1
Let u(g) = g**3 - g**2 - 6*g. Let t(c) = -c**3 + 20*c**2 + 20*c + 24. Let m be t(21). Let n be u(m). Factor 1/8*k**2 + 1/4*k + n.
k*(k + 2)/8
Let f(r) be the third derivative of -5*r**7/14 + 13*r**6/12 + 791*r**5/180 + 47*r**4/18 + 2*r**3/3 - 264*r**2. Find g such that f(g) = 0.
-1, -2/15, 3
Let u(v) be the third derivative of v**6/480 - v**5/80 + v**2 - 20*v. Determine r so that u(r) = 0.
0, 3
Let y(j) be the first derivative of 1/15*j**5 - 2 + 0*j + 0*j**3 + 1/12*j**4 + 1/60*j**6 + 2*j**2. Let h(m) be the second derivative of y(m). Factor h(d).
2*d*(d + 1)**2
Let d be (35/10)/(2/4). Suppose -20 = 3*r + 5*y, -d*r = -3*r - 5*y - 20. Factor 0*m - 16/3*m**3 + r + 4/3*m**2 + 4*m**4.
4*m**2*(m - 1)*(3*m - 1)/3
Let y(o) be the second derivative of o**4/6 - 47*o**3/3 + 68*o. Find d, given that y(d) = 0.
0, 47
Let b = 60 - 58. Factor -b - d + 4*d - 2*d**2 + 3*d - 2*d.
-2*(d - 1)**2
Let k be 25*(-2)/30*-9. Let x be ((-1)/k)/(21/(-126)). Let -1/5*w**4 - 2/5*w**3 + x*w + 1/5 + 0*w**2 = 0. What is w?
-1, 1
Let r be 4/3 - (-19038)/(-90). Let a = r + 212. Factor 3/5*i**2 + 0*i + 9/5*i**4 + 0 + 3/5*i**5 + a*i**3.
3*i**2*(i + 1)**3/5
Suppose t + 0*t - 9 = 0. Let p(z) = z**3 - z**2 + 9*z + 9. Let s be p(t). Solve -14*y**4 + 738*y - s*y + 18*y**5 - 4*y**3 = 0 for y.
-2/9, 0, 1
Let i = 30 + -26. Suppose 0 = m + i - 6. Factor 2/9*u + 8/9*u**3 + 0 - 10/9*u**m.
2*u*(u - 1)*(4*u - 1)/9
Let u(d) be the second derivative of d**5/5 + 13*d**4/3 + 80*d**3/3 + 33*d - 3. Factor u(v).
4*v*(v + 5)*(v + 8)
Let t(g) be the third derivative of -g**5/15 + 4*g**4/3 - 8*g**3 + 136*g**2 - 2. Factor t(u).
-4*(u - 6)*(u - 2)
Factor -2/9*n**2 + 10/3*n + 68/9.
-2*(n - 17)*(n + 2)/9
What is l in -74*l - 42*l - 40 + 32 + 8 - 4*l**2 = 0?
-29, 0
Let p(n) = -n**3 + 15*n**2 + 19*n - 42. Let t be p(16). Let m(o) be the first derivative of -4/5*o - 4/5*o**2 - 4/15*o**3 - t. Determine r so that m(r) = 0.
-1
Factor -2/3*b**2 + 8 + 2/3*b.
-2*(b - 4)*(b + 3)/3
Let x be (10/6)/(5/15). Let g = -2 + x. Factor -2 - 4*l**2 - 2*l**g + 2*l + 5*l**2 + l**2.
-2*(l - 1)**2*(l + 1)
Let z(t) be the third derivative of 8*t**7/245 + 17*t**6/35 + 57*t**5/140 - 55*t**4/56 + 4*t**3/7 + 10*t**2 - 2*t. Suppose z(h) = 0. What is h?
-8, -1, 1/4
Let k(f) be the second derivative of -f**5/100 + 2*f**3/15 - f - 21. Suppose k(w) = 0. What is w?
-2, 0, 2
Let g = 19 + -21. Let l be 5 + g - (1 + 0). Determine k, given that -28 + 0*k**l + 28 - 3*k**2 = 0.
0
Let d(f) be the third derivative of f**7/105 - f**6/20 - 3*f**5/10 + 23*f**4/12 - 4*f**3 - 8*f**2 - 12. Let d(k) = 0. What is k?
-3, 1, 4
Let l(c) = -12*c**4 + 26*c**3 - 30*c**2 - 54*c + 14. Let y(t) = t**4 + 2*t + 1. Let r(d) = -2*l(d) - 28*y(d). Factor r(m).
-4*(m - 1)**2*(m + 1)*(m + 14)
Let k = -505 - -507. Let s(n) be the second derivative of -1/15*n**4 + 5*n + 2/75*n**6 + 1/105*n**7 + 0*n**k + 0*n**5 - 1/15*n**3 + 0. Factor s(p).
2*p*(p - 1)*(p + 1)**3/5
Suppose 28*r - 24*r - 4 = y, 0 = 5*y + 5*r - 5. Determine v so that -12/5*v**3 - 2/5*v**4 + 0 - 18/5*v**2 + y*v = 0.
-3, 0
Let d = 111/550 - 1/50. Factor -4/11*s + 0 + d*s**3 + 2/11*s**2.
2*s*(s - 1)*(s + 2)/11
Let g = -66 - -57. Let p be 0 + 1 - (-8 - g). Let -2/11*t**3 + 0*t + 2/11*t**2 + p = 0. Calculate t.
0, 1
Let n(s) be the third derivative of s**5/15 - 23*s**4/3 + 628*s**2. Let n(l) = 0. Calculate l.
0, 46
Let z(g) be the first derivative of -4*g**3/15 + 88*g**2/5 + 368*g/5 - 353. Suppose z(u) = 0. What is u?
-2, 46
Let o(p) be the third derivative of 1/60*p**5 + 2/3*p**3 + 0*p + 11*p**2 - 5/24*p**4 + 0. Let o(y) = 0. What is y?
1, 4
Factor -2*v**5 + 118*v**3 - v**5 + 72*v**2 + 78*v**4 - 265*v**3 + 0*v**5.
-3*v**2*(v - 24)*(v - 1)**2
Let q(w) be the first derivative of 1/33*w**3 - 1/110*w**5 - 8 - 3*w + 2/11*w**2 - 1/33*w**4. Let y(m) be the first derivative of q(m). Factor y(k).
-2*(k - 1)*(k + 1)*(k + 2)/11
Determine a, given that -14/9*a - 3*a**2 + 25/3*a**3 - 13/9*a**4 + 0 - 7/3*a**5 = 0.
-7/3, -2/7, 0, 1
Suppose -44944*j**3 - 32*j**2 + 44908*j**3 - 2*j**5 + 8*j**4 - 24*j**4 - 10*j = 0. What is j?
-5, -1, 0
Let x(o) be the first derivative of 0*o**2 + 13 - o**5 + 0*o - 1/6*o**6 - o**4 + 0*o**3. Suppose x(b) = 0. What is b?
-4, -1, 0
Let y be (-1 + 95/10)/(1/14). Let a = y + -117. Factor -3*k**3 - 6/5 - 3/5*k**4 - 21/5*k - 27/5*k**a.
-3*(k + 1)**3*(k + 2)/5
Let x(g) be the third derivative of g**8/2240 - g**7/720 - g**6/360 + g**5/15 - 19*g**2. Let t(p) be the third derivative of x(p). Factor t(n).
(n - 1)*(9*n + 2)
Suppose -55*m + 79 = -141. Let j(o) be the second derivative of -2*o + 1/2*o**2 + 0 + 1/12*o**3 - 1/24*o**m. Find v such that j(v) = 0.
-1, 2
Let y(x) be the first derivative of -x**4/3 + 2*x**3/3 - 9*x - 14. Let b(z) be the first derivative of y(z). Determine t so that b(t) = 0.
0, 1
Let k(f) be the second derivative of f**5/60 - f**4/12 + 2*f**2/3 - 27*f. Solve k(b) = 0 for b.
-1, 2
Let -1/8*p**2 + 1/8*p + 3/4 = 0. Calculate p.
-2, 3
Find r, given that -3*r + 0*r + 5*r - 112*r**2 - 2*r - 4*r**3 = 0.
-28, 0
Let t(l) = -l**3 + 3*l**2 - l. Let x be t(2). Let u = 7/454 - -1781/2270. Let -2/5*g**x - u*g + 0 = 0. What is g?
-2, 0
Let o(d) be the third derivative of -d**8/1176 + d**6/60 + d**5/35 + 131*d**2. Suppose o(t) = 0. What is t?
-2, -1, 0, 3
Let b(h) be the first derivative of -33 + 0*h**2 - 1/22*h**4 + 2/55*h**5 + 0*h**3 + 0*h. Find r such that b(r) = 0.
0, 1
Let r(g) = 2*g - 18. Let c be r(11). Suppose 3*i + 5*o = 7*o + 19, 0 = -c*i - o + 7. Determine t, given that -20/3*t**2 - 4*t**i + 0 - 8/3*t = 0.
-1, -2/3, 0
Let r = 194/117 - 15331/4095. Let j = -9/7 - r. Solve 8/5 + j*p**2 - 12/5*p = 0.
1, 2
Let n = 22 - 19. Suppose 5*a - 11 = n*h, -28 = -2*h - 2*h - 4*a. Factor -3*i**2 + 12*i**h - 3*i**4 - 10*i**3 + 4*i**3.
-3*i**2*(i - 1)**2
Let p be 32/70 + 0 + (-40)/(-100). Factor -2/7*t**2 - p + 8/7*t.
-2*(t - 3)*(t - 1)/7
Let w(a) be the third derivative of -a**6/8 + 19*a**5/10 - 11*a**4/2 - 12*a**3 - 152*a**2. Factor w(d).
-3*(d - 6)*(d - 2)*(5*d + 2)
Find i, given that -8 - 440/9*i**2 - 100/3*i**3 - 2/9*i**5 - 290/9*i - 80/9*i**4 = 0.
-36, -1
Suppose -45 = -5*x - 0*x - 5*u, x - 33 = 5*u. Suppose 2*s = 8, 4*n + 3*s + 1 = x. Factor 0 + n*t + 1/2*t**2.
t**2/2
Let i(p) = 2*p - 24*p**2 + 1 + 2 - p**3 + 14*p**2 + 8*p**2. Let o(k) = -k - 1. Let d(w) = -i(w) - 3*o(w). Factor d(q).
q*(q + 1)**2
Factor -16*v + 20*v**2 + 2*v**3 + 0*v**3 - v**3 + 16*v.
v**2*(v + 20)
Suppose 0 = 2*n - 3*s - 16, -34*s + 8 = 2*n - 35*s. Let g(p) be the first derivative of -4 - 1/3*p - 1/9*p**3 - 1/3*p**n. Factor g(q).
-(q + 1)**2/3
Let v(j) be the third derivative of j**6/24 - j**5/12 - 5*j**4/4 - 191*j**2. Find c, given that v(c) = 0.
-2, 0, 3
Let s = -4991662741/2250 - -2218517. Let g = s + -1/250. Let 0 - 