
0, 1, 14
Let n(a) be the third derivative of a**8/168 - 2*a**7/21 + 31*a**6/60 - 13*a**5/15 - 7*a**4/3 + 40*a**3/3 + 473*a**2. Suppose n(c) = 0. Calculate c.
-1, 2, 5
Let m be (-26 - -21)*(-4)/10. Factor 1/3 - 1/6*q**m - 1/6*q.
-(q - 1)*(q + 2)/6
Determine m so that -3*m**4 - 10*m**3 + m**3 + 12*m + 1911*m**2 - 6*m**4 - 1903*m**2 - 2*m**5 = 0.
-2, -3/2, 0, 1
Let n = 93 - 90. Let o be -5 - (-6 + -4) - (1 + n). Factor -q - 1/4*q**2 - o.
-(q + 2)**2/4
Suppose 2*y + 2*l + 30 = -0*y, -4*l - 73 = 5*y. Let k = 13 + y. Find m, given that 3*m**2 + 12*m - 14*m - 2 + m**2 + k = 0.
-1/2, 1
Let a(h) = 21*h - 123. Let n(j) = 6*j - 35. Let d(q) = -5*a(q) + 18*n(q). Let i be d(6). What is k in 3*k**3 + 2*k**2 - k**i + k - 2 - 3*k = 0?
-1, 1
Let c(i) be the third derivative of -i**5/390 + 5*i**4/156 - 4*i**3/39 + 2*i**2 + 8. Find f such that c(f) = 0.
1, 4
Let r = 129 - 119. Let n(t) = -t**3 + 17*t**2 - 70*t + 2. Let k be n(r). Factor -4/9*h + 0 + 2/9*h**3 + 2/9*h**k.
2*h*(h - 1)*(h + 2)/9
Let i(c) be the second derivative of 0*c**2 - 2*c - 1/10*c**6 + c**3 + 3/5*c**5 - 5/4*c**4 + 0. Suppose i(x) = 0. Calculate x.
0, 1, 2
Let l(t) be the first derivative of t**6/216 - 5*t**5/36 + 125*t**4/72 - 6*t**3 - 1. Let z(g) be the third derivative of l(g). Suppose z(m) = 0. What is m?
5
Let y = 116 + -111. Let l(z) = -2*z**2 + 9*z + 7. Let c be l(y). Factor 8/11 - 10/11*o + 2/11*o**c.
2*(o - 4)*(o - 1)/11
Let j(r) be the first derivative of 4/27*r**3 + 0*r + 1/36*r**4 - 9 + 2/9*r**2. Find g such that j(g) = 0.
-2, 0
Let w(t) be the second derivative of -t**5/5 + 4*t**4/3 - 2*t**3/3 - 12*t**2 - 88*t + 2. Let w(g) = 0. Calculate g.
-1, 2, 3
Let g = -22 - -22. Suppose -5*q + a = -a - 101, -3*q - 5*a + 42 = g. Find c, given that q*c**3 - 3 + 9 - 6*c**2 + 3*c - 22*c**3 = 0.
-2, -1, 1
Let y = 49100/343651 + -1/49093. Factor -6/7*v**2 + 0*v + y*v**3 + 0.
v**2*(v - 6)/7
Suppose 0 = -6*l + 11*l + g - 19, -5*l + 3*g = -3. Let u(k) be the second derivative of -4*k**2 + 0 - k + 1/3*k**4 - 2/3*k**l. Factor u(i).
4*(i - 2)*(i + 1)
Let g(y) = 30*y**4 + 29*y**3 - 27*y**2 + 13. Let r(c) = -14*c**4 - 14*c**3 + 12*c**2 - 6. Let i(b) = -6*g(b) - 13*r(b). Factor i(a).
2*a**2*(a + 1)*(a + 3)
Let q(j) be the first derivative of 15*j**4 + 124*j**3/3 - 16*j - 349. Factor q(m).
4*(m + 2)*(3*m - 1)*(5*m + 2)
Let j(d) be the first derivative of 3*d**5/5 - 105*d**4/2 + 1225*d**3 + 126. Factor j(b).
3*b**2*(b - 35)**2
Let w = 7/39 + 2/13. Let v be (-20)/(-3) - (-4)/4*-6. Determine c, given that 0 - c**3 + v*c + w*c**2 = 0.
-2/3, 0, 1
Let h be (-85)/12 + (-8)/(-36)*6 + 6. Factor -11/4 - h*y**2 - 3*y.
-(y + 1)*(y + 11)/4
Let i(g) be the first derivative of 9*g**5/20 + 3*g**4/8 - g**3 - 3*g**2/4 + 3*g/4 + 538. Find o such that i(o) = 0.
-1, 1/3, 1
Let h(u) be the first derivative of 2*u**3/39 + u**2 + 24*u/13 - 124. What is b in h(b) = 0?
-12, -1
Let k(s) be the third derivative of -5*s**8/84 - 16*s**7/105 + 2*s**6/15 + 2*s**5/3 + s**4/6 - 4*s**3/3 + 219*s**2. Suppose k(y) = 0. What is y?
-1, 2/5, 1
Let x(r) be the third derivative of r**5/330 - 37*r**4/132 - 38*r**3/33 + 7*r**2 - 13. Solve x(z) = 0 for z.
-1, 38
Let o(u) = -3 + 3 - 30*u + 4*u. Let b be o(-1). Determine l so that b*l - 14*l**4 + 32 + 22*l**3 - 36 + 24*l**3 - 54*l**2 = 0.
2/7, 1
Let p(y) be the second derivative of -5*y**4/12 - 65*y**3/6 - 61*y. Factor p(l).
-5*l*(l + 13)
Let d be -1 + 3 + 16/8. Let -3 + 0*c**4 - 3*c - 3*c**d + c**3 - 5*c**5 + 2*c**5 + 5*c**3 + 6*c**2 = 0. Calculate c.
-1, 1
Let y(k) be the third derivative of -k**7/168 - 13*k**6/240 - 7*k**5/48 - k**4/16 + 286*k**2. Factor y(f).
-f*(f + 2)*(f + 3)*(5*f + 1)/4
Let a(y) be the third derivative of -1/80*y**5 + 1/4*y**4 + 0*y - 2*y**3 + 49*y**2 + 0. Let a(n) = 0. Calculate n.
4
Let o(f) be the second derivative of -f**4/15 + 764*f**3/15 - 72962*f**2/5 - 4*f - 69. Factor o(h).
-4*(h - 191)**2/5
Suppose -10*u + 444 + 36 = 0. Let g(n) be the second derivative of 6*n**5 + 20*n**4 + 40*n**3 + 0 + 4*n + n**6 + u*n**2 + 1/14*n**7. Factor g(o).
3*(o + 2)**5
Let q(y) = y**3 - 17*y**2 + 28*y + 10. Let z be q(15). Let p be (-4)/(-10)*z/(-4). Factor 2/3*j**4 + 2/3*j**3 - p*j**2 - 4/3 - 10/3*j.
2*(j - 2)*(j + 1)**3/3
Let n(f) be the second derivative of 2/75*f**6 + 2/5*f**4 - 4/25*f**5 + 0 - 8/15*f**3 + 2/5*f**2 - 3*f. Find s, given that n(s) = 0.
1
Suppose -2*w - 3 = -c, -c - 511*w + 3 = -506*w. Factor -2/5*n**c + 6/5*n + 4/5 + 0*n**2.
-2*(n - 2)*(n + 1)**2/5
Solve -15 - 3/4*q**2 + 63/4*q = 0 for q.
1, 20
Let m(i) be the second derivative of i**5/60 - i**4/9 - 5*i**3/18 + 405*i. Suppose m(s) = 0. What is s?
-1, 0, 5
Let v(a) be the first derivative of -3*a**5/5 - 33*a**4 - 525*a**3 - 1323*a**2 - 268. Factor v(q).
-3*q*(q + 2)*(q + 21)**2
Let i(z) be the third derivative of -z**8/336 - 13*z**7/315 - 7*z**6/36 - 7*z**5/15 - 47*z**4/72 - 5*z**3/9 - 140*z**2. Let i(m) = 0. What is m?
-5, -1, -2/3
Let q(v) be the third derivative of 0*v**3 + 0*v - 38*v**2 + 0*v**4 + 0 + 1/320*v**6 - 1/160*v**5. Suppose q(c) = 0. Calculate c.
0, 1
Let k = 250/319 + 10234/1595. Factor k*p + 6/5*p**2 + 54/5.
6*(p + 3)**2/5
Let b(t) be the second derivative of -3*t**5/20 + 3*t**4/2 - 9*t**3/2 + 6*t**2 + 265*t. Solve b(c) = 0 for c.
1, 4
Factor -6*n**2 + 6*n**2 + 0*n**2 + 45*n**3 - 48*n**4 + 11*n**5 - 8*n**5.
3*n**3*(n - 15)*(n - 1)
Let s(d) be the third derivative of -d**8/420 + 23*d**7/525 - 7*d**6/25 + 8*d**5/15 + 16*d**4/15 - 45*d**2. Find w, given that s(w) = 0.
-1/2, 0, 4
Let d = -18 - -27. Determine c, given that 4*c**2 + d*c**5 - 6*c**5 - 18*c**3 + 24*c**4 - 13*c**5 = 0.
0, 2/5, 1
Let w(z) be the first derivative of 5*z**4 - 68*z**3/3 + 32*z**2 - 16*z - 65. Solve w(d) = 0.
2/5, 1, 2
Let f(k) be the second derivative of k**6/36 - k**5/24 - 5*k**4/24 + 7*k**3/6 + 11*k. Let o(l) be the second derivative of f(l). Solve o(s) = 0 for s.
-1/2, 1
Let d(p) = p**3 - 3*p**2 + p - 1. Let u be d(3). Let f be -3 + (-149)/(-39) + u/(-3). Factor -8/13 - f*o**2 + 8/13*o.
-2*(o - 2)**2/13
Let u(q) be the second derivative of -q**8/6720 + q**7/1260 - q**6/720 - 11*q**4/12 - 11*q. Let c(t) be the third derivative of u(t). Solve c(s) = 0 for s.
0, 1
Let k(o) be the second derivative of o**5/30 - o**4/12 - 2*o**3/3 - o**2/2 + 11*o. Let s(w) be the first derivative of k(w). Factor s(v).
2*(v - 2)*(v + 1)
Let f(h) = h**3 + 8*h**2 + 7*h + 3. Let j be f(-7). Suppose -t - j*m - 15 = -4*t, 0 = -2*t + 3*m + 13. Solve 2/5*a**3 + 2/5*a - 4/5*a**t + 0 = 0 for a.
0, 1
Let d(k) be the third derivative of k**5/150 + 5*k**4/6 + 125*k**3/3 + 2*k**2 - k. Suppose d(l) = 0. Calculate l.
-25
Let b = -911 - -915. Solve 5/6*t - 1/3*t**2 - 1/3 - 1/6*t**5 + 2/3*t**b - 2/3*t**3 = 0.
-1, 1, 2
Let b(u) be the first derivative of -2*u**3/3 - 70*u**2 - 2450*u + 44. Factor b(v).
-2*(v + 35)**2
Let c(y) be the third derivative of 1/36*y**4 + 0*y + 1/630*y**7 + 0*y**3 - 6*y**2 + 0 + 0*y**6 - 1/60*y**5. Suppose c(z) = 0. What is z?
-2, 0, 1
Let x = 62 + -52. Let l(r) = -4*r**4 - 13*r**3 + r**2 + 5*r + 5. Let t(h) = -2*h**4 - 6*h**3 + 2*h + 2. Let v(z) = x*t(z) - 4*l(z). Factor v(q).
-4*q**2*(q + 1)**2
Let i(q) be the third derivative of -27*q**2 + 5/72*q**6 - 1/18*q**5 + 0*q**3 - 2/63*q**7 + 5/1008*q**8 + 0*q + 0 + 0*q**4. Factor i(u).
5*u**2*(u - 2)*(u - 1)**2/3
Let g(q) = -3*q**3 + 13*q**2 + 13*q + 14. Let r(b) = b**3 - b**2 - b - 1. Let d(f) = g(f) + 5*r(f). Let l(x) be the first derivative of d(x). Factor l(o).
2*(o + 2)*(3*o + 2)
Let t be ((-28)/10)/((-945)/270). Factor t*b + 0 + 4/5*b**2.
4*b*(b + 1)/5
Find g such that 166/5*g**2 + 8/5*g**3 - 42/5*g + 0 = 0.
-21, 0, 1/4
Let r(d) be the first derivative of -1/3*d**3 - 9 + 0*d**2 - 1/4*d**4 + 0*d + 1/6*d**6 + 1/5*d**5. Solve r(g) = 0 for g.
-1, 0, 1
Let r(f) be the first derivative of 1/26*f**4 + 0*f**2 - 4/39*f**3 + 5 + 0*f. Factor r(u).
2*u**2*(u - 2)/13
Let s(y) be the first derivative of -2*y**3/9 + 32*y/3 + 336. Factor s(k).
-2*(k - 4)*(k + 4)/3
Factor 0 - 11/2*p - 1/4*p**3 + 13/4*p**2.
-p*(p - 11)*(p - 2)/4
Suppose 5*r + 2*k - 16 = 0, 4*r - 204 + 193 = -k. Find o, given that 0 - 3/2*o**4 + 3/2*o + 3/2*o**r - 3/2*o**3 = 0.
-1, 0, 1
Let q(l) = l**2 + 4*l + 2. Let o = -3 - 1. Let m be q(o). Let m*w**2 + 4*w + 0*w**2 + 2 + 0 = 0. Calculate w.
-1
Let w(y) be the first derivative of -11 + 4/3*y -