108*(-2 - (-265)/130). Let k = b - 460/117. Solve -k*q**3 + 2/9*q**4 - 2/9*q**2 + 0*q + 0 + 2/9*q**5 = 0 for q.
-1, 0, 1
Let c(l) be the third derivative of l**7/5040 - 7*l**6/2160 + l**5/48 - l**4/16 - 7*l**3/6 + 18*l**2. Let w(y) be the first derivative of c(y). Factor w(u).
(u - 3)**2*(u - 1)/6
Suppose -50*u = -24*u + 150*u - 352. What is t in 0 + t + 1/5*t**u = 0?
-5, 0
Let a = -3185/2 + 1542. Let z = a - -51. Find b, given that -2 - 3*b**3 - z*b**4 - 6*b - 13/2*b**2 = 0.
-2, -1
Let b(s) be the third derivative of -5/3*s**4 - 1/30*s**5 - 100/3*s**3 - 43*s**2 + 0*s + 0. What is v in b(v) = 0?
-10
Suppose 69 = 3*n - 240. Let d = n + -99. Suppose -20/7*j**3 - 4*j**2 - 4/7*j**d + 0 - 12/7*j = 0. What is j?
-3, -1, 0
Let r(d) be the first derivative of d**7/252 + d**6/180 - d**5/120 - d**4/72 + 8*d + 5. Let x(k) be the first derivative of r(k). Find g, given that x(g) = 0.
-1, 0, 1
Let o(r) be the second derivative of r**7/70 - r**6/5 + 27*r**5/25 - 29*r**4/10 + 43*r**3/10 - 18*r**2/5 - 100*r. Factor o(i).
3*(i - 4)*(i - 3)*(i - 1)**3/5
Find q such that -3/2*q**5 + 15*q**4 + 9*q**2 + 0 - 42*q**3 + 135/2*q = 0.
-1, 0, 3, 5
Let d(b) be the third derivative of -b**7/490 - 3*b**6/280 + b**5/14 + 17*b**2 + 2. Factor d(t).
-3*t**2*(t - 2)*(t + 5)/7
Let a(n) be the third derivative of n**6/120 + n**5/60 - n**4/12 - 67*n**2. Factor a(r).
r*(r - 1)*(r + 2)
Suppose 0 = 3*y + 3*h - 5 + 2, -4*y - h + 10 = 0. Factor 9*r - 12*r**2 - 10 + 0 + y*r**3 + 10.
3*r*(r - 3)*(r - 1)
Let j(f) be the third derivative of -f**6/1080 + f**5/180 - f**4/72 + f**3/54 + 17*f**2. Factor j(p).
-(p - 1)**3/9
Let i(x) be the third derivative of x**5/330 + 3*x**4/4 + 98*x**3/33 - 174*x**2 - 2. Factor i(l).
2*(l + 1)*(l + 98)/11
Let f(q) be the first derivative of 3*q + 9/4*q**2 + 2 + 1/2*q**3. Factor f(n).
3*(n + 1)*(n + 2)/2
Let u(q) = -5*q**3 - 3*q**2 - q. Let l be u(-2). Solve -36*v**3 + 2 + l*v**4 - 7*v**2 - 9*v**5 + 2*v**3 + 7*v + 12*v**3 - v**2 = 0.
-1/3, 1, 2
Let h(l) be the second derivative of 12*l + 0*l**4 + 1/60*l**6 + 1/2*l**2 - 1/10*l**5 + 0 + 4/3*l**3. Let t(o) be the first derivative of h(o). Factor t(c).
2*(c - 2)**2*(c + 1)
Let q(l) = l**2 + 6*l - 432. Let p be q(-24). Factor p*u + 1/8*u**2 + 0 - 1/8*u**4 + 0*u**3.
-u**2*(u - 1)*(u + 1)/8
Let v(z) be the first derivative of z**5/6 + 5*z**4/2 - 215*z**3/18 + 25*z**2/2 - 363. Let v(n) = 0. Calculate n.
-15, 0, 1, 2
Let s(z) be the second derivative of z**9/20160 + z**8/8960 + 7*z**4/12 - 13*z. Let i(o) be the third derivative of s(o). Factor i(r).
3*r**3*(r + 1)/4
Let s be 10/(-14)*(-245)/2310. Let a(m) be the second derivative of -1/11*m**2 + s*m**4 + 0 + 4/33*m**3 - 4*m. Factor a(k).
2*(k + 1)*(5*k - 1)/11
Let s(y) be the third derivative of -1/672*y**8 + 1/240*y**6 - 1/120*y**5 + 0*y**4 + 0*y**3 + 0*y - 12*y**2 + 0 + 1/420*y**7. Determine r so that s(r) = 0.
-1, 0, 1
Let k(b) be the third derivative of -b**8/4032 + b**7/1008 - 2*b**5/15 + 8*b**2. Let n(i) be the third derivative of k(i). Factor n(z).
-5*z*(z - 1)
Let t(r) be the first derivative of 5*r**4/4 + 20*r**3 + 225*r**2/2 + 250*r - 150. Let t(w) = 0. Calculate w.
-5, -2
Find j such that -11*j**3 + 28*j**2 - 677*j + 651*j + 9*j**3 = 0.
0, 1, 13
Let b = -103 - -105. Let k(h) be the first derivative of 1/3*h**3 + 4 - 2*h + 1/2*h**b. Factor k(m).
(m - 1)*(m + 2)
Let y = -80 + 105. Solve 30*z - 70*z**3 - 80*z**4 + 15*z**5 - 14 - 1 + 105*z**4 + y*z - 10*z**2 = 0 for z.
-3, -1, 1/3, 1
Let n(w) be the first derivative of -1/2*w**2 + 4 - 1/108*w**4 + 0*w + 0*w**3 + 1/540*w**6 + 0*w**5. Let q(i) be the second derivative of n(i). Factor q(k).
2*k*(k - 1)*(k + 1)/9
Let l be ((64/112)/(-2))/((-5)/35). Factor -5/6*p**l + 5 + 25/6*p.
-5*(p - 6)*(p + 1)/6
Let r(w) = -w**2 + w. Let p(g) = g**3 - 4*g**2 - g + 5. Let s be p(4). Let b(m) = 3*m**3 + m**2 - 4*m. Let q(f) = s*b(f) + r(f). Determine z so that q(z) = 0.
-1, 0, 1
Let b be 14/35 - ((-322)/120 + 3). Let p(x) be the first derivative of b*x**3 + 0*x + 5 + 1/8*x**2. Factor p(a).
a*(a + 1)/4
Let h(n) be the third derivative of -n**8/5040 - n**7/2520 + n**6/360 + n**5/15 - 3*n**2. Let y(q) be the third derivative of h(q). Let y(f) = 0. Calculate f.
-1, 1/2
Let y(l) be the second derivative of 0 + 1/21*l**7 + 35*l - 5/8*l**5 - 5/12*l**4 - 2*l**2 + 3*l**3 + 1/20*l**6. Determine c so that y(c) = 0.
-2, 1/4, 1, 2
Let x be (77/(-42) - -2)/((-8)/(-18)). Let b(g) be the first derivative of 1/4*g**2 + x*g**4 + 2/3*g**3 + 4 + 0*g. Suppose b(a) = 0. What is a?
-1, -1/3, 0
Let i(z) = -z**4 - 23*z**3 + 51*z**2 + 324*z + 435. Let r(m) = 4*m**4 + 68*m**3 - 148*m**2 - 972*m - 1304. Let c(o) = 8*i(o) + 3*r(o). Factor c(a).
4*(a - 4)*(a + 3)**3
Let b = 4271/10 - 427. Let l(m) be the first derivative of -1 - b*m**4 - 6/5*m - 2/15*m**3 + m**2. Factor l(a).
-2*(a - 1)**2*(a + 3)/5
What is o in 0 + 3/7*o + 2/7*o**2 - 5/7*o**3 = 0?
-3/5, 0, 1
Let l = 2 + 0. Suppose 17 = -y + 23. Factor 3 - 14*v**2 + 15*v**l + y*v + 6.
(v + 3)**2
Suppose f - 21 = -4*q, 0 = 5*f + q + 2*q - 37. Factor 0*p**3 + 238*p**2 - 9*p**3 - p**5 + 4*p**f - 232*p**2.
3*p**2*(p - 1)**2*(p + 2)
Let y = 51797 + -51793. Factor 81/2*a**y + 50*a - 99*a**3 - 167/2*a**2 - 6.
(a - 3)*(a + 1)*(9*a - 2)**2/2
Let f(t) be the second derivative of -361*t**4/15 + 608*t**3/15 - 128*t**2/5 - 437*t. Factor f(v).
-4*(19*v - 8)**2/5
Determine l, given that -64/7 + 4/7*l**3 - 124/7*l - 8*l**2 = 0.
-1, 16
Let s(w) be the second derivative of -23*w - 1/30*w**6 - 1/56*w**7 + 1/24*w**3 + 1/12*w**4 + 0*w**2 + 0 + 1/40*w**5. Determine k so that s(k) = 0.
-1, -1/3, 0, 1
Determine r, given that 4/3 - 1/6*r**2 + 7/6*r = 0.
-1, 8
Suppose 0 = -q - 2 + 5. Suppose q*p = -2*p + 10. Let 6*u**2 + 2*u**4 + 4*u**3 + p*u**2 - 6*u**4 = 0. Calculate u.
-1, 0, 2
Suppose 12 = -7*o + 11*o. Let y(j) be the first derivative of -1/3*j**3 + 0*j**2 + 0*j + o - 1/4*j**4. Factor y(v).
-v**2*(v + 1)
Let h(j) be the third derivative of -j**6/30 + 4*j**5/15 + 7*j**4/2 - 2*j**2 - 141*j. Factor h(l).
-4*l*(l - 7)*(l + 3)
Let x(i) be the third derivative of -i**7/70 - 13*i**6/20 - 229*i**5/20 - 195*i**4/2 - 450*i**3 - i**2 + 103*i. Suppose x(s) = 0. What is s?
-10, -3
Let v(g) be the first derivative of 5*g**3/3 + 20*g**2 + 35*g + 177. What is n in v(n) = 0?
-7, -1
Let u be (-5 - (-3)/1) + 4. Suppose -j = 5*z + 8, u*j = 3*z + z + 12. Factor 4/9*m**3 - 4/9*m**j + 2/3*m**4 - 2/3*m + 2/9*m**5 - 2/9.
2*(m - 1)*(m + 1)**4/9
Let u = -2227/120 - -93/5. Let x(z) be the first derivative of 5/8*z**4 - 1/4*z**5 + 5 + u*z**6 - 5/6*z**3 - 1/4*z + 5/8*z**2. Suppose x(h) = 0. What is h?
1
Let r(v) be the second derivative of v**7/168 - v**6/24 + v**5/80 + 7*v**4/16 - 3*v**3/4 + 83*v - 6. Let r(p) = 0. Calculate p.
-2, 0, 1, 3
Let q = 1475/198 - -5/99. Let z = -346 - -349. Factor -3/2*d**5 - 15*d**z + q*d**4 + 3/2 - 15/2*d + 15*d**2.
-3*(d - 1)**5/2
Suppose -5*p + 1780*a - 1781*a = -16, -3*a = -5*p - 8. Find j such that 15/4*j**p - 9/4*j - 3/4*j**3 - 27/4 = 0.
-1, 3
Let s(p) be the second derivative of -p**6/90 + p**4/9 - 12*p - 2. Solve s(b) = 0.
-2, 0, 2
Let a(t) be the third derivative of t**6/180 + 2*t**5/9 + 25*t**4/9 + 3*t**2 - 35. What is x in a(x) = 0?
-10, 0
Let q(v) be the third derivative of v**5/80 - 17*v**4/32 + 21*v**3/4 - 475*v**2. Let q(x) = 0. What is x?
3, 14
Suppose q + 4*q + 4*j = 268, 4*j + 68 = q. Let o = q + -54. Let -4/7 - 38/7*c**3 + 2*c + 10/7*c**o - 30/7*c**4 = 0. Calculate c.
-1, 1/3, 2/5
Let j = 12 + -9. Let 13*m + 7*m**3 - m**3 - 8*m - m**j + 10*m**2 = 0. What is m?
-1, 0
Let a = -5756/3 + 1920. Let y(f) be the first derivative of 0*f + a*f**3 + 0*f**4 - 7 + 0*f**2 - 4/5*f**5. Determine l so that y(l) = 0.
-1, 0, 1
Suppose -7 + 57 = -5*y. Let c(d) = -7*d**4 + 4*d**3 + 3*d. Let h(f) = 22*f**4 - 12*f**3 - 10*f. Let k(o) = y*c(o) - 3*h(o). Solve k(v) = 0.
0, 1
Let k be 48/(-9) - -6 - (-92)/6. Suppose 4*g - 8*g + k = 0. Factor -3/4*u**g + 3/4*u**2 - 3/2*u**3 + 0 + 3/2*u.
-3*u*(u - 1)*(u + 1)*(u + 2)/4
Let d(n) be the first derivative of n**8/2520 - n**6/180 + n**5/90 + 8*n**3/3 - 10. Let x(u) be the third derivative of d(u). Factor x(f).
2*f*(f - 1)**2*(f + 2)/3
Let j(r) be the first derivative of r**7/378 + r**6/90 + r**5/180 - r**4/36 - r**3/27 - 9*r - 12. Let h(m) be the first derivative of j(m). Factor h(i).
i*(