t g = 319 + -955/3. Let d(i) be the third derivative of 0*i - 3/10*i**5 + 25*i**2 - 1/105*i**7 + 7/12*i**4 + 1/12*i**6 - g*i**3 + 0. Factor d(y).
-2*(y - 2)*(y - 1)**3
Let d(y) = -8*y**3 - 192*y**2 - 956*y + 28. Let q(z) = -9*z**3 - 191*z**2 - 954*z + 32. Let r(m) = -8*d(m) + 7*q(m). What is a in r(a) = 0?
-194, -5, 0
Suppose 8003*g = 8046*g - 172. Let f(i) = -i**3 + 3*i**2 + 4*i. Let z be f(4). Solve 0*b - 3/5*b**g - b**3 + 9/5*b**5 - 1/5*b**2 + z = 0 for b.
-1/3, 0, 1
Let d(n) be the second derivative of -n**5/450 + 13*n**4/90 - 115*n**2/2 + 38*n. Let l(v) be the first derivative of d(v). Factor l(u).
-2*u*(u - 26)/15
Let x(p) = 4*p**4 + 19*p**3 - 19*p**2 - 103*p. Let y(u) = -4*u**4 - 16*u**3 + 20*u**2 + 100*u. Let m(o) = 4*x(o) + 3*y(o). Determine b, given that m(b) = 0.
-7, -2, 0, 2
Let b = 68797/9 + -7644. Let r(k) be the second derivative of 4/9*k**3 - b*k**2 - 2/3*k**4 - 27*k + 0. Solve r(s) = 0 for s.
1/6
Let u be ((-208)/3640)/(9/(-315)). Let -1/2*f - 10 - 1/2*f**4 + 21/2*f**u + 1/2*f**3 = 0. What is f?
-4, -1, 1, 5
Let f(t) be the first derivative of -2*t**3/39 + 17*t**2/13 - 32*t/13 + 584. Suppose f(i) = 0. What is i?
1, 16
Let o = 874 - 13106/15. Let x(i) be the third derivative of 1/10*i**4 - 1/75*i**5 - o*i**3 - 16*i**2 + 0 + 0*i. Factor x(h).
-4*(h - 2)*(h - 1)/5
Suppose 1740 = 171*q + 1227. Let 5/4*i**4 - 15*i**q + 0 + 25*i**2 + 0*i = 0. Calculate i.
0, 2, 10
Suppose 5*n + 0*n = 3*g + 21, 2*g + 13 = 3*n. Suppose -w - 10 + 28 = -5*r, 0 = 2*w + r - 3. Factor -h**n - w*h**3 + 20*h - 461 + 4*h**2 + 473.
-4*(h - 3)*(h + 1)**2
Suppose 12 = 2*y + v, 473*v - 20 = 468*v. Let u(o) be the second derivative of 0 + 5/12*o**y + 1125/2*o**2 - 25*o**3 - 46*o. Factor u(d).
5*(d - 15)**2
Let x be (-108)/1332 - (-25425)/5550. Factor -1/4*h**2 - x - 11/4*h.
-(h + 2)*(h + 9)/4
Let y(z) = -2*z**3 - z**2 + 6*z + 2. Let f be y(2). Let p be (22/(-4) - -4)/(f/12). Solve 6/11*k**p + 0 + 4/11*k**2 + 0*k = 0.
-2/3, 0
Let l(h) be the third derivative of -h**7/1995 + h**6/570 + 13*h**5/570 - 7*h**4/114 - 8*h**3/19 + 374*h**2. Solve l(o) = 0.
-3, -1, 2, 4
Let n(f) be the second derivative of -f**4/18 + 15*f**3 - 327*f. Let n(k) = 0. What is k?
0, 135
Suppose 38*b - 44 = 30*b - 14*b. Determine g so that -3*g + 13/6*g**3 - 7/6*g**4 + 1/2*g**b + 1/6*g**5 + 0 = 0.
-1, 0, 2, 3
Let s(o) be the third derivative of -1/5*o**5 + 0 + 3/8*o**4 + 53*o**2 + 0*o - 1/40*o**6 + 9*o**3. Factor s(k).
-3*(k - 2)*(k + 3)**2
Let b(j) be the third derivative of -j**5/150 + 19*j**4/15 + 1157*j**3/15 - 5160*j**2 + 2*j. Factor b(q).
-2*(q - 89)*(q + 13)/5
Factor -40691192/15*h + 2/15*h**4 - 41141648/15 - 1642/15*h**3 + 149604/5*h**2.
2*(h - 274)**3*(h + 1)/15
Suppose -3*d - 317 = -404. Suppose 115*i**4 - 35*i**5 - d*i**3 - 49*i**3 + 45*i**3 + 20*i**2 - 67*i**3 = 0. What is i?
0, 2/7, 1, 2
Let f(h) be the third derivative of -1/180*h**6 - 5/12*h**4 + 7/90*h**5 + 0 + 0*h + 17*h**2 + h**3. Factor f(b).
-2*(b - 3)**2*(b - 1)/3
Let o = 357 - 203. Let y = -152 + o. Solve -3/7 - 3/7*k**y + 6/7*k = 0 for k.
1
Let t(s) = 35*s + 459. Let u be t(-13). Let c be u + (-9)/6*414/189. Find g such that 10/7*g**3 + 1/7*g**5 + 1/7 + 5/7*g**4 + c*g + 10/7*g**2 = 0.
-1
Let s(d) = d**3 + 6*d**2 - 9*d - 6. Let w be s(-7). Suppose -70*v + 66*v + w = 0. Solve -v*o**2 - 2*o**3 + 4/7 + 2/7*o**4 + 2/7*o + 4/7*o**5 = 0 for o.
-1, 1/2, 2
Let h(f) = -f**3 + 28*f**2 + 28*f - 13. Let i(u) = u**3 - 23*u**2 - 28*u + 14. Let s(l) = -6*h(l) - 7*i(l). Factor s(z).
-(z - 2)*(z - 1)*(z + 10)
Let x(f) be the second derivative of 3*f**5/20 + f**4/4 - 5*f**3/2 + 9*f**2/2 + 1390*f. Suppose x(p) = 0. What is p?
-3, 1
Let r(i) be the second derivative of 1/2*i**3 - 1/5*i**6 + i**4 - 3/10*i**5 + 4 + 6*i + 1/14*i**7 - 3*i**2. What is k in r(k) = 0?
-1, 1, 2
Suppose -298*r + 3576*r - 39336 = 0. Factor r - 9*h + 3/2*h**2.
3*(h - 4)*(h - 2)/2
Let w(m) = m**3 - 29*m**2 + 26*m + 61. Let n be w(28). Factor 2*h**2 - h**4 - 5*h**4 + 2*h**3 - 11*h**n + 4*h**4 + 9*h**5.
-2*h**2*(h - 1)*(h + 1)**2
Suppose -20 = -49*a + 39*a. Let c(h) = 4*h**3 - 4*h**2 - 9. Let v(d) = 3*d**3 - 3*d**2 - 6. Let x(b) = a*c(b) - 3*v(b). Factor x(i).
-i**2*(i - 1)
Let m(i) be the third derivative of -i**8/672 - 11*i**7/420 - i**6/60 + 8*i**5/15 + 2*i**4/3 - 20*i**3/3 - i**2 - 877*i. Suppose m(p) = 0. What is p?
-10, -2, 1, 2
Solve -4*f**2 - 98 - 176*f - 337 + 46*f + 5*f**2 + 4*f**2 = 0.
-3, 29
Suppose 3*d - q + 37 = 45, -q - 3 = -2*d. Let z(k) be the third derivative of 1/105*k**d + 14/3*k**3 + 1/3*k**4 + 35*k**2 + 0*k + 0. Factor z(h).
4*(h + 7)**2/7
Let t be (-28 + 2)*150/(-975). Factor -7/5*w**2 - 4/5*w + 1/5*w**t - 2/5*w**3 + 0.
w*(w - 4)*(w + 1)**2/5
Let k(f) be the third derivative of 0*f**4 + 0 + 1/200*f**6 + 3/200*f**5 + 13*f**2 + 2*f + 0*f**3 + 1/2100*f**7. Let k(s) = 0. What is s?
-3, 0
Suppose -33*j + 34080 = -j. What is b in 1041 + 44*b**2 - 51*b**4 - 42*b - j + 57*b**3 + 31*b**2 - 15*b**5 = 0?
-4, -1, -2/5, 1
Let s(n) = 9*n - 113. Let p be s(17). Let c be (-16)/p*(-270)/21. Factor 12/7*w - 1/7*w**2 - c.
-(w - 6)**2/7
Let f = 548 - 550. Let l be -38 + 38 - 72/f. Factor 0 + 6*v**2 - l*v**3 + 63/2*v**4 + 147/2*v**5 + 0*v.
3*v**2*(v + 1)*(7*v - 2)**2/2
Let f be (-60)/(-375) + 21/((-22050)/(-25557)). Solve -7*y - f - 1/2*y**2 = 0.
-7
Suppose 0 = 4*h + h - 590. Find q such that -223*q**4 + 3*q**3 - 3*q**5 + h*q**4 + 117*q**4 - 12*q**2 = 0.
-1, 0, 1, 4
Suppose 78*u = 144*u - 83*u. Let k(n) be the second derivative of -7*n + 2/15*n**6 + u*n**3 + 1/5*n**5 + 0*n**4 + 0*n**2 + 0. Factor k(q).
4*q**3*(q + 1)
Let t(d) be the second derivative of 0 + 10*d**2 - 1/120*d**4 - 27*d + 1/300*d**5 + 0*d**3. Let p(n) be the first derivative of t(n). Solve p(w) = 0 for w.
0, 1
Let p(n) be the third derivative of -n**8/784 + 9*n**7/490 + 23*n**6/280 - 9*n**5/140 - 11*n**4/28 - n**2 - n + 2467. Solve p(o) = 0 for o.
-2, -1, 0, 1, 11
Let z(g) be the third derivative of 0*g - 162*g**3 + 226*g**2 - 9/2*g**4 - 1/20*g**5 + 0. Solve z(h) = 0 for h.
-18
Suppose 0 = -5*j - 20, -4*j - 1 + 0 = 3*l. Factor 15*t**2 + 33 + 27 - 60 - l*t**4 - 10*t**3.
-5*t**2*(t - 1)*(t + 3)
Suppose 125 = 22*d - 205. Let x be (22 - 18) + (-5)/(d/12). Factor x + 2/15*b**4 + 16/5*b**2 - 6/5*b**3 - 32/15*b.
2*b*(b - 4)**2*(b - 1)/15
Let d(c) be the third derivative of -6*c**2 + 1/60*c**5 - 1/24*c**4 + 0*c**3 + 0*c + 0. Let p(j) = -j**2 - 7*j + 8. Let y(i) = 5*d(i) + p(i). Factor y(a).
4*(a - 2)*(a - 1)
Let -2/3*f**3 - 38/3*f**2 + 0 - 12*f = 0. What is f?
-18, -1, 0
Find c such that 0*c + 49/4*c**3 + 147/2*c**2 + 1/4*c**4 + 0 = 0.
-42, -7, 0
Let k(z) be the first derivative of 80/21*z**3 - 17/7*z**2 - 8/7*z - 14 - 12/35*z**5 - 13/14*z**4. Solve k(u) = 0.
-4, -1/6, 1
Let h(u) = 36*u + 254. Let w be h(-7). Solve 5320 - 3*r**w - 5316 + 2*r**2 = 0 for r.
-2, 2
Let l be 4/(-8)*(-2 - (-2 - -4)). Factor -6*o**l + 123 - 66 - 21*o - 75 - 2*o**2 - o**3.
-(o + 2)*(o + 3)**2
Let m(u) be the first derivative of 3/2*u**6 - 16 + 147/2*u**4 + 126*u**3 + 81/2*u**2 + 87/5*u**5 - 81*u. Factor m(r).
3*(r + 1)*(r + 3)**3*(3*r - 1)
Let t = -195610/3 + 65204. Suppose 17 = 4*p - 0*b - b, -2*p - 14 = 4*b. Find l such that 0 + t*l**p - 1/3*l**2 + 1/3*l**4 - 2/3*l = 0.
-2, -1, 0, 1
Let w = -32 - -17. Let y = w - -15. Find j such that y*j**4 - 3*j**2 + 15*j**3 + 5*j - 20*j - 4 + 9*j**4 - 2 = 0.
-1, -2/3, 1
Let v(h) = h**3 + 2*h**2 + 12. Let k be v(-3). Let c be (2/36)/((-7)/(-28)). Factor 0*s**2 - 4/9*s**k + c - 2/9*s**4 + 4/9*s.
-2*(s - 1)*(s + 1)**3/9
Let o(j) = -29*j**2 - 43*j - 72. Let g(n) = 5*n**2 + 7*n + 12. Suppose -3*p = -f - 0*p - 37, 171 = -5*f + p. Let l(i) = f*g(i) - 6*o(i). Factor l(h).
4*(h + 2)*(h + 3)
Suppose 2*s = f + 137 - 133, -3*s = f + 4. Let o(j) be the third derivative of 1/60*j**5 - 1/4*j**4 + 0*j + s + 3/2*j**3 + 7*j**2. Let o(m) = 0. What is m?
3
Let j = -103997/100 - -1040. Let y(w) be the second derivative of 7/2*w**3 + 15/2*w**2 + 42*w + 0 + 11/20*w**4 + j*w**5. Determine p, given that y(p) = 0.
-5, -1
Factor -1884/5*k**2 - 443682/5*k - 2/5*k**3 + 0.
-2*k*(k + 471)**2/5
Let q(d) = -14*d**3 + 2*d**2 - 4*d. Let c be q(-2). Determine o, given that -18*o**3 - c*o**4 + 18 + 182*o**2 + 286*o**3 + 17698*o - 17830*o - 64*o**5 = 0.
-3, -1, 1/4, 3/2
Let b(k) be the second derivative of -k**7/840 + 3*k**6/160 + k**