x(c) = 0.
-3, 1
Suppose 0 = -102*u + 23*u - 431 + 479 + 347. Let -12/5 + 72/5*d + 27*d**3 + 9/5*d**u - 57/5*d**4 - 147/5*d**2 = 0. Calculate d.
1/3, 1, 2
Let n(q) be the first derivative of -q**3/9 + 16*q**2/3 + 68*q/3 - 113. Factor n(y).
-(y - 34)*(y + 2)/3
Let c(z) be the first derivative of z**4/2 + 40*z**3 + 227*z**2 + 336*z + 54. Factor c(l).
2*(l + 1)*(l + 3)*(l + 56)
Let s(t) = 7*t**2 - 10*t - 3. Let h(p) = 23*p**2 - 29*p - 10. Let u(k) = -3*h(k) + 10*s(k). Factor u(a).
a*(a - 13)
Let k(r) be the third derivative of r**8/6720 + r**7/240 - 8*r**5/5 - 76*r**2. Let s(w) be the third derivative of k(w). Find a, given that s(a) = 0.
-7, 0
Let o = -235099/600 - -2351/6. Let a(g) be the third derivative of -10*g + 0 - 4/15*g**3 - 1/30*g**5 - o*g**6 - 17/120*g**4 + 2*g**2. Solve a(s) = 0 for s.
-8, -1
Let x(i) be the third derivative of 2*i**6/45 - 2*i**5/15 - 5*i**4/24 + 25*i**3/18 - 68*i**2 + 2. Factor x(k).
(k + 1)*(4*k - 5)**2/3
Let i(b) be the first derivative of 1/35*b**5 - 2/21*b**3 + 3/7*b**2 - 5 - 8*b + 1/105*b**6 - 2/21*b**4. Let l(n) be the first derivative of i(n). Factor l(j).
2*(j - 1)**2*(j + 1)*(j + 3)/7
Solve -692/7*c**2 + 4/7*c**3 + 27360/7*c + 32400 = 0.
-7, 90
Let a(b) be the first derivative of -b**3/3 - 1110*b**2 - 1232100*b + 365. Factor a(h).
-(h + 1110)**2
Suppose -42 + 81 = -187*t + 227*t - 81. Suppose 2/5*d**4 - 16/5 - 4/5*d**2 + 24/5*d - 6/5*d**t = 0. Calculate d.
-2, 1, 2
Determine s so that 500*s - 132/5*s**2 + 152/5 = 0.
-2/33, 19
Let y(c) be the third derivative of -c**6/120 - 13*c**5/60 + 23*c**4/24 - 17*c**3 + 2*c**2 + 259*c. Let g be y(-15). Factor -4/3*k**2 + 2 + 1/3*k + 1/3*k**g.
(k - 3)*(k - 2)*(k + 1)/3
Let j be (10*(-66)/7040)/(270/(-4)). Let d(p) be the third derivative of 18*p**2 + 1/3*p**4 + 13/360*p**5 + 0*p + j*p**6 + p**3 + 0. Factor d(w).
(w + 1)*(w + 6)**2/6
What is m in -1920/11*m - 6/11*m**4 - 2400/11 - 144/11*m**2 + 96/11*m**3 = 0?
-2, 10
Let f(h) be the first derivative of 5*h**4/4 - 5*h**3/3 - 30*h**2 - 865. Factor f(w).
5*w*(w - 4)*(w + 3)
Let y(p) = -p**2 + p + 1. Let n(b) be the second derivative of 5*b**4/6 - b**3 - 9*b**2/2 - 64*b. Let t(j) = 2*n(j) + 18*y(j). Factor t(l).
2*l*(l + 3)
Let s(r) be the first derivative of -112/3*r**2 + 100/27*r**3 + 64*r - 46 - 1/9*r**4. Determine q so that s(q) = 0.
1, 12
Suppose -2*q + t - 6*t = -45, -2*q + 4*t + 36 = 0. Factor 3*s**4 + 520 - 15*s - 520 - 23*s**4 + 5*s**5 + 10*s**3 + q*s**2.
5*s*(s - 3)*(s - 1)**2*(s + 1)
Let a(l) be the third derivative of l**6/240 + l**5/15 + 13*l**4/48 + l**3/2 + 999*l**2. Solve a(g) = 0.
-6, -1
Factor 34/7*l - 2/21*l**3 + 16/7*l**2 - 5780/21.
-2*(l - 17)**2*(l + 10)/21
Let l(g) be the second derivative of 0*g**3 + 0*g**5 - 1/3780*g**7 + g + 0*g**6 + 0*g**2 + 5/6*g**4 + 4. Let u(k) be the third derivative of l(k). Factor u(f).
-2*f**2/3
Determine n so that 81*n + 67*n - 203*n + 206 + 70*n + 46 - 3*n**2 = 0.
-7, 12
Let i(t) be the third derivative of t**7/315 + 37*t**6/60 + 109*t**5/30 + 325*t**4/36 + 12*t**3 - 1677*t**2. Solve i(k) = 0 for k.
-108, -1
Suppose 15*p + 37 = 7. Let v be ((-10)/75)/(0 + 1/p). Factor 2/3*h**3 - 6/5*h**2 - v + 14/15*h - 2/15*h**4.
-2*(h - 2)*(h - 1)**3/15
Find z such that 5137432*z - 48 + 10*z**5 - 38*z**2 - 5137388*z - 78*z**3 + 73*z**2 - 2*z**4 + 39*z**2 = 0.
-3, -4/5, 1, 2
Factor -43 + 241*s + 9*s**2 - 8*s**2 + 37*s + 43.
s*(s + 278)
Let f(i) be the third derivative of -5/96*i**4 + 1/120*i**5 + 1/60*i**6 + 0 + 207*i**2 + 1/24*i**3 + 0*i. Factor f(t).
(t + 1)*(2*t - 1)*(4*t - 1)/4
Suppose 70*g = 67*g + 288. Solve 55*h + g + 23 + h**2 + 25 - 31*h = 0.
-12
Let c(t) = -17*t**3 + 13*t**2 + 10*t - 12. Let r be c(-4). Factor -4*b + 1248*b**3 + 3*b**2 + b**4 - 4 - r*b**3 + 0*b**4.
(b - 1)*(b + 1)*(b + 2)**2
Let c = -18/19 + 55/38. Let s(y) be the first derivative of 1/4*y**4 + 0*y + 7/3*y**3 + 7 + y**2 - c*y**6 - 7/5*y**5. What is l in s(l) = 0?
-2, -1, -1/3, 0, 1
Let g(f) = f**3 - 30*f**2 - 31*f + 5. Let u be g(31). Let -7*b**3 + 2*b**4 - 2272*b**5 - b**3 + 2273*b**u - 18*b**2 - 9*b = 0. Calculate b.
-3, -1, 0, 3
Let b = -43 + 45. Let h(m) = 2*m**3 - 2*m**2 + m. Let o be h(b). Solve -k**3 + o*k**3 - 9*k**2 - 3*k**4 + 15*k - 12*k + 0*k**4 = 0.
0, 1
Let r be -4 + 35/5 - 1107/105. Let l = -36/7 - r. Factor 12/5*c**2 + 4/5 - 4/5*c**3 - l*c.
-4*(c - 1)**3/5
Let a(n) = n**3 + 3*n**2 - 8*n + 12. Suppose 0*s = 4*s + 20. Let z be a(s). Factor -160*x**2 + 14*x**4 + 148*x**2 - z*x**4 + 3*x**5 + 9*x**3 - 12*x.
3*x*(x - 1)*(x + 1)*(x + 2)**2
Factor 7516*n + 5*n**2 + 907 + n**2 - 1223 + 4*n**2 - 2692.
2*(n + 752)*(5*n - 2)
Let p be ((-324)/(-24) - 9) + 1/(-2). Let t(q) be the first derivative of -30 + q**2 - 1/2*q**p - 14*q + 14/3*q**3. Factor t(c).
-2*(c - 7)*(c - 1)*(c + 1)
Suppose -7*d + 7*d + 2*d - 6*d = 0. Let x(a) be the third derivative of 0*a + 22/3*a**5 + d + 120*a**3 + 1/42*a**7 + 2/3*a**6 + 40*a**4 - 42*a**2. Factor x(p).
5*(p + 2)**2*(p + 6)**2
Let s(c) be the second derivative of -3*c**5/140 - 23*c**4/28 + 52*c**3/7 - 162*c**2/7 - 164*c. Factor s(k).
-3*(k - 2)**2*(k + 27)/7
Let a(w) be the third derivative of -w**5/390 + 41*w**4/39 + 55*w**3/13 + 2*w**2 + 2601*w + 1. Factor a(x).
-2*(x - 165)*(x + 1)/13
Let k(n) be the third derivative of -15*n**2 + 0*n**3 - 1/84*n**8 - 2/15*n**5 + 3/10*n**6 + 0 - 4/3*n**4 + 4/105*n**7 + 5*n. What is b in k(b) = 0?
-2, -1, 0, 1, 4
Let m(z) be the third derivative of 0*z**4 - 2/105*z**7 + 1/10*z**6 + 0*z**3 + 4 - 2/15*z**5 - 2*z**2 + 0*z. Factor m(i).
-4*i**2*(i - 2)*(i - 1)
Let n(q) be the first derivative of -2/5*q**5 - q**2 - 2*q + 80 - 1/3*q**6 + 4/3*q**3 + q**4. Factor n(f).
-2*(f - 1)**2*(f + 1)**3
Let l be (-38)/(-57)*-198*8/(-40). Suppose 1694/5*r**3 - 24*r + l*r**2 - 16/5 = 0. Calculate r.
-2/11, 2/7
Let t(l) = 2*l**3 - 9*l**2 - 14*l + 5. Let r be t(6). Suppose 3*w + r = 110. Factor -4*h**2 + w*h + 103 - 99 - 23*h - 4*h**3.
-4*(h - 1)*(h + 1)**2
Let h(a) be the first derivative of -a**4/48 - 37*a**3/36 - 14*a**2 - 75*a + 504. Factor h(b).
-(b + 6)**2*(b + 25)/12
Find i, given that 0 + 718/11*i**2 + 348/11*i - 1000/11*i**3 - 6*i**4 = 0.
-174/11, -1/3, 0, 1
Let j = 289 - 287. Factor 20*o - 75 + 5*o + 5*o - 3*o**j.
-3*(o - 5)**2
Determine q so that -4*q**2 + 372*q - 224 + 254*q - 506*q = 0.
2, 28
Let -980 - 5*d**2 - 142*d + 408*d - 543*d - 708*d = 0. Calculate d.
-196, -1
Let m(z) be the third derivative of z**8/2688 + z**7/84 + 5*z**6/48 - 24*z**2 + 76. Find x, given that m(x) = 0.
-10, 0
Suppose -3*j + 12 = j. Let s be (1 - (-20 - 420/(-20)))/(-1). Factor s*l + 3/7*l**4 - 3/7*l**5 + 0*l**j + 0*l**2 + 0.
-3*l**4*(l - 1)/7
Suppose 6*f = 3*r + r + f - 12, 0 = 4*f. Let j(s) = s - 20. Let m be j(20). Suppose 0*c - 15/2*c**r + 3*c**2 - 3/2*c**5 + 6*c**4 + m = 0. Calculate c.
0, 1, 2
Let h(v) be the third derivative of v**6/660 - 3*v**4/44 + 1585*v**2. Factor h(y).
2*y*(y - 3)*(y + 3)/11
Find m such that -5/7*m**4 + 4/7*m**5 + 2/7*m**2 - m**3 + 0*m + 0 = 0.
-1, 0, 1/4, 2
Let w(k) be the first derivative of -k**3/12 - 15*k**2/4 + 16*k + 867. Factor w(x).
-(x - 2)*(x + 32)/4
Let h(q) be the first derivative of -q**4 + 6*q**2 + 44 - 8/3*q**3 + 0*q. Factor h(g).
-4*g*(g - 1)*(g + 3)
Let c(m) = -2*m**2 - m - 8. Let u(i) = -9*i**2 + 623*i + 614. Let n(d) = 2*c(d) - u(d). Factor n(h).
5*(h - 126)*(h + 1)
Let y(n) be the first derivative of -4*n**5/15 + 10*n**4/3 - 68*n**3/9 - 56*n**2/3 + 344. Factor y(s).
-4*s*(s - 7)*(s - 4)*(s + 1)/3
Let s(u) be the second derivative of -8*u**2 + 36*u + 13/90*u**5 - 29/27*u**4 + 4*u**3 + 1 - 1/135*u**6. Let s(o) = 0. Calculate o.
2, 3, 6
Factor -4255443/4 - 3/4*x**2 - 3573/2*x.
-3*(x + 1191)**2/4
Factor -615/8*b**3 + 0 + 249/8*b**2 - 25/8*b**4 - 25/8*b.
-b*(b + 25)*(5*b - 1)**2/8
Let a = 60 + -60. Let i be (-6)/(-3) - (a/3 + -1). Find b such that i*b**2 + 2*b + 54 - 39 - 12*b - 8*b = 0.
1, 5
Let i(f) be the second derivative of -f**6/30 + f**5/2 + f**4 - 5*f**3/3 - 11*f**2/2 - 2008*f. Suppose i(n) = 0. Calculate n.
-1, 1, 11
Suppose -59 = 7*n + 88. Let t = n + 42. Suppose -g**2 - 64*g + 23*g + 18*g + t*g + g**3 = 0. Calculate g.
-1, 0, 2
Let y = 229/1683 + -14/561. Let i(v) be the first derivative of -1/3*v**2 - 24 + v - y*v**3. Solve i(w) = 0.
-3, 1
Let j(i) be the third derivative of 5*i**8/112 - 19*i**7/210 - 19*i**6/40 + 9*i