
-1, 2
Let j = -990 + 991. Let t(k) be the first derivative of 0*k**2 + 0*k - 1/18*k**4 - j - 2/27*k**3. Suppose t(p) = 0. What is p?
-1, 0
Let j = 2371 - 2369. Factor -1/6*f + 0 + 0*f**j + 1/6*f**3.
f*(f - 1)*(f + 1)/6
Let o = 471 - 468. Let k(g) be the third derivative of 6*g**2 + 0 - 2/3*g**4 - 1/10*g**6 + 0*g**o - 1/105*g**7 + 0*g - 2/5*g**5. Factor k(r).
-2*r*(r + 2)**3
Let c = 9 - 1. Suppose -5*z - 3*k + 2*k = -16, 8 = -2*k. Find n, given that 13*n - 12*n**2 - 2*n**z - 2 + 8*n**3 + 3*n - c*n = 0.
1
Let b(y) be the third derivative of y**9/120960 + 3*y**5/20 + 2*y**2. Let c(k) be the third derivative of b(k). Factor c(g).
g**3/2
Solve 2/17*r**4 + 82/17*r**2 + 26/17*r**3 + 94/17*r + 36/17 = 0.
-9, -2, -1
Let t(n) be the first derivative of -5*n**4/14 + 34*n**3/21 - 16*n**2/7 + 8*n/7 - 17. Determine r, given that t(r) = 0.
2/5, 1, 2
Let k(q) be the second derivative of -q**4/4 + 17*q**3/2 + 57*q**2 - 311*q. Solve k(f) = 0 for f.
-2, 19
Let g(p) be the second derivative of p**3/2 - 7*p**2/2 - p. Let h be g(3). Solve 11 + 3*r**3 + 3 - h - 9*r**2 = 0.
-1, 2
Let w(x) be the first derivative of 19 + 0*x + 1/3*x**2 + 1/9*x**3. Factor w(d).
d*(d + 2)/3
Let b(j) be the second derivative of 2*j**7/9 + 2*j**6/9 - 3*j**5/5 - 5*j**4/9 + 4*j**3/9 + 179*j. Let b(d) = 0. What is d?
-1, 0, 2/7, 1
Let g(i) = -38*i**2 - i - 11. Let q(x) = 7*x**2 + 2. Let r(l) = -2*g(l) - 11*q(l). Let r(j) = 0. What is j?
0, 2
Let v be (-1 + -1 - -24) + (-6 - -4). Factor -v*d - 9*d**3 + 16*d**2 - 3 + 1 + 10 + 5*d**3.
-4*(d - 2)*(d - 1)**2
Solve -38/7 + 2/7*v**2 - 36/7*v = 0 for v.
-1, 19
Suppose -14*g + 17*g = 0. Let u(f) be the third derivative of -2*f**2 - 1/120*f**6 - 1/8*f**4 + 0*f + 1/20*f**5 + g + 1/6*f**3. Factor u(p).
-(p - 1)**3
Suppose -4*y = 5*c - 43, -6*c + 9*c - 13 = 4*y. Factor -2/9*u - 2/3*u**y + 4/9 + 2/9*u**3 + 2/9*u**4.
2*(u - 1)**2*(u + 1)*(u + 2)/9
Let l = 50 + -53. Let w = -3 - l. Find h, given that -1/2*h - 3*h**3 + 2*h**2 + 2*h**4 + w - 1/2*h**5 = 0.
0, 1
Let k = 15559 + -15556. Let u = 53/18 + -13/9. Factor -3 + k*v**2 + u*v**3 - 3/2*v.
3*(v - 1)*(v + 1)*(v + 2)/2
Let i(n) be the third derivative of n**5/105 + n**4/14 - 9*n**2 + 5*n. Suppose i(r) = 0. Calculate r.
-3, 0
Let w be 10 + 990/(-105) - 1/14. Let u(r) be the third derivative of 0*r**4 + 0 + w*r**3 + 0*r**6 - 1/10*r**5 + 0*r + 1/70*r**7 + 15*r**2. Factor u(j).
3*(j - 1)**2*(j + 1)**2
Let p be (-6)/(-4) + (0 - 1). Let x = -389/12 - -199/6. Suppose 0*z**2 - x*z - p + 1/4*z**3 = 0. Calculate z.
-1, 2
Factor 528*o**3 - 1056*o**3 + 7*o + 530*o**3 + o**2 + o**2 + 16 - 27*o.
2*(o - 2)*(o - 1)*(o + 4)
Factor 18*b**2 - 11239*b - b**4 + 52*b**3 + 11239*b + 35*b**2.
-b**2*(b - 53)*(b + 1)
Let v(w) = -13*w**4 + 344*w**3 - 4368*w**2 - 4697*w - 7. Let g(j) = -4*j**4 + 114*j**3 - 1456*j**2 - 1566*j - 2. Let n(d) = -7*g(d) + 2*v(d). Factor n(k).
2*k*(k - 28)**2*(k + 1)
Let j = -329 - -336. Let r(g) be the third derivative of 1/90*g**5 + 0 - j*g**2 - 1/360*g**6 + 0*g**3 + 0*g - 1/72*g**4. Factor r(c).
-c*(c - 1)**2/3
Let d(g) = -2*g - 9. Let x be d(-8). Let z be x/4 - 4/(-16). Let m**5 - z*m**4 + 0*m**5 + m**4 = 0. Calculate m.
0, 1
Suppose -4*f = -4*c - 32, -2*f + 4*c = -5*f + 52. Let 3*p**5 - f*p**4 - 15*p**5 - 8*p**3 - 8*p**4 = 0. What is p?
-1, -2/3, 0
Let x(j) be the second derivative of -j**8/43680 + j**7/8190 + j**6/1560 - j**4/12 + 6*j. Let q(h) be the third derivative of x(h). Factor q(c).
-2*c*(c - 3)*(c + 1)/13
Let z(p) be the third derivative of 0*p - 1/6*p**4 + 0*p**3 - 4*p**2 - 1/15*p**5 - 1/120*p**6 + 0. Solve z(f) = 0.
-2, 0
Let l be 28/(-126) - 184/(-18). Suppose l*f = 4*f. Factor f - 2/7*t**2 + 0*t.
-2*t**2/7
Suppose 0 = -v + 22 + 86. Suppose -5*h = -133 + v. Suppose 16*x**4 + 32/3*x**h + 0 + 6*x**3 + 2/3*x**2 + 0*x = 0. Calculate x.
-1, -1/4, 0
Let b(i) = i + 12. Let z be b(-13). Let w be 2/(-21)*-27 - (z - -3). Factor -w*n + 0 + 2/7*n**2.
2*n*(n - 2)/7
Factor 484/5*j**3 + 16384/5 + 44032/5*j + 7872/5*j**2 + 2*j**4.
2*(j + 16)**3*(5*j + 2)/5
Let t(b) be the first derivative of b**3 + 0*b + 1/60*b**6 - 5/2*b**2 - 1/12*b**4 - 1/10*b**5 + 6. Let s(g) be the second derivative of t(g). Factor s(w).
2*(w - 3)*(w - 1)*(w + 1)
Let t be 1/(2 - 8 - 133/(-21)). Let k be 46/(-12) + 1 + 3. Factor 1/6*x**t - k*x**4 + 1/6*x**2 + 0 - 1/6*x.
-x*(x - 1)**2*(x + 1)/6
Let j be ((-6)/10)/3 + 23/65. Let r = 23/65 - j. Find x such that r*x**2 + 2/5*x - 3/5 = 0.
-3, 1
Let d(l) = 4*l**3 + 36*l**2 + 96*l + 114. Let f(k) = 4*k**3 + 36*k**2 + 98*k + 113. Let a(y) = 5*d(y) - 6*f(y). Factor a(z).
-4*(z + 3)**3
Suppose 42 = g + 2*l, l + 212 = 4*g - 2*l. Let -c**4 + 4*c**4 - g*c**3 + 47*c**3 = 0. Calculate c.
0, 1
Let x(z) be the second derivative of z**4/4 + 5*z**3/2 - 75*z**2 + 112*z. Factor x(i).
3*(i - 5)*(i + 10)
Let o(p) be the second derivative of -1/360*p**6 + 0 + 3*p**2 + 6*p - 1/9*p**4 + 1/36*p**5 + 2/9*p**3. Let w(j) be the first derivative of o(j). Factor w(t).
-(t - 2)**2*(t - 1)/3
Let n(o) = 3*o**3 + 17*o**2 + 1809*o - 4*o**3 - 1825*o. Let w be n(16). Determine k so that -24/7*k - 18/7*k**3 + 3/7*k**4 + w + 36/7*k**2 = 0.
0, 2
Let z(n) be the third derivative of n**6/60 + 3*n**5/10 - n**4/12 - 3*n**3 + 7*n**2 - 14*n. Factor z(q).
2*(q - 1)*(q + 1)*(q + 9)
Let b(r) be the second derivative of r**6/10 + 6*r**5/5 - 15*r**4/4 - 27*r**3 - r + 167. Factor b(x).
3*x*(x - 3)*(x + 2)*(x + 9)
Let y be 123/287 + (-351)/84 + (0 - -4). Factor -1/2*k + y*k**3 + 1/4*k**2 + 0.
k*(k - 1)*(k + 2)/4
Let v(q) be the third derivative of 2/735*q**7 - 1/21*q**4 + 0*q**5 + 0*q + 0 + 1/105*q**6 - 2/21*q**3 + 9*q**2. Find c such that v(c) = 0.
-1, 1
Let n(t) = -5*t**2 - 7*t - 4. Let j(a) = 11*a**2 + 15*a + 8. Let l(y) = -4*j(y) - 9*n(y). Let v be l(-3). Factor 2 - 2*q - v*q + 6*q + q**2 + 3*q.
(q + 1)*(q + 2)
Factor -384/7 - 6/7*d**2 + 96/7*d.
-6*(d - 8)**2/7
Let p = 14776/225 + -1614/25. Factor 4/9*s + 2/9*s**4 + p*s**2 + 8/9*s**3 + 0.
2*s*(s + 1)**2*(s + 2)/9
Let z(w) be the second derivative of 2*w**7/21 - 3*w**5/5 + 2*w**4/3 + 281*w. Find u such that z(u) = 0.
-2, 0, 1
Suppose 4*i = 9*i + 105. Let x = -19 - i. Solve -5*h + 17*h + 78*h**x - 81*h**2 = 0 for h.
0, 4
Factor -23/9*a**3 + 0 - 22/9*a**2 - 1/9*a**4 + 0*a.
-a**2*(a + 1)*(a + 22)/9
Let n(h) be the second derivative of -3*h**5/2 - 35*h**4/12 - 5*h**3/6 - 335*h. Factor n(w).
-5*w*(w + 1)*(6*w + 1)
Suppose -5*j + 5 = -3*k, -4*k + 9*k - 3 = -3*j. Suppose 5*d - 28 = -m, 4*m = -10*d + 5*d + 37. Factor 0 + k*o + 1/4*o**4 - 1/4*o**m + 0*o**2.
o**3*(o - 1)/4
Find k such that 0 + 1/2*k**2 - 1/8*k**4 - 1/8*k**5 + 0*k + 1/2*k**3 = 0.
-2, -1, 0, 2
Let a(n) = 2*n**2 + n + 1. Let f be (-1)/((((-2)/(-5))/1)/(-2)). Let x(r) = r**2 + r + 1. Let v(w) = f*a(w) - 5*x(w). Suppose v(s) = 0. What is s?
0
Let s be (-29 - -17 - -8)*(-1)/5. Factor -s*u + 2/5*u**2 - 6/5.
2*(u - 3)*(u + 1)/5
Let z be ((-736)/96 + 15/3)*-1. Find f such that 16/3*f - 4/3*f**3 + z*f**2 - 32/3 = 0.
-2, 2
Let z(p) be the first derivative of 4*p**3/3 - 14*p**2 + 40*p + 26. Suppose z(q) = 0. Calculate q.
2, 5
Let g(m) = 10*m**3 - 9*m**2 - 60. Let s(r) = 7*r**3 - 6*r**2 - 40. Let w(c) = -5*g(c) + 7*s(c). Let o(d) be the first derivative of w(d). Factor o(j).
-3*j*(j - 2)
Let u(j) be the third derivative of 0 + 5/6*j**3 + 1/60*j**5 + 0*j - 1/4*j**4 - 4*j**2. Solve u(i) = 0 for i.
1, 5
Let f be (-53)/(-225) + 3*6/(-81). Let w(n) be the third derivative of -f*n**6 + 1/15*n**3 - 1/15*n**4 + 0*n + 0 + 1/525*n**7 + 1/25*n**5 - 6*n**2. Factor w(g).
2*(g - 1)**4/5
Let f(o) be the first derivative of -3*o**5/80 + o**4/6 - 7*o**3/24 + o**2/4 + 18*o + 10. Let i(l) be the first derivative of f(l). Factor i(k).
-(k - 1)**2*(3*k - 2)/4
Let b(k) be the third derivative of -k**6/40 + k**5/4 + 3*k**4/4 + 133*k**2. Find n, given that b(n) = 0.
-1, 0, 6
Let o(c) be the first derivative of c**6/20 + 9*c**5/40 + 3*c**4/8 + c**3/4 + 14*c - 13. Let g(x) be the first derivative of o(x). Let g(y) = 0. Calculate y.
-1, 0
Let c(i) = -7*i**3 + 17*i**3 + 7 - 7*i - 9*i**3 + 2*i**2. Let v be c(-4). What is h in 1/4*h**4 + 0*h**v - 3/4*h**2 + 1/2*h + 0 = 0?
-2, 0, 1
Let u(i) be the second derivative of 2*i**7/7 - 22*i**6/15 + 14*i**5/5 - 2*i**4 - 2*i**3/3 + 2*i**2 - 70*i. Factor u(z).
4*(z - 1)**4*(3*z + 1)
Let k be (-13)/5 + (-8)/20. Let o(g) = -4*g**2