 r(x) = -x**3 - 3*x**2 + 6*x + 5. Let c be r(j). What is t in 0*t - c*t**2 + t + 23*t**2 + t**3 = 0?
0, 1
Let q(v) be the first derivative of 441*v**4/26 - 34132*v**3/13 + 4873*v**2/13 - 232*v/13 + 3464. Suppose q(h) = 0. Calculate h.
1/21, 116
Let n(o) be the third derivative of o**6/360 + 73*o**5/180 + 35*o**4/9 + 46*o**3/3 - 217*o**2. Factor n(v).
(v + 2)**2*(v + 69)/3
Let l(n) be the first derivative of -n**5/30 - n**4 + 19*n**3/9 + 152*n + 75. Let c(k) be the first derivative of l(k). Factor c(s).
-2*s*(s - 1)*(s + 19)/3
Let q(r) be the second derivative of 7/57*r**3 + 35 + 1/114*r**4 + 10/19*r**2 - r. Find s, given that q(s) = 0.
-5, -2
Suppose 2*f**3 + 7/2*f**2 - 1/4*f**5 - 7/4*f - 5/2 - f**4 = 0. What is f?
-5, -1, 1, 2
Let u(w) be the third derivative of -w**6/420 - 3*w**5/70 + 19*w**4/28 + 65*w**3/21 + 5718*w**2. Factor u(m).
-2*(m - 5)*(m + 1)*(m + 13)/7
Suppose -4*g + 709 = 677. Factor g*h + 5 + h**2 + 0*h - 4*h - 17.
(h - 2)*(h + 6)
Let n(p) be the second derivative of -p**4/48 - 37*p**3/12 - 18*p**2 + 27*p. Factor n(t).
-(t + 2)*(t + 72)/4
Let g(t) be the third derivative of 22*t**2 + 0*t**3 + 1/30*t**6 + 0 + 169/6*t**4 + 26/15*t**5 + 0*t. Factor g(y).
4*y*(y + 13)**2
Let c(g) be the second derivative of 60*g + 0*g**3 - 2/105*g**6 - 9/140*g**5 + 0 + 0*g**2 - 1/42*g**4. Factor c(w).
-w**2*(w + 2)*(4*w + 1)/7
Let r(h) be the first derivative of h**6/540 + 4*h**5/135 + 5*h**4/108 - 14*h**3/27 + 35*h**2 - 143. Let s(v) be the second derivative of r(v). Factor s(w).
2*(w - 1)*(w + 2)*(w + 7)/9
What is h in 6/7*h**2 - 2/7*h**4 + 86/7*h**3 - 262/7*h + 172/7 = 0?
-2, 1, 43
Let l(i) be the second derivative of -i**5/60 - 5*i**4/12 - 8*i**3/3 + 47*i**2 + 9*i - 4. Let v(g) be the first derivative of l(g). Factor v(d).
-(d + 2)*(d + 8)
Let v be (-6422)/(-342)*(-84)/(-364). Suppose 8/3*d**2 - 2 - v*d = 0. Calculate d.
-3/8, 2
Let w = 0 - 4. Let n be 10/w*(-36)/45. Determine p, given that 2*p**3 + 71*p**2 + 6*p - 39*p**n - 24*p**2 = 0.
-3, -1, 0
Let x(v) = 120*v**2 + 120*v - 135. Let m(s) = 7*s**2 + 7*s - 8. Let u = -55 + 36. Let g = u - -21. Let q(l) = g*x(l) - 35*m(l). Factor q(r).
-5*(r - 1)*(r + 2)
Let g(n) be the second derivative of 0*n**3 + 0*n**5 + 0*n**2 + 0*n**4 - 2*n + 64 - 2/75*n**6 - 1/105*n**7. Factor g(f).
-2*f**4*(f + 2)/5
Let m(b) be the first derivative of 0*b**3 - 1/40*b**5 - 16*b - 1/60*b**6 + 0*b**2 + 19 + 1/12*b**4. Let z(j) be the first derivative of m(j). Factor z(q).
-q**2*(q - 1)*(q + 2)/2
Let k(y) be the first derivative of -4*y**3/15 + 452*y**2/5 + 908*y/5 - 3558. Factor k(o).
-4*(o - 227)*(o + 1)/5
Factor 340 + 508/3*w - 1/3*w**2.
-(w - 510)*(w + 2)/3
Let v(o) = o. Let s(q) = -8*q + 38. Let x(u) = -s(u) - 6*v(u). Let b be x(20). Factor -18 + 3*j**3 + 3*j**3 + 9*j**b - 24*j + 30 - 3*j**4.
-3*(j - 2)*(j - 1)**2*(j + 2)
Let l(a) be the third derivative of a**5/480 - 91*a**4/48 - 61*a**3/4 + 9*a**2 + 9*a. Factor l(m).
(m - 366)*(m + 2)/8
Let u = 2753/8 - 13741/40. Suppose -3/5*m**2 - 1/5*m**4 + u*m**3 + 0 + 1/5*m = 0. Calculate m.
0, 1
Let r be (-860)/(-85) + ((-72)/(-12) - 15) + -1. Factor 0 + r*d**4 - 30/17*d**3 - 250/17*d + 150/17*d**2.
2*d*(d - 5)**3/17
Let y(t) be the first derivative of t**5/210 - t**4/42 - t**3/7 + 143*t**2/2 + 58. Let r(s) be the second derivative of y(s). Factor r(z).
2*(z - 3)*(z + 1)/7
Let n be (33 + -2 + 165464/(-5328))/(2/(-64)). Factor 0 + 10/3*k + 2/9*k**3 - n*k**2.
2*k*(k - 5)*(k - 3)/9
Let o(w) = -6*w**4 - 76*w**3 - 372*w**2 - 376*w - 7. Let b(n) = -n**4 + 2*n**3 - 1. Let a(q) = 21*b(q) - 3*o(q). Suppose a(t) = 0. What is t?
-2, 0, 94
Factor 38 - 17*d - 14*d - 3*d + 10*d + 7 + 3*d**2.
3*(d - 5)*(d - 3)
Suppose 2*j = f - 19, -4*f = 5*j - 212 + 136. Determine w, given that -14/3*w**2 - 24*w**4 - f*w**3 + 0 - 1/3*w = 0.
-1/3, -1/8, 0
Let f(o) be the second derivative of -13/27*o**3 + 1 + 2/9*o**4 - 4/45*o**6 - 1/189*o**7 + 7/45*o**5 + 3*o + 0*o**2. Determine l, given that f(l) = 0.
-13, -1, 0, 1
Let i(q) be the second derivative of -q**4/90 + 44*q**3/45 - 96*q**2/5 + 11*q - 197. Factor i(z).
-2*(z - 36)*(z - 8)/15
Let f(o) = 92*o**3 + 20840*o**2 - 41756*o + 20944. Let v(y) = 7*y**3 + 1603*y**2 - 3212*y + 1611. Let s(m) = -3*f(m) + 40*v(m). Factor s(a).
4*(a - 1)**2*(a + 402)
Let y(n) = n**2 - 21*n + 98. Let q be y(15). Factor 48*f**2 + 23*f**2 - 73*f**2 - q + 8*f.
-2*(f - 2)**2
Find n such that 3676/7*n - 1689122/7 - 2/7*n**2 = 0.
919
Let w(m) be the first derivative of m**5/5 - 7*m**4 + 33*m**3 - 36*m**2 - 1186. Factor w(c).
c*(c - 24)*(c - 3)*(c - 1)
Let j(z) = -2*z**3 - 20*z**2 + 36*z - 12. Let u(b) = 2*b**3 + 20*b**2 - 30*b + 10. Let m(y) = -5*j(y) - 6*u(y). Factor m(p).
-2*p**2*(p + 10)
Let m = 1673 + -1670. Let w(v) be the second derivative of 1/78*v**4 - 26*v - 2/39*v**m - 3/13*v**2 + 0. Factor w(l).
2*(l - 3)*(l + 1)/13
Let a(k) = -k**3 + 106*k**2 - 2589*k + 194. Let w be a(38). Let -88/9*p + 286/9*p**3 - 56/9*p**w - 16/9 - 98/9*p**5 - 28/9*p**2 = 0. Calculate p.
-2, -2/7, 1
Let g(a) be the first derivative of 0*a**2 + 0*a + 9/25*a**5 + 78 - 3/10*a**4 - 1/5*a**3. Let g(r) = 0. What is r?
-1/3, 0, 1
Let v(r) be the first derivative of 1/14*r**4 + 2/21*r**3 + 2/105*r**5 + 0*r + 1/21*r**2 - 9. Factor v(o).
2*o*(o + 1)**3/21
Let m be (648/(-9))/((-2)/(-6)). Let l be (-1 - 328/m)/(2/6). Factor -l*i**2 - 2/9*i**5 - 10/9*i**4 - 4/9*i - 2*i**3 + 0.
-2*i*(i + 1)**3*(i + 2)/9
Suppose 7*x - 80 = -73. Let m be ((-1)/7*x)/((-2)/4). Factor -1/7 - 1/7*c**5 - 1/7*c + m*c**3 + 2/7*c**2 - 1/7*c**4.
-(c - 1)**2*(c + 1)**3/7
Let i be (-25432)/154 + (-5)/(-35). Let g be 10/(-25)*(2 - i/(-70)). Suppose 1/7*z**2 + g + 2/7*z = 0. Calculate z.
-1
Find t, given that 0 + 20/7*t**4 + 22/7*t**3 + 0*t + 2/7*t**5 - 20*t**2 = 0.
-7, -5, 0, 2
Solve -1969/3*s**2 - 1448/3*s - 502/3*s**3 + 21*s**4 - 44/3 = 0 for s.
-2, -1, -2/63, 11
Suppose -2*p - f = -5 + 1, p + 5*f + 7 = 0. Find v such that 773871 + p*v**3 - 384975 + 54150*v - v**3 + 570*v**2 + 1325854 = 0.
-95
Let h = -391940/21 - -18669. Let j = -74/21 + h. Factor -j - 2/3*k**2 - 7/3*k.
-(k + 1)*(2*k + 5)/3
Let g = -14184 - -14186. Let k(h) be the second derivative of -22*h - 3/5*h**5 - 2/15*h**6 - 2/3*h**3 + 0*h**g + 0 - h**4. Factor k(w).
-4*w*(w + 1)**3
Let p = -210 + 277. Factor 31*i + 42*i - p*i - i**2 - i**2.
-2*i*(i - 3)
Let x(l) be the third derivative of -1/60*l**5 + 0 + 0*l - 11/6*l**3 + 28*l**2 - 1/2*l**4. Determine y so that x(y) = 0.
-11, -1
Let n = -141326 + 1837294/13. Suppose -18/13*m**5 - 16/13*m**2 - n*m**3 + 0*m + 0 - 60/13*m**4 = 0. What is m?
-2, -2/3, 0
Let g = -932/89 - 182858/267. Let z = -694 - g. Factor 1/3*q**3 + 0 - 1/3*q**4 - 4/3*q + z*q**2.
-q*(q - 2)*(q - 1)*(q + 2)/3
Factor -208849/2 - 1/2*l**2 + 457*l.
-(l - 457)**2/2
Let y = 3560 + -10670/3. Let c(s) be the first derivative of 15*s - 19 + y*s**3 - 35/2*s**2. Factor c(l).
5*(l - 3)*(2*l - 1)
Suppose -22*o - 212 = -212. Let c(w) be the first derivative of 0*w - 1/10*w**4 + 0*w**2 + o*w**3 - 2/25*w**5 - 12. Factor c(x).
-2*x**3*(x + 1)/5
Find w such that 4383*w + 30*w**3 - 8655*w + 4404*w - 3*w**4 - 99*w**2 - 60 = 0.
1, 2, 5
Let s = -213 - -215. Factor 19 - 72 + 0*h**s - 27*h + 3*h**2 + 23.
3*(h - 10)*(h + 1)
Let v(i) be the first derivative of -6655*i - 77 + 1815/2*i**2 + 5/4*i**4 - 55*i**3. Factor v(r).
5*(r - 11)**3
Let w be 2/(6*3/423). Suppose 44*m + 315 = w*m. Factor -113*h**3 + m*h**3 + 3*h**2 + 2*h**4 + 2*h**4 + h**2.
4*h**2*(h - 1)**2
Let g(p) = -p**2 + 5*p + 3. Let b be g(5). Let o be (-1)/b + 10/(-6) - -66. Factor -13*i**3 + 36*i**2 + 28*i**4 + o*i + 4*i**5 + 64*i**2 + 16 + 89*i**3.
4*(i + 1)**3*(i + 2)**2
Let q be -57 + (-38 - (-57 - 38)). Factor -279/7*z**3 + 114/7*z**2 + q + 0*z - 15/7*z**4.
-3*z**2*(z + 19)*(5*z - 2)/7
Let b(s) be the third derivative of -s**7/1680 + 17*s**6/960 - 91*s**5/480 + 49*s**4/64 - 1194*s**2 + 1. Factor b(a).
-a*(a - 7)**2*(a - 3)/8
Suppose f - 47 = -4*k, f - 58 = 70*k - 75*k. Let 2/11*w**f + 50/11 + 30/11*w - 18/11*w**2 = 0. What is w?
-1, 5
Let r(y) be the first derivative of y**5/2 + 20*y**4 + 145*y**3/6 - 155*y**2/2 - 3842. Determine z, given that r(z) = 0.
-31, -2, 0, 1
Let u(a) be the third derivative of -a**7/1050 - 19*a**6/300 - 47*a**5/100 - 43*a**4/30 - 34*a**3/15 - 13*a**2 - 5. Factor u(g).
-(g + 1)**2*(g + 2)*(g + 34)/5
Let 