-3, 0
Let j = -177/26 + 21253/3120. Let t(r) be the third derivative of -3/16*r**4 + 0*r - 20*r**2 + 0 + j*r**5 + 27/8*r**3. Find s such that t(s) = 0.
9
Suppose -1/7*o**2 - 6404/7*o - 10252804/7 = 0. Calculate o.
-3202
Let r(h) = -3*h**4 + 46*h**3 - 178. Let x(j) = -j**4 - j**3. Let w(y) = -r(y) + 2*x(y). Let d(b) be the first derivative of w(b). Factor d(s).
4*s**2*(s - 36)
Let s = -804511/5 - -160903. Suppose 1/5*u**3 + 0*u - s - 1/5*u**5 + 7/5*u**2 - 3/5*u**4 = 0. What is u?
-2, -1, 1
Let d be 2/18 - (-429)/27. Let k = d - 13. Factor -40*s**4 + 21 + 19 + 14*s**2 + 35*s**4 - 4*s**2 + 15*s**k - 60*s.
-5*(s - 2)**2*(s - 1)*(s + 2)
Let o(a) be the third derivative of a**7/525 + 11*a**6/150 + 11*a**5/50 - 34*a**4/15 + 16*a**3/3 - 2*a**2 + 87*a. Suppose o(h) = 0. What is h?
-20, -4, 1
Let p(u) be the first derivative of u**7/3780 - 2*u**6/405 + 4*u**5/135 + 37*u**3 - 2*u + 59. Let x(r) be the third derivative of p(r). Factor x(c).
2*c*(c - 4)**2/9
Let s(q) be the third derivative of q**5/30 - 419*q**4/6 + 175561*q**3/3 - 2816*q**2. Factor s(g).
2*(g - 419)**2
Suppose 0 = -231*g + 228*g + 12. Suppose -l - g = -5*a + 3, 4*l - 10 = a. Determine c, given that 0*c**2 + 2*c - 2/3*c**l - 4/3 = 0.
-2, 1
Let f be (22 + (-1624)/84)/(24/27). Solve -12/5 - 34/5*w + 2/5*w**4 - 6*w**2 - 6/5*w**f = 0.
-1, 6
Let 45*m + 2653*m**5 - 39*m**3 - 24*m - 18 - 2637*m**5 - 24*m**4 + 40*m**2 = 0. What is m?
-1, 3/4, 2
Suppose 12 = 4*p - c - 3*c, p = -4*c + 13. Let i = -5 - -12. Factor 20*d**4 - 8*d**p + i*d**5 - 36*d**3 - 8*d - 3*d**5 + 28*d**2.
-4*d*(d - 2)*(d - 1)**3
Let d(r) be the first derivative of -2*r**5/45 + 7*r**4/9 - 70*r**3/27 - 50*r**2/9 + 3363. Find i, given that d(i) = 0.
-1, 0, 5, 10
Let f(o) be the second derivative of 7*o**5/60 + 19*o**4/18 + 11*o**3/18 - 10*o**2/3 + 3855*o. Factor f(d).
(d + 1)*(d + 5)*(7*d - 4)/3
Let s(m) be the second derivative of m**5/10 + m**4/3 - 32*m**3/3 - 96*m**2 - 10*m + 9. Factor s(n).
2*(n - 6)*(n + 4)**2
Let y = 695941/84 + -8285. Let f(v) be the third derivative of 0 - 1/15*v**6 - 1/6*v**4 - 1/12*v**3 + 11*v**2 - y*v**7 + 0*v - 3/20*v**5. Factor f(z).
-(z + 1)**3*(5*z + 1)/2
Let b(t) be the second derivative of -t**5/480 - t**4/48 - t**3/12 + 30*t**2 + 74*t. Let a(c) be the first derivative of b(c). Let a(m) = 0. Calculate m.
-2
Let v(n) be the second derivative of 2*n**2 - 14 - 1/6*n**4 - 3*n + 1/3*n**3. Suppose v(r) = 0. What is r?
-1, 2
Suppose 24*c + 17 = 79 + 10. Let b(d) be the third derivative of 0*d**c + 2/33*d**4 + 1/330*d**5 + 15*d**2 + 2 + 0*d. Factor b(m).
2*m*(m + 8)/11
Let g(s) = -2*s**3 + 6*s**2 + 378*s + 706. Let z(m) = 3*m**3 - 13*m**2 - 757*m - 1413. Let h(a) = 5*g(a) + 2*z(a). Factor h(y).
-4*(y - 11)*(y + 2)*(y + 8)
Factor 0*a + 1/5*a**4 + 0 + 6/5*a**2 + a**3.
a**2*(a + 2)*(a + 3)/5
Let t(o) = 2*o**3 + 55*o**2 - 52*o - 3. Let z(g) = 8*g**3 + 209*g**2 - 208*g - 11. Let s(r) = -22*t(r) + 6*z(r). Determine d so that s(d) = 0.
-13, 0, 2
Let t(p) = 39*p**2 - 2958*p - 1200. Let l(i) = 15*i**2 - 1183*i - 480. Let d be 424/88 + 8/44. Let s(z) = d*t(z) - 12*l(z). Factor s(a).
3*(a - 40)*(5*a + 2)
Let a(m) = -7*m**2 - 8*m**2 - m + 16*m**2. Let j(o) = 31*o**2 + 17*o - 8. Let f be -2 + 2 - (-11)/11. Let i(u) = f*j(u) - 3*a(u). Suppose i(q) = 0. Calculate q.
-1, 2/7
Let z(m) be the first derivative of m**6/3 + 6*m**5/5 + m**4/2 - 2*m**3 - 2*m**2 - 2836. Factor z(g).
2*g*(g - 1)*(g + 1)**2*(g + 2)
Let x(r) = r**4 + 3*r**3 - 2. Let k(w) = 15*w**4 + 2850*w**3 - 6485*w**2 + 4464*w - 828. Let f(u) = -3*k(u) + 24*x(u). Solve f(g) = 0 for g.
-406, 2/7, 1
Let b(j) be the third derivative of -81/14*j**4 + 1/490*j**7 + 108/7*j**3 + 0*j - 61*j**2 + 0 + 9/10*j**5 - 19/280*j**6. Factor b(d).
3*(d - 6)**3*(d - 1)/7
Let p be (12/350)/((2496/(-130))/(-32)). Let c(x) be the first derivative of -2/21*x**3 - 22 + 0*x + p*x**5 + 0*x**4 + 0*x**2. Suppose c(b) = 0. What is b?
-1, 0, 1
Let v(a) be the second derivative of -2*a**7/21 - 154*a**6/15 - 1514*a**5/5 - 988*a**4/3 + 5776*a**3 - 837*a. Let v(b) = 0. Calculate b.
-38, -3, 0, 2
Let g(i) = i**3 + 3*i**2 - 79*i - 355. Let q be g(-7). Let 1/2*f**q - 2*f + 0 = 0. What is f?
0, 4
Solve -71/5*a + 132 + 1/5*a**2 = 0.
11, 60
Let r(d) be the second derivative of 5*d**4/12 - 2480*d**3/3 + 615040*d**2 - 642*d - 2. Determine x so that r(x) = 0.
496
Let f(s) be the first derivative of 1/36*s**6 + 0*s**4 - 1/10*s**5 + 0*s**3 + 0*s**2 + 40 + 0*s. Find c such that f(c) = 0.
0, 3
Suppose 0 = 11*a - 522 - 314. Suppose a*d - 81*d = 2*q - 10, 2*d + q - 5 = 0. Let 2*r**2 + d*r + 0 - 1/6*r**4 + 1/6*r**5 - 4/3*r**3 = 0. What is r?
-3, 0, 2
Let f be 16 + (-423)/63 - ((-3 - -10) + 2). Suppose 0 = -i + o + 3, -5*i - o = 2*o - 7. Find u such that 2*u + 0 + f*u**i = 0.
-7, 0
Let i = -185/277 - -1/831. Let s = i + 8/5. Factor -32/15*d - s*d**2 - 8/15.
-2*(d + 2)*(7*d + 2)/15
Let v(d) = d**3 - d**2 + 4*d - 5. Let l(w) = -14*w**3 - 14*w**2 + 10*w + 30. Let j(t) = -l(t) - 12*v(t). Factor j(m).
2*(m - 1)**2*(m + 15)
Let m(q) be the first derivative of q**5/5 - 13*q**4/4 - 5*q**3 + 13*q**2/2 + 14*q + 6980. Let m(w) = 0. Calculate w.
-1, 1, 14
Let i = -124/9 - -275/18. What is c in 27/2 + 15*c + i*c**2 = 0?
-9, -1
Let d(s) be the third derivative of 43*s - 3*s**2 - 20/3*s**5 + 0 - 6*s**3 - 25/12*s**6 - 35/4*s**4. Let d(c) = 0. What is c?
-3/5, -2/5
Suppose -80 = -7*f - 3*f. Suppose f*r - 7*r = 7. Solve r*b**4 - 12*b**3 - 15*b**2 - 24*b**4 - 6*b + 14*b**4 = 0.
-2, -1, 0
Let f = -1258 + 1259. Let m be f/((-30)/(-237)) + 8/(-20). Factor -15/2*j**2 + 5*j**3 + 5 - m*j.
5*(j - 2)*(j + 1)*(2*j - 1)/2
Let h(v) be the third derivative of -7*v**2 + 0 + 2*v + 1/6*v**4 - 1/30*v**6 + 1/5*v**5 - 2*v**3. Factor h(i).
-4*(i - 3)*(i - 1)*(i + 1)
Let s(o) be the third derivative of 38*o + 0 - o**2 - 1/78*o**4 - 1/13*o**3 + 1/390*o**5. Factor s(v).
2*(v - 3)*(v + 1)/13
Factor -289/4*n**3 - 10 - 1411/2*n**2 + 169*n.
-(n + 10)*(17*n - 2)**2/4
Let a be 397/16 + 375/2000. Let i(b) be the first derivative of -11/6*b**2 + a + b**3 + 2/3*b. Determine r so that i(r) = 0.
2/9, 1
Find k, given that 0 + 0*k + 3081/4*k**2 - 3/8*k**3 = 0.
0, 2054
Let n be 2 + -3 + 18/6. Factor 52*u**2 - 30 + 62*u**2 - 25*u - 119*u**n.
-5*(u + 2)*(u + 3)
Suppose 2*z - 15*j - 13 = -16*j, z - 2*j + 6 = 0. Suppose -20 = -5*v + 2*t, -z*v + 31 = 5*t + 15. Factor -4/5*y**3 - 2/5*y**v + 0*y - 2/5*y**2 + 0.
-2*y**2*(y + 1)**2/5
Let j(p) = -8*p + 203. Let g be j(25). Factor -136*i**3 + 140*i**g + 5 + 2 - 7 + 4*i**4.
4*i**3*(i + 1)
Let a(y) = -y**4 - 3*y**3 + y**2 + y + 6. Let c(v) = -12*v**4 - 93*v**3 + 204*v**2 + 339*v - 2178. Let g(x) = -15*a(x) + c(x). Suppose g(b) = 0. Calculate b.
-3, 6, 7
Let u = -2812 + 19756/7. Factor -2/7*f**2 - 648/7 + u*f.
-2*(f - 18)**2/7
Let z be ((-252)/(-27) + -12)/(2/(-3)). Factor -2*f**3 - 2*f**5 + 7*f**5 - z*f**4 - 7*f**5.
-2*f**3*(f + 1)**2
Suppose 171 = -4*k + 7*k. Let p = -55 + k. Determine h so that -77*h**p + 0*h**3 - 3*h**3 + 648 - 324*h + 131*h**2 = 0.
6
Let c = 62434/7 - 8918. Let h(m) be the first derivative of -c*m + 25 + 1/6*m**6 + 26/7*m**2 + 103/28*m**4 - 44/35*m**5 - 110/21*m**3. Solve h(u) = 0.
2/7, 1, 2
Determine c so that 0*c**5 + 28*c - 68*c**2 - 156427*c**4 + 51*c**3 - c**5 + 156417*c**4 = 0.
-14, 0, 1, 2
Let b = 672 + -666. Let t be (-3)/((30/b)/(-5)). Determine a, given that 0 + t*a**2 - 2/3*a - a**3 - 4/3*a**4 = 0.
-2, 0, 1/4, 1
Suppose -1982 = -432*w - 118*w - 441*w. Factor 0 + 14/5*k**3 + 0*k + 2*k**4 + 2/5*k**5 + 6/5*k**w.
2*k**2*(k + 1)**2*(k + 3)/5
Let a = -163 + 168. Factor -10*n**3 + 6263*n**5 + 18*n**2 - 11*n**3 - 6260*n**a.
3*n**2*(n - 2)*(n - 1)*(n + 3)
Factor 0 + 2/9*y**4 + 0*y - 8/9*y**3 + 8/9*y**2.
2*y**2*(y - 2)**2/9
Let b(r) be the first derivative of -r**6/1260 + 17*r**5/140 + r**3/3 + 9*r**2/2 - 119. Let h(y) be the third derivative of b(y). Factor h(w).
-2*w*(w - 51)/7
Suppose -r + 17 = 3*w, r = -r + 10. Factor 9*z + 19*z + 46*z**2 - 74*z**2 + 4*z - w*z**3.
-4*z*(z - 1)*(z + 8)
Let o(t) be the third derivative of -t**6/30 - 194*t**5 - 470450*t**4 - 1825346000*t**3/3 - 161*t**2 + 3. Factor o(q).
-4*(q + 970)**3
Solve 4 - 4 + 150*h**2 - 377*h**3 + 379*h**3 = 0 for h.
-75, 0
Suppose 4*y - 66 = -3*i, -5*i + 5 = 3*y - 50. Let o be 4 - 10/y*6. Solve o*n**2 + 28*n**3 - 16*n - 3*n**3 - 10*n**4 + 8 - 11*