-1
Let n be -8 + (-6 - -3 - 143/(-11)). Factor -1/6*w**4 + 1/6*w**5 + 0 + 0*w + 1/6*w**n - 1/6*w**3.
w**2*(w - 1)**2*(w + 1)/6
Let k(d) be the third derivative of d**5/240 + 41*d**4/96 + 13*d**3/4 - d**2 - 1605*d. Factor k(b).
(b + 2)*(b + 39)/4
Let p(g) = -g**3 - 38*g**2 + 42*g + 119. Let d be p(-39). Find b, given that -4 + 69 - 75*b**d - 210*b - 212 = 0.
-7/5
Let j(y) be the first derivative of -18 + 5/6*y**6 + 20/3*y**3 + 2*y**5 + 0*y**2 + 0*y - 35/4*y**4. Solve j(s) = 0 for s.
-4, 0, 1
Let s = -73 - -90. Let l(w) = -3*w**3 + 29*w**2 + 27*w - 9. Let y(m) = -8*m**3 + 85*m**2 + 80*m - 27. Let i(b) = s*l(b) - 6*y(b). Factor i(k).
-(k + 3)**2*(3*k - 1)
Let f = -612152 - -1224323/2. Factor -y**3 - 4 - f*y**2 - 25/2*y.
-(y + 1)*(y + 8)*(2*y + 1)/2
Suppose -2/7*d**2 - 628/7 + 90*d = 0. What is d?
1, 314
Let x(b) be the second derivative of b**5/50 + 2*b**4/5 + 17*b**3/15 - 6*b**2 + 5*b - 119. Factor x(t).
2*(t - 1)*(t + 3)*(t + 10)/5
Solve 0*z + 0 - 28/13*z**3 + 2/13*z**4 + 0*z**2 = 0.
0, 14
Let l(m) = -25*m**2 - 1540*m. Let w(a) = a**3 + 44*a**2 + 83*a - 77. Let k be w(-42). Let c(j) = 2*j**2 + 128*j. Let i(h) = k*c(h) - 3*l(h). Factor i(o).
5*o*(o + 28)
Let t(w) be the third derivative of 4*w**5/15 - 103*w**4/72 - 7*w**3/6 - 51*w**2 - 2*w - 28. What is o in t(o) = 0?
-3/16, 7/3
Let s be ((-3)/6)/(1/(-2)). Let x be 11 - -2 - (s + 2). Factor -7*d**3 - x*d**3 + 22*d**3 - 5*d.
5*d*(d - 1)*(d + 1)
Factor -111 - 45 + 2*c**2 - 96*c + 170*c.
2*(c - 2)*(c + 39)
Let k(x) be the third derivative of x**7/630 + x**6/20 + x**4/12 - 31*x**3/6 + 17*x**2. Let c(j) be the second derivative of k(j). Factor c(t).
4*t*(t + 9)
Let h be (9/90)/((-8)/(-69)) - (-1)/(-16). Factor h*p - 1/5*p**2 + 0.
-p*(p - 4)/5
Let t(y) be the second derivative of -1/114*y**4 + 29/57*y**3 - y - 28/19*y**2 - 13. Factor t(k).
-2*(k - 28)*(k - 1)/19
Factor 33*q**2 + 7*q**3 - 224*q + 1/4*q**4 + 256.
(q - 2)**2*(q + 16)**2/4
Let z(n) be the first derivative of -n**3/5 + 1548*n**2/5 - 798768*n/5 + 1602. Let z(d) = 0. What is d?
516
Let h(f) be the first derivative of -12*f**2 - 20/3*f**3 + 2*f**4 - 134 + 0*f + 4/5*f**5. Factor h(b).
4*b*(b - 2)*(b + 1)*(b + 3)
Let v(r) be the second derivative of r**4/21 + 104*r**3/21 - 216*r**2/7 - r - 950. Factor v(k).
4*(k - 2)*(k + 54)/7
Let q(p) be the third derivative of 0*p**3 - 1/180*p**5 + 0 - 6*p + 2*p**2 - 2/315*p**7 + 7/720*p**6 + 0*p**4 + 1/672*p**8. Factor q(o).
o**2*(o - 1)**2*(3*o - 2)/6
Let -2/23*u**3 + 26/23*u + 0 - 24/23*u**2 = 0. Calculate u.
-13, 0, 1
Let v(w) be the third derivative of -w**8/1176 + 17*w**7/735 + w**6/420 - 17*w**5/210 - 4*w**2 + 53. What is a in v(a) = 0?
-1, 0, 1, 17
Let h(c) be the first derivative of 64 + 0*c + 2/25*c**5 - 16/15*c**3 + 1/2*c**4 - 48/5*c**2. Factor h(d).
2*d*(d - 3)*(d + 4)**2/5
Let n = -507593/11 + 46145. Let y(s) = 2*s. Let g be y(1). Suppose -n*x**3 + 8/11*x**g + 2*x + 12/11 = 0. Calculate x.
-1, 6
Let x(y) = -2*y**2 - 46*y - 132. Let c(n) = -n**2 - 15*n - 44. Suppose -109*q + 102*q + 56 = 0. Let v(h) = q*c(h) - 3*x(h). Determine z, given that v(z) = 0.
-2, 11
Factor -704/5 - 1/5*r**3 - 27/5*r**2 - 48*r.
-(r + 8)**2*(r + 11)/5
Let k(l) be the second derivative of l**6/150 + 127*l**5/100 + 121*l**4/60 - 209*l**3/10 + 189*l**2/5 - 76*l + 39. Suppose k(j) = 0. Calculate j.
-126, -3, 1
Suppose -5*y = 7 - 12. Let s be (-2 - 1)/(y - 30/12). Factor 5*g**s + 245 + 62*g + 12*g - 4*g.
5*(g + 7)**2
Let h(t) = 1323*t - 273859. Let x be h(207). Factor 24/5 - 3/5*w**x - 21/5*w.
-3*(w - 1)*(w + 8)/5
Let -372/7 + 4/7*x**3 - 260/7*x + 116/7*x**2 = 0. What is x?
-31, -1, 3
Let z = -397/126 + 200/63. Let o(j) be the second derivative of 1/70*j**5 - 24*j + 0*j**3 + 0 - z*j**4 + 0*j**2. Factor o(y).
2*y**2*(y - 1)/7
Let q be (62/(-8) - -7)/((-22)/(1584/135)). Suppose -2/5*i - q*i**5 - 6/5 - 6/5*i**4 + 4/5*i**3 + 12/5*i**2 = 0. What is i?
-3, -1, 1
Suppose 19687*s - 19700*s + 26 = 0. Factor 5/3*q - 1/3*q**s + 14/3.
-(q - 7)*(q + 2)/3
Let r(b) be the first derivative of b**3/8 - 1593*b**2/8 + 845883*b/8 - 1453. Determine z, given that r(z) = 0.
531
Let d(i) be the second derivative of i**6/15 - i**5/35 - 2*i**4/7 + 2*i**3/21 + 5*i**2/7 - 411*i. Determine c, given that d(c) = 0.
-1, -5/7, 1
Let g(y) be the second derivative of 2*y**4/3 - 5*y**3/6 + 36*y. Let t(o) = -7*o**2 + 4*o. Let b(k) = -6*g(k) - 7*t(k). Factor b(d).
d*(d + 2)
Let g = 3544 + -3518. Let j(m) be the first derivative of 8/15*m**3 - g + 1/20*m**4 + 0*m + 8/5*m**2. Let j(o) = 0. What is o?
-4, 0
Suppose -c - 5*y = 0, 0 = -c - y + 3 + 1. Suppose -5*j - 3*m - 5 = 0, -2*j - c*m + 9*m = -24. Factor 15*p**2 - 22*p**2 - 17*p**j + 4*p**4 - 4*p**3.
4*p**2*(p - 3)*(p + 2)
Let o be 29 + (-348)/96*8. Let o*f + 18/5*f**3 + 4/5*f**2 + 6/5*f**4 + 0 - 8/5*f**5 = 0. Calculate f.
-1, -1/4, 0, 2
Let n = 10378 + -31124/3. Let w(q) be the second derivative of -n*q**3 + 0 - 1/3*q**4 - 8*q**2 - 45*q. Find k, given that w(k) = 0.
-4, -1
Let c(z) be the first derivative of -z**8/336 + z**7/24 - z**6/12 - 4*z**3 - 13. Let o(u) be the third derivative of c(u). Suppose o(p) = 0. Calculate p.
0, 1, 6
Suppose 15*m - 10 = 20. Let p be (-21)/(-15)*(-1 + (1 - -5)) + -5. Factor -1/3*c**p - 2*c + 0 + 1/3*c**4 + m*c**3.
c*(c - 1)*(c + 1)*(c + 6)/3
Suppose 0 = -3*t - 3*b, -2 = -4*t - 20*b + 17*b. Solve -22*l**2 + 24*l**t - 6*l**2 - 8234 + 134 - 360*l = 0 for l.
-45
Let d be ((-2800)/1050)/(140/(-21)). Determine j, given that d*j**3 + 14*j + 22/5*j**2 + 10 = 0.
-5, -1
Let m(a) be the first derivative of a**9/1512 + a**8/280 + a**7/210 - 17*a**3/3 + a**2 - 109. Let l(v) be the third derivative of m(v). Factor l(w).
2*w**3*(w + 1)*(w + 2)
Let u(m) be the third derivative of 9*m**6/8 + 10*m**5/3 - 35*m**4/6 - 6*m**2 + 291*m. Determine y, given that u(y) = 0.
-2, 0, 14/27
Let a(o) = 11*o**2 + 55*o + 292. Let g(d) = 5*d**2 + 28*d + 145. Let l(w) = -4*a(w) + 9*g(w). Let x be l(-5). Factor 1/4*f + 1/6 + 1/12*f**x.
(f + 1)*(f + 2)/12
Let a be (-468)/(-390) + (32/(-10) - -2). Suppose a = -92*q + 72*q + 40. Factor -1/2*y**2 - 1/2*y**3 + 2*y + q.
-(y - 2)*(y + 1)*(y + 2)/2
Let d(s) be the second derivative of -s**4/3 + 272*s**3 - 83232*s**2 - 455*s. Determine y so that d(y) = 0.
204
Let p(t) = 10*t + 5. Let q(d) = 249*d**2 - 6 - 124*d**2 - 124*d**2 - 9*d. Let i(r) = -6*p(r) - 5*q(r). Solve i(z) = 0.
-3, 0
Suppose 3*z = 5*m + 65, 0 = 330*z - 326*z - 2*m - 40. Factor 12/7 + 3/7*p**2 - 3/7*p**z - 3/7*p**4 + 15/7*p**3 - 24/7*p.
-3*(p - 1)**3*(p + 2)**2/7
Let h be (112/21)/((-2)/(-6)). Suppose -6 = 2*i - h. Determine d, given that -59*d**3 + 0*d**i + 2*d**2 + 65*d**3 + 2*d**5 + 6*d**4 = 0.
-1, 0
Let i(l) = l**3 + 7*l**2 + 10. Let n be i(-6). Let g = -36 + n. Suppose 2*y + 1 + 5*y**2 + 15*y**2 - 29*y**2 + g*y**2 = 0. Calculate y.
-1
Let i(x) = -130*x - 59. Let q be i(-2). Let t be 3/5*(q/(-18) + 12). Factor 0 + 3/2*f**2 + t*f.
f*(3*f + 1)/2
Find f, given that -68/11*f - 186/11 - 2/11*f**2 = 0.
-31, -3
Let t(d) = -396*d - 789. Let h be t(-2). Factor -2/13*s**h + 2/13*s**4 - 2/13*s**2 + 0 + 2/13*s.
2*s*(s - 1)**2*(s + 1)/13
Let x be (-5)/1 - (-132)/(-66)*15/(-6). Let f(w) be the third derivative of 0 + 1/20*w**5 - 1/4*w**4 + 0*w**3 + 2*w**2 + x*w. Factor f(q).
3*q*(q - 2)
Suppose 70 = -2*j + 3*a, -2*j - 19 = -a + 43. Let h be (-58)/j - (2 - (-21)/(-2)). Factor h*d**2 + 9/2*d**3 + 33/4*d - 3/4*d**4 + 9/4 - 3/4*d**5.
-3*(d - 3)*(d + 1)**4/4
Let g = -109/64 + 4913/2880. Let j(k) be the third derivative of 0*k + 1/36*k**4 + g*k**5 + 0 + 0*k**3 - 2*k**2. Find h, given that j(h) = 0.
-4, 0
Suppose 94*k + 1 = -1 + 2. Let x(s) be the second derivative of -1/5*s**2 + k + 5/2*s**5 - s - 5/2*s**4 + s**3. Factor x(v).
2*(5*v - 1)**3/5
Let b(z) be the first derivative of -64 - 7/9*z**3 + 20/3*z**2 - 44/3*z - 1/12*z**4. Suppose b(x) = 0. Calculate x.
-11, 2
Let q be (18/(-27))/(-4*(-1)/(-54)). Let 15*j**2 + q*j**2 - 9*j**3 + 12*j - 2581*j**4 + 2554*j**4 = 0. Calculate j.
-2/3, 0, 1
Suppose 4*h = -o - 0*o + 35, 5*o - h = 154. Suppose -15*j**2 + o*j**2 - 20*j - 20*j**2 - 24 = 0. What is j?
-3, -2
Let v be (-594)/(-30) + (-5)/(50/8). Suppose -v + 35 = 8*o. Factor -12*b**3 + 44/3*b**2 - 26/3*b + 14/3*b**4 - 2/3*b**5 + o.
-2*(b - 3)*(b - 1)**4/3
Let g(q) be the third derivative of 0 + 56*q**2 + 0*q - 1/75*q**5 - 4/3*q**4 - 1