1/12*l**5 - 5/6*l**3. Determine u, given that m(u) = 0.
-1, 1
Suppose -432*u + 1166 + 871 = 741. Factor 3/4*k**3 + u*k**2 + 0 + 9/4*k.
3*k*(k + 1)*(k + 3)/4
Let m(x) = 667*x + 8679. Let g be m(-13). Factor -8/3 - 26/3*v**2 + 4*v**3 + g*v - 2/3*v**4.
-2*(v - 2)**2*(v - 1)**2/3
Let n(g) be the first derivative of -69/2*g**2 - 36*g + 2*g**3 + 43. Suppose n(f) = 0. What is f?
-1/2, 12
Let n(k) be the first derivative of k**4/12 + 31*k**3/3 + 179*k**2/6 - 91*k + 11682. Find v, given that n(v) = 0.
-91, -3, 1
Let a(l) = -26*l**3 - 52*l**2 + 3*l. Let g(r) = 83*r**3 + 156*r**2 - 10*r. Let k(v) = 10*a(v) + 3*g(v). Let k(d) = 0. What is d?
-52/11, 0
Let y be (-9)/10*2210/(-11934)*2312/6. Factor 68/9*r - y - 2/9*r**2.
-2*(r - 17)**2/9
Let y(z) = -6*z**2 - 364*z - 1126. Let g(d) = 47*d**2 + 2917*d + 9010. Let r(u) = 4*g(u) + 31*y(u). Factor r(p).
2*(p + 3)*(p + 189)
Determine t so that 0 + 766/3*t - 2/3*t**2 = 0.
0, 383
Let k = -1328881 + 1328884. Find s, given that 2/7*s**k + 0 + 8*s**2 + 56*s = 0.
-14, 0
Let -4886*p + 4673*p**2 - 8822*p + 4210960 - 17908345 - 4675*p**2 - 9791273 = 0. What is p?
-3427
Let h(v) = -v**3 - v**2 + v. Suppose 62*d - 70 = 57*d. Let z(o) = d*o + 12*o**2 + 12 + 9*o + 4*o. Let m(f) = -3*h(f) + z(f). Factor m(r).
3*(r + 1)*(r + 2)**2
Let s(f) be the first derivative of 3*f**4/8 - 120*f**3 - 1283. Let s(l) = 0. What is l?
0, 240
Let t = 4/20801 + 312007/41602. Let p = -1 + 1. Factor p + t*u + 5/2*u**2.
5*u*(u + 3)/2
Let f = -1148 - -1162. Let s be 4/f + 9 + (-763)/98. Solve -s*q + 0 + 5/2*q**2 - 1/2*q**3 - 1/2*q**4 = 0.
-3, 0, 1
Suppose 3*l - 14*l = 4*l + 6*l. Let d(q) be the second derivative of -q**4 + 0 + l*q**2 - 3/20*q**5 - 8*q + 2*q**3 + 1/10*q**6. Determine x so that d(x) = 0.
-2, 0, 1, 2
Let 74 + 61*k - 40*k + 123 + 235 - 3*k**2 = 0. What is k?
-9, 16
Let d(z) be the first derivative of 0*z + 0*z**5 + 89 + 2/3*z**6 + 0*z**3 - 2*z**4 + 2*z**2. Factor d(w).
4*w*(w - 1)**2*(w + 1)**2
Solve -256*p**2 - 136*p**5 - 104*p**4 + 360 - 472*p**3 + 246*p**5 - 106*p**5 + 468*p = 0.
-3, -1, 1, 30
Let r(l) be the first derivative of 2*l**3/3 - 660*l**2 + 217800*l - 378. Suppose r(b) = 0. Calculate b.
330
Let n = 5244 + -5244. Let g(o) be the second derivative of 1/190*o**5 + n*o**2 + 4*o + 5/114*o**4 + 0*o**3 + 0. Factor g(v).
2*v**2*(v + 5)/19
Let n(b) be the second derivative of 4/5*b**2 + 1/25*b**5 - 2/15*b**3 - b - 2 - 2/15*b**4. Determine i so that n(i) = 0.
-1, 1, 2
Let s(h) = -2*h**2 + 8*h + 6. Let d be s(7). Let b = 61 + d. Determine g, given that 5*g**4 + 4 - b*g**3 + 4 + 20*g - 25*g**2 + 12 + 5*g**5 = 0.
-2, -1, 1, 2
Let o(a) be the first derivative of -4/3*a**3 - 6*a**2 - 58 - 8*a. Factor o(b).
-4*(b + 1)*(b + 2)
Let w be -7 + 1/(39/1846). Let b(u) be the first derivative of 4*u - 20 + w*u**3 - 22*u**2. Factor b(c).
(11*c - 2)**2
Let u(z) = -7*z**2. Let q(s) = -s**2 + 7*s + 78. Let a be q(11). Let m(h) = 40*h**2 + 2*h. Let i(k) = a*u(k) + 6*m(k). Suppose i(b) = 0. Calculate b.
-6, 0
Suppose -2*x + 41*x - 4*x + 38*x = 0. Let l(v) be the second derivative of x*v**2 - 6*v - 1/6*v**4 + 0*v**3 + 0 + 1/5*v**5 + 1/84*v**7 - 1/12*v**6. Factor l(m).
m**2*(m - 2)**2*(m - 1)/2
Let l(z) be the second derivative of -z**7/84 + 4*z**6/45 - z**5/15 - 4*z**4/3 - 38*z**3/3 - 2*z - 10. Let s(m) be the second derivative of l(m). Factor s(o).
-2*(o - 2)**2*(5*o + 4)
Let p be 4*(-1)/1*(-100)/80. Determine j, given that -j**p + 10*j - 5*j**5 - 38*j**2 - 20*j**2 + 53*j**3 - 2*j**5 + 25*j**3 - 22*j**4 = 0.
-5, 0, 1/4, 1
Let c(m) be the second derivative of -m**7/336 - 11*m**6/240 - 3*m**5/20 + 3*m**4/8 - 1224*m. Factor c(z).
-z**2*(z - 1)*(z + 6)**2/8
Let l be (-10)/(-18) + 1/(-3). Let q(o) = 18446*o + 92230. Let h be q(-5). Factor h + l*f**2 - 2/3*f.
2*f*(f - 3)/9
Suppose -403/6*y + 9 + 25/6*y**3 + 110*y**2 = 0. Calculate y.
-27, 1/5, 2/5
Let p = 3091 - 3085. Let z(i) be the second derivative of 1/3*i**4 - 4/3*i**3 + 0 - p*i**2 - 4*i. Factor z(k).
4*(k - 3)*(k + 1)
Factor -3/4*w**2 + 33 - 21/4*w.
-3*(w - 4)*(w + 11)/4
Let o be ((-25)/2)/(7/(-14)). Find w, given that 23 - 15*w**3 - 74*w**2 + o*w + 39*w + w**3 + 1 = 0.
-6, -2/7, 1
Let u = 74819 + -74816. Factor -3/4 + 3/4*a**4 - 3/2*a**u + 3/2*a + 0*a**2.
3*(a - 1)**3*(a + 1)/4
Let h(x) = -82*x**3 + 55*x**2 + 35*x - 12. Let a(f) = 165*f**3 - 109*f**2 - 71*f + 22. Let s(z) = -4*a(z) - 7*h(z). Factor s(l).
-(l - 1)*(2*l + 1)*(43*l - 4)
Let s be -38 + 12192/224 - 16. Suppose 24/7*p**2 - 45/7*p - s*p**3 + 0 = 0. Calculate p.
0, 3, 5
Determine v, given that -537/2*v - 33/8 - 195/8*v**2 = 0.
-11, -1/65
Let 374*u**3 - 6*u + 780*u**3 - 10*u + 420*u**4 + 4*u - 322*u**2 = 0. What is u?
-3, -1/30, 0, 2/7
Suppose -8 = -4*h - 5*u, -31*u + 26*u = 0. Factor 3*j**2 + 380 - j + 44*j - 424 - h*j**2.
(j - 1)*(j + 44)
Let r(o) be the first derivative of 3/5*o**5 + 21*o**3 - 6*o**4 - 63 - 33*o**2 + 24*o. Factor r(u).
3*(u - 4)*(u - 2)*(u - 1)**2
Let q(z) be the third derivative of -z**8/84 + 2*z**7/15 + 7*z**6/10 - 247*z**5/15 + 260*z**4/3 - 200*z**3 + 6*z**2 - z - 38. Solve q(m) = 0.
-6, 1, 2, 5
Let x(o) be the second derivative of -o**8/420 - o**7/42 - 2*o**6/45 + 56*o**3/3 + o**2/2 - 21*o - 5. Let d(t) be the second derivative of x(t). Factor d(b).
-4*b**2*(b + 1)*(b + 4)
Let k = 10 + 13. Let i = k - 18. Find u such that 5*u**2 + 10*u - 55*u**3 + 180*u**5 + 0*u - 181*u**3 + 46*u**3 - i*u**4 = 0.
-1, -2/9, 0, 1/4, 1
Let q(j) be the second derivative of -j**5/5 + 26*j**4/3 - 320*j**3/3 + 576*j**2 - 3*j - 65. Find t such that q(t) = 0.
4, 18
Let h be (-770)/(-30) + 35/15. Factor 31*t + 9*t + 0 - 12 - h*t**2.
-4*(t - 1)*(7*t - 3)
Let j(b) = 66*b**4 - 408*b**3 + 3744*b**2 + 9027*b + 4809. Let c(x) = -13*x**4 + 82*x**3 - 749*x**2 - 1806*x - 962. Let d(t) = -51*c(t) - 10*j(t). Factor d(a).
3*(a - 18)**2*(a + 1)**2
Let f(j) be the third derivative of -j**5/540 - 11*j**4/6 - 726*j**3 - 558*j**2 + 2. Factor f(x).
-(x + 198)**2/9
Let o(b) be the third derivative of -b**6/1320 + 7*b**4/264 - b**3/11 + 648*b**2. Factor o(w).
-(w - 2)*(w - 1)*(w + 3)/11
Let n(v) = 28*v**2 + 89*v + 34. Let m(x) be the third derivative of 3*x**5/20 + 5*x**4/4 + 2*x**3 + 155*x**2. Let l(i) = 21*m(i) - 6*n(i). Factor l(g).
3*(g + 4)*(7*g + 4)
Suppose 1 = 2*h - 3*f, -2*f + 1 = -4*h + f. Let w(j) = -3*j**3 + j**2 + 3*j + 3. Let x be w(h). Solve 2*q - 2*q**3 + 3/2*q**x + 2 - 7/2*q**2 = 0 for q.
-1, -2/3, 1, 2
Let 9*a**2 - 17*a + 111*a**3 - 20*a**3 - 13*a - 26*a**3 - 32*a**3 - 3*a**5 - 9*a**4 = 0. What is a?
-5, -1, 0, 1, 2
Let y(o) be the third derivative of -o**8/2184 - 144*o**7/455 - 3888*o**6/65 - 1870*o**2. Let y(q) = 0. Calculate q.
-216, 0
Let w = -1488/7 - -261881/1232. Let b = 1227/880 - w. Factor -b*o - o**2 - 2/5.
-(o + 1)*(5*o + 2)/5
Let g(m) be the first derivative of -m**5/60 + m**4/9 - m**3/18 - m**2 - 34*m + 190. Let b(r) be the first derivative of g(r). Factor b(h).
-(h - 3)*(h - 2)*(h + 1)/3
Let u(l) = -10*l**3 + 163*l**2 + 3182*l - 11088. Let p(x) = -26*x**3 + 490*x**2 + 9546*x - 33266. Let n(z) = -3*p(z) + 8*u(z). Factor n(t).
-2*(t - 3)*(t + 43)**2
Let c(d) be the second derivative of -3/4*d**5 + 2 + 54*d + 1/10*d**6 + 0*d**2 + 0*d**3 + 3/2*d**4. Find x, given that c(x) = 0.
0, 2, 3
Let m(u) be the first derivative of -u**3/8 - 4179*u**2/16 - 522*u - 5308. Suppose m(s) = 0. What is s?
-1392, -1
Let a(q) be the third derivative of -q**5/60 + 71*q**4/12 - 5041*q**3/6 + 1073*q**2 - 2*q. Factor a(z).
-(z - 71)**2
Let t(q) be the second derivative of -23 + 0*q**2 + 21/20*q**5 - 3*q**3 + 1/10*q**6 - 1/14*q**7 - q - 1/4*q**4. Suppose t(x) = 0. What is x?
-2, -1, 0, 1, 3
Suppose -23*x + 4 = -21*x. Factor -18*y + 4*y + 772*y**2 + 2*y**3 + 8 - 768*y**x.
2*(y - 1)**2*(y + 4)
Let h(s) be the third derivative of s**7/630 - 31*s**6/360 - 4*s**5/15 - 229*s**4/24 + 212*s**2 + 2*s. Let m(j) be the second derivative of h(j). Factor m(k).
2*(k - 16)*(2*k + 1)
Let f(y) = 17*y**3 + 64*y**2 + 163*y + 84. Let s(n) = -6*n**3 - 21*n**2 - 54*n - 27. Let x(k) = -3*f(k) - 8*s(k). Let x(d) = 0. Calculate d.
-4, -3, -1
Let b = -20016 + 20034. Let z(j) be the third derivative of -1/40*j**5 + 3/4*j**3 - b*j**2 + 0 + 0*j + 1/8*j**4. Factor z(i).
-3*(i - 3)*(i + 1)/2
Let d(t) be the first derivative of 114 - 32/3*t - 1/15*t**5 + 2/3*t**3 + 5/12*t**4 - 16/3*t**2. Supp