a.
-2*a*(a - 1)**2*(a + 1)**2/3
Suppose 4*v - 2*b = 26, 3*b - 3 + 2 = -2*v. Suppose 113 = v*o - 77. Factor -o*m + 20*m - m**3 + 22*m.
-m*(m - 2)*(m + 2)
Let t(p) be the second derivative of -1/130*p**5 + 1/65*p**6 - 1/26*p**4 + 2/39*p**3 - 43 + 0*p**2 - 1/273*p**7 + p. Determine o, given that t(o) = 0.
-1, 0, 1, 2
Let n be (252/2688)/(6/32). Let f(b) be the second derivative of -1/2*b**3 + 3/20*b**5 - 11*b + n*b**4 + 0 - 3*b**2. Determine v so that f(v) = 0.
-2, -1, 1
Suppose 40/17 - 6/17*h**2 + 2/17*h**4 - 56/17*h + 20/17*h**3 = 0. Calculate h.
-10, -2, 1
Suppose 4*m - 10*r = -7*r - 357, 0 = -m + r - 88. Let d be 31/m + (20/3)/4. Factor -8 - d*g**2 + 20/3*g.
-4*(g - 3)*(g - 2)/3
Let a be (-9 + 24*13/104*3)/5. Suppose 15*j**2 + 5/2*j**4 + a - 4*j - 27/2*j**3 = 0. What is j?
0, 2/5, 1, 4
Let a = 28 - 109/4. Let c be ((-25)/(-15))/(4/12 + 0). Factor -a*q - 15/8*q**4 + 0 - 27/8*q**3 - 3/8*q**c - 21/8*q**2.
-3*q*(q + 1)**3*(q + 2)/8
Let a(p) be the third derivative of p**5/15 - 31*p**4 + 2678*p**2. Determine y, given that a(y) = 0.
0, 186
Suppose -918 = -11*t + 17*t. Let o be (-1 - 0)*0 - 102/t. Find i, given that -o*i + 0 - 2/3*i**2 = 0.
-1, 0
Let j(z) be the third derivative of z**7/2520 - z**6/80 - 11*z**5/60 - 67*z**4/12 - 48*z**2. Let x(d) be the second derivative of j(d). Factor x(y).
(y - 11)*(y + 2)
Factor 140450/3 - 1058/3*c**2 - 2/3*c**3 - 139390/3*c.
-2*(c - 1)*(c + 265)**2/3
Let l(y) = -y**2 + 28*y - 5. Let t be l(33). Let q = t + 173. Factor 8/5 - 14/5*w**2 + 8/5*w + 4/5*w**q.
2*(w - 2)**2*(2*w + 1)/5
Let b(v) = v**3 - 115*v**2 - 1810*v + 518. Let f be b(129). Suppose 80/7 - 82/7*w + 2/7*w**f = 0. Calculate w.
1, 40
Let h = 14984 + -164818/11. Find k, given that 2/11*k**4 + 12/11 - 14/11*k + h*k**3 - 6/11*k**2 = 0.
-3, -2, 1
Let s(z) be the third derivative of -4*z**7/15 + 647*z**6/30 - 766*z**5/15 + 43*z**4/6 + 60*z**3 - 959*z**2 - 2. Let s(m) = 0. What is m?
-2/7, 1/2, 1, 45
Let z be (-19)/((-50065)/(-1116))*(-20)/8. Find i, given that 20/17*i + 0 + z*i**2 - 2/17*i**3 = 0.
-1, 0, 10
Let b = 244 - 242. Let f be (-2)/4*(2 + -14). Let 0*d**b + 4*d**2 + f*d + 36 + 18*d = 0. Calculate d.
-3
Let b(z) be the third derivative of 0*z + 1/1200*z**6 - 7/600*z**5 + 0 + 0*z**4 + 72*z**2 - 1/3360*z**8 + 1/700*z**7 + 1/15*z**3. Find o, given that b(o) = 0.
-1, 1, 2
Suppose 172*d - 181*d = 45. Let y be 1*(-15)/(-9)*(-1)/d. Factor 0*i + 1/3*i**2 - 1/3*i**4 + 0 - 1/3*i**3 + y*i**5.
i**2*(i - 1)**2*(i + 1)/3
Factor 2/17*w**2 - 1892/17*w + 447458/17.
2*(w - 473)**2/17
Let 34306*j + 0*j**2 - 6*j**2 - 11 - 34 - 34273*j = 0. What is j?
5/2, 3
Let s(r) = -3*r**4 - 21*r**3 + 45*r**2 - 39*r + 14. Let x(o) = 3*o**4 + 18*o**3 - 45*o**2 + 42*o - 15. Let k(h) = 3*s(h) + 4*x(h). Find i such that k(i) = 0.
-6, 1
Let h(m) = -2*m**2 - 4*m + 2. Let i(l) = -9*l**2 + 60*l - 378. Let x(k) = 3*h(k) - i(k). Let x(c) = 0. What is c?
8, 16
Let r = 43/949 - -3667/2847. Find h, given that 1/3*h**2 - h - r = 0.
-1, 4
Let g(t) = -82*t**2 + 140*t + 2. Let z(b) = 80*b**2 - 147*b - 3. Let l(u) = 7*g(u) + 6*z(u). Solve l(c) = 0.
2/47, 1
Let y(q) be the third derivative of 34/75*q**4 - 97*q**2 + 31/750*q**5 + 2*q - 1/1500*q**6 + 28/15*q**3 + 0. Solve y(w) = 0 for w.
-2, 35
Suppose 8 = c + 8. Factor -4*w + 6*w**2 + 8*w - 24 + c*w - w**3.
-(w - 6)*(w - 2)*(w + 2)
Let s(j) be the third derivative of j**8/112 - 31*j**7/70 + 14*j**6/5 - 27*j**5/5 - 3126*j**2. Factor s(h).
3*h**2*(h - 27)*(h - 2)**2
Let m(s) be the third derivative of 0*s + 0*s**4 - 1/60*s**6 + 1/30*s**5 + 71*s**2 + 0 + 0*s**3. Factor m(k).
-2*k**2*(k - 1)
Solve -14*y**2 - 172/3*y - 16/3 = 0.
-4, -2/21
Let p(z) = 2*z**3 + 70*z**2 - 340*z - 12. Let r(o) = -o**3 - o**2 + 14*o + 2. Let k(g) = -p(g) - 6*r(g). Factor k(y).
4*y*(y - 8)**2
Suppose 3*g = 19 - 4. Suppose -7*r + 9 = -g. Let -4*l - 112*l**2 - 120*l**r - l**3 + 230*l**2 + 7*l = 0. What is l?
-3, 0, 1
Let z(h) = -336*h**3 + 890*h**2 - 456*h + 62. Let d(o) = 1007*o**3 - 2673*o**2 + 1372*o - 185. Let y(x) = -4*d(x) - 14*z(x). Let y(b) = 0. Calculate b.
4/13, 2
Let c(p) = 12*p**3 + 804*p - 380 + 32*p**3 - 194*p**2 - 202*p**2. Let m(l) = -9*l**3 + 79*l**2 - 161*l + 76. Let g(o) = 5*c(o) + 24*m(o). Factor g(u).
4*(u - 19)*(u - 1)**2
Let f(g) be the second derivative of -4*g**5/15 + 327*g**4/2 - 90160*g**3/3 - 33856*g**2/3 - 3753*g. Factor f(l).
-2*(l - 184)**2*(8*l + 1)/3
Let r be (4/4)/(((-1)/10)/(-1)). Suppose -8*g = -r*g + 6. Factor -135 - 3*b**3 + 133 + 5*b**g + 6*b - 6*b**2.
2*(b - 1)**3
Let a(f) be the first derivative of f**4/10 + 26*f**3/15 - 198*f**2/5 + 9592. Factor a(q).
2*q*(q - 9)*(q + 22)/5
Factor -41*g**3 - 560*g**5 - 7*g**4 + 13*g**3 - 559*g**5 - 20*g**2 + 1120*g**5.
g**2*(g - 10)*(g + 1)*(g + 2)
Let p(k) be the third derivative of k**5/120 + 115*k**4/72 - 77*k**3/36 + 42*k**2 - 13. Factor p(b).
(b + 77)*(3*b - 1)/6
Suppose -5 = -3*j - q - 23, -2*j + 4*q = 12. Let g(k) = -7*k - 39. Let z be g(j). Suppose z*l**2 + 0 - 3/5*l = 0. What is l?
0, 1/5
Suppose -3*t + 4*q + 1 = 8*q, -4*q = 2*t - 6. Let s be (t + 9 + -4)/((-6)/2). Factor -2/3*l - 5/3*l**2 + l**3 + s.
l*(l - 2)*(3*l + 1)/3
Factor 15*n + 84*n**2 - 964*n**3 + 942*n**3 - 23*n - 2*n**4 - 112.
-2*(n - 2)**2*(n + 1)*(n + 14)
Suppose 5 + 25 = 3*q. Factor -12 - 12*u - 2*u**2 - q*u + 6*u - 20.
-2*(u + 4)**2
Let v = -156777 + 156777. Let 1/4*a**2 + 5/2*a + v = 0. What is a?
-10, 0
Let n(k) be the first derivative of -23040*k - 163 + 240*k**2 - 5/6*k**3. Find p, given that n(p) = 0.
96
Let t(b) be the third derivative of b**5/15 - 7*b**4 - 192*b**3 - 28*b**2 + 18. Factor t(q).
4*(q - 48)*(q + 6)
Let i(j) be the first derivative of -15 + 39/20*j**5 - 9*j - 21/2*j**2 - 3/8*j**6 + 93/16*j**4 - 1/4*j**3. Suppose i(h) = 0. Calculate h.
-1, -2/3, 1, 6
Factor 5/2*v**3 - 139*v + 52 + 43/2*v**2.
(v - 4)*(v + 13)*(5*v - 2)/2
Let y(j) = 141*j + 4093. Let h be y(-28). Let n be 0 - (-1)/(2/32). Suppose 145 - h + 4*x**3 + n*x**2 = 0. Calculate x.
-4, 0
Suppose 2*o = 5*o - 5*v - 38, 5*o = 5*v + 70. Suppose o - 3 = g. Let 7*a + 4*a**2 + 13 + g*a + 183 + 36*a = 0. Calculate a.
-7
Suppose 5*w + 3 = -2*t, 4 = -2*w - 6. Suppose 19 - 16 = 4*s + h, -2*s - t = 3*h. Factor -1/2*i**4 + 1/8*i - 1/8*i**3 + 1/2*i**s + 0.
-i*(i - 1)*(i + 1)*(4*i + 1)/8
Let j(v) be the second derivative of 1/2*v**4 + 0 + 10*v + 15/2*v**2 - 7/10*v**6 + 1/14*v**7 - 11/2*v**3 + 3/2*v**5. Find i such that j(i) = 0.
-1, 1, 5
Let g(s) be the first derivative of 5*s**3/3 - 160*s**2 - 2485*s + 8363. Determine v so that g(v) = 0.
-7, 71
Let o(x) = x**2 - 2*x - 41. Let s be o(8). Suppose 2*r - 2*n = 7*r - 29, -s = -3*r + 4*n. Factor -1/3*b**3 + 1/3*b**r + 1/3*b**4 + 0 - 1/3*b**2 + 0*b.
b**2*(b - 1)*(b + 1)**2/3
Factor 117/4 + 59/2*v + 1/4*v**2.
(v + 1)*(v + 117)/4
Let t(w) be the second derivative of w**7/105 + 74*w**6/75 - 114*w**5/25 + 23*w**4/3 - 77*w**3/15 - 1692*w. Factor t(y).
2*y*(y - 1)**3*(y + 77)/5
Let y(r) be the second derivative of r**5/12 - 25*r**4/36 + 5*r**3/9 + 20*r**2/3 + 801*r + 4. Factor y(q).
5*(q - 4)*(q - 2)*(q + 1)/3
Factor 532*m - 2/3*m**2 - 1594/3.
-2*(m - 797)*(m - 1)/3
Suppose -8442 + 41762 = -64*u + 149*u. Find x such that -41/2*x**3 + u + 308*x + 1/2*x**5 + 7/2*x**4 - 215/2*x**2 = 0.
-7, -1, 4
Suppose 79*r + 3 = 80*r. Suppose -4*y + 10 = -r*l, -l - 10 = 14*y - 17*y. Determine u, given that 0 - 1/6*u**4 + 0*u - 1/6*u**l - 1/3*u**3 = 0.
-1, 0
Let y(g) be the first derivative of -g**6/960 + g**4/64 + 51*g**3 - 173. Let h(f) be the third derivative of y(f). Solve h(p) = 0.
-1, 1
Let d be -14 + (-5 - 3/(-1)). Let g be 1/((-2)/3*8/d). Let 16 - 55*z + 43*z + 5*z**2 - g*z**2 = 0. Calculate z.
2, 4
Let r be (-8 + (8 - 2))*11/(-396). Let p(o) be the second derivative of 0 - r*o**4 - 27*o + 7/3*o**2 + 2/3*o**3. Let p(h) = 0. Calculate h.
-1, 7
Let d(p) = 105*p**2 + 5*p - 5. Let o be d(1). Suppose o = -t + 36*t. Let -3/2*g**t + 0 + g + 5/2*g**2 = 0. What is g?
-1/3, 0, 2
Let o(n) be the second derivative of 1/110*n**5 - 2/33*n**3 - 1/66*n**4 + 0 + 0*n**2 + 23*n. Determine m, given that o(m) = 0.
-1, 0, 2
Let g(x) = -10*x**3 + 5*x**2 + 5*x + 5. Let p = -36 + 47. Let j(m) = p*m**3 - 6 - 3 - 5*m + 3 - 5*m**2 - m**4. Let l(b) = -6*g(b) - 5*j(b). Factor l(c).
5*c*(c - 1)*(c + 1)**2
Let c(j) be the first derivative of 30*j**2 - 2/3*j**3 - 450*j - 44.