m**3 + 1/2*m**2.
m**2*(m + 1)**2/2
Suppose -2*r = 9*l - 60 + 29, 4*r - 2*l = 2. Factor -1/4*f**r - 2*f - 15/4.
-(f + 3)*(f + 5)/4
Let n = 805 + -795. Suppose -6 = 8*p - n*p. Determine s so that 4/9*s**2 - 1/9*s**p + 2/9 - 5/9*s = 0.
1, 2
Let n = 246167 - 246166. Let v be (-2)/5*(-125)/20. Let n + 1/2*h**3 + 2*h**2 + v*h = 0. What is h?
-2, -1
Let x = 66937 + -736303/11. Factor 2/11*w**2 - x*w + 0.
2*w*(w - 2)/11
Suppose 2*k + 8 = 0, 2*k = -3*z - 2*k - 4. Let p be 2/z*-4 + 5. Determine r so that 4*r - 5*r**3 - 10*r**2 + 6*r**4 + 4*r**2 + r**p = 0.
-1, 0, 2/3, 1
Let x = 372 + 2431. Suppose 164*o**2 + 20 - 2819*o**4 + x*o**4 + 168*o + 12*o**3 + 12 = 0. What is o?
-2, -1, -1/4, 4
Let l be (-1 + (-162)/(-120))*5/20. Let g(h) be the second derivative of 0*h**3 - l*h**5 + 0*h**2 + 1/30*h**6 - 1/24*h**4 + 0 + 9*h. Solve g(o) = 0 for o.
-1/4, 0, 2
Let v(a) be the third derivative of -a**7/70 + a**6/8 + 7*a**5/20 - 41*a**4/8 + 15*a**3 + 7*a**2 - 104. Determine x, given that v(x) = 0.
-3, 1, 2, 5
Let b be (-4)/(-18) + 345/27. Suppose -11*g + b + 9 = 0. Find h, given that -2/3*h**3 + 2/3*h**g + 2/3*h - 2/3 = 0.
-1, 1
Factor -2679 - 19376*n + 88*n**4 - 1636*n**3 - 1568 - 8649 - 9720*n**2 - 92*n**4.
-4*(n + 2)**3*(n + 403)
Let p(s) = -s**3 - 22*s**2 - 47*s - 2268. Let g be p(-24). Let z(q) be the second derivative of 0 - g*q**3 - 22*q + 216*q**2 + 1/4*q**4. Factor z(r).
3*(r - 12)**2
Let y be (-4)/(-6) - 34148/(-6). Let h = -5608 - -11300. Determine b, given that 4*b - h + y - b**3 - b**2 + 5*b**2 - b**4 = 0.
-2, -1, 0, 2
Let t be ((-589)/(-31) + -19)*-1. Solve t - 2/19*l**2 - 2/19*l**3 + 12/19*l = 0.
-3, 0, 2
Let s be 10008/(-973)*(-3)/6. Factor 0*l - 54/7 + 2/7*l**4 + s*l**2 - 16/7*l**3.
2*(l - 3)**3*(l + 1)/7
Let z(h) be the first derivative of -h**4/2 + 26*h**3 + 126*h**2 + 1223. Factor z(a).
-2*a*(a - 42)*(a + 3)
Suppose 0 = 5*w - 3*w. Suppose c - q - 6 = -4*q, c - 3*q = w. Factor 36*s**2 + 24*s + 192 + 4*s**c + 5*s**3 + 120*s - 6*s**3.
3*(s + 4)**3
Let m(j) be the first derivative of j**6/180 + j**5/12 + 7*j**4/18 + 2*j**3/3 - 56*j + 16. Let w(d) be the first derivative of m(d). Solve w(p) = 0.
-6, -2, 0
Suppose -22 + 36 = 92*w - 170. Solve -35/8*s**3 + 21/4*s + w - 9/8*s**2 = 0 for s.
-1, -2/5, 8/7
Suppose 2*z = 1 + 3. Find d such that 3*d**2 - 110*d + d**z + 5*d**2 - 4*d**2 - 115 = 0.
-1, 23
Let n(w) be the first derivative of -w**4/30 + 56*w**3/15 - 208*w**2/5 + 2432*w/15 + 3236. What is i in n(i) = 0?
4, 76
Let s(m) be the first derivative of -m**3 + 345*m**2 - 687*m + 3595. Solve s(u) = 0.
1, 229
Let m(y) = -5*y + 75. Let n be m(5). Let g be ((-15)/n)/3 + 29/90. Factor -10/9*p + g*p**2 + 8/9.
2*(p - 4)*(p - 1)/9
Let p = -162 + 164. Find n, given that -5*n + 7*n**2 - 9*n**p - 6 + n**2 = 0.
-3, -2
Let r(n) = 28*n + 81. Let q be r(-3). Let l be q - 52/(-24)*3/2. Factor l*d - 3/4*d**2 + 1/2.
-(d - 1)*(3*d + 2)/4
Let l = 261389/378 - 1383/2. Let m(u) be the second derivative of 0*u**3 + l*u**7 + 0*u**2 + 2/135*u**6 - 8*u + 0*u**4 + 0 + 1/90*u**5. Factor m(a).
2*a**3*(a + 1)**2/9
Let i = -88 - -82. Let v be i/(-4) - (-21)/42. Determine y, given that -138*y**2 + 2 - 45*y**4 + 28*y**v - 7 + 120*y**3 + 40*y = 0.
1/3, 1
Let d(y) be the first derivative of -96/7*y**2 - 5*y - 24/7*y**3 - 3/7*y**4 - 7 - 3/140*y**5. Let l(w) be the first derivative of d(w). Factor l(p).
-3*(p + 4)**3/7
Let v(q) be the second derivative of 0*q**6 - 3 - 6/7*q**3 - 12/7*q**2 + 3*q + 1/14*q**4 + 3/20*q**5 - 1/98*q**7. Solve v(c) = 0.
-2, -1, 2
Let q(x) = 6*x**5 - 40*x**4 - 60*x**3 - 40*x**2 - 18*x - 16. Let y(h) = -h**5 + 3*h**4 + 2*h**3 - h**2 + 2. Let c(b) = q(b) + 8*y(b). Factor c(w).
-2*w*(w + 1)**2*(w + 3)**2
Factor 136/3*w**2 - 16/3*w + 0 + 148/3*w**3 + 38/3*w**4.
2*w*(w + 2)**2*(19*w - 2)/3
Suppose -8*y - 104/7 - 2/7*y**2 = 0. What is y?
-26, -2
Let l(j) be the first derivative of -j**3/6 - 955*j**2/4 + 478*j - 9981. Let l(u) = 0. What is u?
-956, 1
Let z(s) be the second derivative of 2*s - 3/70*s**5 + 0*s**3 - 1/147*s**7 + 0*s**2 - 1/35*s**6 - 1/42*s**4 - 2. What is k in z(k) = 0?
-1, 0
Let u be 357/72 + -8 + 7. Let z = -59/24 + u. What is g in -3/2 + 3/2*g - 3/2*g**3 + z*g**2 = 0?
-1, 1
Let t be (-1243)/(-113) + -8*(0 - -1). Determine u, given that 39*u - 63/2*u**2 - 63/4 + 9*u**t - 3/4*u**4 = 0.
1, 3, 7
Let k(m) be the second derivative of -m**5/190 + 199*m**4/114 + 134*m**3/19 - 22*m + 211. Factor k(p).
-2*p*(p - 201)*(p + 2)/19
Let x(h) = -11*h**5 - 47*h**4 + 108*h**3 - 8*h**2 - 107*h + 57. Let l(o) = 3*o**5 + o**4 + o**3 - o**2 + o - 1. Let q(j) = -2*l(j) - x(j). Factor q(t).
5*(t - 1)**3*(t + 1)*(t + 11)
Let u(k) be the first derivative of -4/3*k + 51 - 49/12*k**4 + 4*k**2 - 7/3*k**3. Suppose u(a) = 0. Calculate a.
-1, 2/7
Let r(j) be the second derivative of j**5/12 + 95*j**4/12 - 1120*j**3/9 + 12*j + 206. Factor r(l).
5*l*(l - 7)*(l + 64)/3
Let n(b) be the second derivative of -21*b - 1/48*b**4 - 7/2*b**3 - 441/2*b**2 - 3. Suppose n(l) = 0. What is l?
-42
Let b(w) = w**3 + 11*w**2 - 12*w + 2. Let z be b(-12). Let l be (-3)/((-9)/24*2). Factor 10*o**5 + 23*o**4 - 30*o**l + z*o**3 + 19*o**4.
2*o**3*(o + 1)*(5*o + 1)
Let x(b) be the first derivative of -4*b**5/5 + 91*b**4 + 252*b**3 - 558*b**2 - 2615. Suppose x(k) = 0. What is k?
-3, 0, 1, 93
Factor -13454*z**3 - 36/7 + 5190/7*z - 26536*z**2.
-2*(z + 2)*(217*z - 3)**2/7
Solve 4897*o + 1083*o**2 + 372*o**3 + 43*o + 1418*o**2 + 583*o**2 + 4*o**4 - 8400 = 0.
-84, -5, 1
Suppose -21*s = -32*s + 330. Let m(n) = n**2 + n - 2. Let f(o) = 7*o**2 + 11*o - 6. Let q(l) = s*m(l) - 5*f(l). Factor q(g).
-5*(g + 2)*(g + 3)
Let w(k) = -32*k + 192. Let d be (-8 - -3)/(-1*35/42). Let b be w(d). Solve b - 2/13*a**3 + 0*a + 0*a**2 + 2/13*a**4 = 0 for a.
0, 1
Let j = -2175741/2387 - -10004/11. Let d = j + 81/31. Factor 2/7*z**2 + d*z + 0.
2*z*(z + 2)/7
Let m(v) be the second derivative of -v**6/105 - v**5/14 + 11*v**4/21 - 16*v**3/21 + v - 8953. Let m(k) = 0. What is k?
-8, 0, 1, 2
Factor 0 + 44/23*a**2 - 2/23*a - 42/23*a**3.
-2*a*(a - 1)*(21*a - 1)/23
Let -116/11*c**2 - 70/11*c**4 + 186/11 - 252/11*c**3 - 2/11*c**5 + 254/11*c = 0. Calculate c.
-31, -3, -1, 1
Let d(y) be the second derivative of -y**6/6 + y**5 + 95*y**4/6 + 50*y**3 + 135*y**2/2 + 192*y - 1. Determine r, given that d(r) = 0.
-3, -1, 9
Factor 324 + 12*z**3 + 378*z - 4*z**4 + 144*z**2 - 2/3*z**5.
-2*(z - 6)*(z + 3)**4/3
Let g(v) be the first derivative of 170 + 15/4*v**4 - 15/2*v**2 - v**3 + 3/5*v**5 + 0*v. Factor g(w).
3*w*(w - 1)*(w + 1)*(w + 5)
What is j in -939/2*j + 293907/4 + 3/4*j**2 = 0?
313
Let z(b) be the third derivative of 0*b - 5/6*b**4 + 0 - 1/84*b**8 + 0*b**3 - 3/5*b**6 + 16/15*b**5 - 26*b**2 + 16/105*b**7. Solve z(v) = 0 for v.
0, 1, 5
Let c = 789/11438 + 2/817. Let f(v) be the first derivative of 0*v**2 - 33 + 0*v + c*v**4 - 4/21*v**3 + 2/35*v**5. Factor f(r).
2*r**2*(r - 1)*(r + 2)/7
Let k = -268/417 - -2323/1668. Factor -3*b**2 + 9/2 - k*b - 3/4*b**3.
-3*(b - 1)*(b + 2)*(b + 3)/4
Let g(x) be the third derivative of -2*x**2 + 0*x + 1/20*x**5 + 7 + 0*x**3 + 1/14*x**4 - 1/140*x**6. Find l such that g(l) = 0.
-1/2, 0, 4
Let c = -268 + 271. Factor 6*n**3 - 5 - 18*n**4 + 81*n + 71*n**2 - 12*n**c - 11*n**2 + 35 - 3*n**5.
-3*(n - 2)*(n + 1)**3*(n + 5)
Let y(b) = 609*b**2 - 198*b - 21. Let l(s) = -611*s**2 + 199*s + 22. Let i(c) = -2*c**2 + c. Let j(n) = -2*i(n) + l(n). Let f(x) = 3*j(x) + 4*y(x). Factor f(t).
3*(5*t - 2)*(41*t + 3)
Let l(r) = -r**2 + 206*r - 10526. Let c be l(94). Let z = 2201/36 + -241/4. Factor 2/3*j**c - z + 0*j - 2/9*j**3.
-2*(j - 2)**2*(j + 1)/9
Let k(z) = -4*z**4 - 18*z**3 - 44*z**2 + 54*z - 6. Let q(g) = -g**4 - 2*g**3 + 2*g**2 + 9*g - 1. Let h(i) = k(i) - 6*q(i). Factor h(a).
2*a**2*(a - 7)*(a + 4)
Find p such that -2672*p + 309*p**2 + 188*p**3 + 20 - 233 + 35 - 1241*p**2 + 66 = 0.
-2, -2/47, 7
Let i(m) be the first derivative of -5*m**3/9 + 55*m**2/6 + 70*m - 174. Factor i(f).
-5*(f - 14)*(f + 3)/3
Let d(o) be the first derivative of -o**6/15 - 48*o**5/25 + 11*o**4/2 + 148*o**3/15 - 108*o**2/5 - 208*o/5 + 1049. Determine g, given that d(g) = 0.
-26, -1, 2
Let i(o) = -12*o**2 + 1405*o - 5533. Let l be i(113). Factor -3 + 13/2*z + 1/2*z**3 - l*z**2.
(z - 6)*(z - 1)**2/2
Let n be -3 + 4/((-68)/(-53)). Let i = 162670/51 + -9566/3. Factor