4 = 0. Calculate x.
-3, 0, 1, 5
Let v(p) be the second derivative of -1/50*p**6 + 9/20*p**4 - 1 + 0*p**2 + 0*p**5 - 56*p + 0*p**3. Factor v(a).
-3*a**2*(a - 3)*(a + 3)/5
Let q be (405 - 411)/(3/(-2)). Let n(t) be the second derivative of -3*t**2 - 3/4*t**q - 3/20*t**5 + 9*t + 5/2*t**3 + 1/10*t**6 + 0. Factor n(w).
3*(w - 1)**3*(w + 2)
Suppose 6*h - 4*g - 6 = h, h + g - 3 = 0. Determine m so that 16 - 60*m + 95*m + 2*m**h - 63*m + 10 = 0.
1, 13
Let o be 4/30 + (-876)/(-180). Solve -377*x**2 + 397*x**2 + 46*x + 24 + 3*x**3 - o*x**3 = 0.
-1, 12
Suppose -253 = 150*k - 226 - 477. Let q(l) be the first derivative of 4/3*l**k - 2*l**2 - 7 + 0*l. What is r in q(r) = 0?
0, 1
Let p(x) be the third derivative of -x**6/240 + 41*x**5/40 - 155*x**4/2 - 961*x**3/3 - 4*x**2 - 53. Factor p(w).
-(w - 62)**2*(w + 1)/2
Suppose 0*g = 3*g + 5*i - 36, -2*i + 36 = 3*g. Factor -9*b - 3 - g*b - 7*b - 9*b**2 + 23*b - 4*b - 3*b**3.
-3*(b + 1)**3
Let s(k) be the first derivative of -k**4/60 + 4*k**3/5 + 67*k + 25. Let x(i) be the first derivative of s(i). Factor x(a).
-a*(a - 24)/5
Let p(b) be the second derivative of b**4/18 + b**3/18 - b**2/2 + b - 1152. Factor p(x).
(x - 1)*(2*x + 3)/3
Let w = -22102 + 66310/3. Let q(n) be the first derivative of -w*n**3 - 8*n + 6 - 6*n**2. Factor q(m).
-4*(m + 1)*(m + 2)
Suppose -q - 2 + 16 = 3*y, 3*y = -4*q + 20. Factor -14*a**2 + 15 + 8 - 51*a**2 - q*a + 17 + 27*a.
-5*(a - 1)*(13*a + 8)
What is q in 324*q**4 + 3692/5*q**3 + 10*q**5 + 12 + 722/5*q + 2784/5*q**2 = 0?
-30, -1, -1/5
Suppose 792 - 735*t + 13*t - 46*t + 2*t**2 - 26*t = 0. Calculate t.
1, 396
Let p = 703675/3 - 234558. Find u such that p + 5/2*u**3 + 16/3*u**2 + 19/6*u = 0.
-1, -2/15
Solve 208/5*t + 36*t**2 - 64/5 + 47/5*t**3 + 4/5*t**4 = 0 for t.
-4, 1/4
Let f be 115700/2225 + 1 + -51. Solve -30*t - 600 - 3/8*t**f = 0 for t.
-40
Let f(p) = 15*p**3 - 10*p**2 - 54*p + 3. Let r(w) = -44*w**3 + 32*w**2 + 164*w - 8. Let h(o) = 8*f(o) + 3*r(o). Factor h(u).
-4*u*(u - 3)*(3*u + 5)
Let r(v) = v**2 + 11*v - 37. Let p be r(4). Let t be p/(-92)*((-39)/9 - 1). Factor 0 + t*g**2 + 0*g + 2/3*g**4 - 2*g**3.
2*g**2*(g - 2)*(g - 1)/3
Let i = 14102 + -14099. Factor 2/5*g + 6 - 2/5*g**i - 6*g**2.
-2*(g - 1)*(g + 1)*(g + 15)/5
Let t(m) = -277*m**2 + 4044*m - 14396. Let k(b) = -551*b**2 + 8079*b - 28791. Let i(w) = -4*k(w) + 9*t(w). Find q such that i(q) = 0.
120/17
Factor 1989 - 551 - 1436*p - 1078*p**2 + 2152*p**2 - 1076*p**2.
-2*(p - 1)*(p + 719)
Factor 1032252/5*a - 1028196/5 - 812*a**2 + 4/5*a**3.
4*(a - 507)**2*(a - 1)/5
Suppose 14*t = 8*t + 2664. Let b = 2223/5 - t. Factor -9/5*z**2 + 12/5*z + b*z**4 + 12/5 - 6/5*z**3.
3*(z - 2)**2*(z + 1)**2/5
Let v = -56 + 84. Factor v*u + 2*u + 5*u**4 - 30*u**3 - 60 + 57*u**2 - 12*u**2 - 10*u.
5*(u - 3)*(u - 2)**2*(u + 1)
Let z(t) be the first derivative of -4900*t**5 + 2896*t**2 + 625/3*t**6 - 576*t + 27 + 9300*t**4 - 21920/3*t**3. Find w, given that z(w) = 0.
2/5, 18
Let l(v) be the first derivative of -243*v**4/20 - 9*v**3 + 48*v**2/5 - 12*v/5 + 606. Factor l(z).
-3*(z + 1)*(9*z - 2)**2/5
Let n(j) be the second derivative of -j**4/3 + 912*j**3 - 935712*j**2 - 4*j + 881. Factor n(r).
-4*(r - 684)**2
Let i(d) be the first derivative of -d**4/3 + 8*d**3/3 - 3*d - 36. Let a(y) be the first derivative of i(y). Factor a(f).
-4*f*(f - 4)
Suppose 14*j + o - 257 = 0, -5*j - 61 = -7*j - 5*o. Let h(u) be the first derivative of j + 2/3*u**2 + 0*u - 1/9*u**3. Suppose h(c) = 0. What is c?
0, 4
Let v(h) = 3*h**2 + 26*h - 2. Let i(w) = -14*w**2 - 122*w + 9. Let j(g) = -4*i(g) - 18*v(g). Factor j(a).
2*a*(a + 10)
Let z(v) be the first derivative of v**3 + 807*v**2/2 - 1626*v - 4354. Find w such that z(w) = 0.
-271, 2
Solve 3*j**5 + 10*j**4 + 20*j + 3542 - 4*j - 5*j**5 + 324 - 674 - 2402*j**2 + 786*j**3 = 0 for j.
-19, -1, 2, 21
Let f(y) be the first derivative of -2*y**5/5 - 37*y**4/2 - 646*y**3/3 + 361*y**2 - 27. What is k in f(k) = 0?
-19, 0, 1
Let m(i) be the second derivative of i**7/21 - 3*i**6/5 + 29*i**5/10 - 13*i**4/2 + 6*i**3 + 5545*i. Suppose m(y) = 0. Calculate y.
0, 1, 2, 3
Factor 2045813/3*t + 729*t**3 - 9/2*t**4 + 4330747/6 - 39120*t**2.
-(t + 1)*(3*t - 163)**3/6
Suppose 25*f - 56*f + 21*f = 0. Let s(l) be the third derivative of f*l + 11*l**2 + 0 + 1/10*l**4 + 6/5*l**3 + 1/300*l**5. Suppose s(x) = 0. Calculate x.
-6
Suppose -37 + 29 = -2*m. Determine o so that -726*o + 9*o**2 + 618*o + m*o**3 + 56 + 39*o**2 + 0*o**3 = 0.
-14, 1
Let w be (-736)/(-176) + 6/(-33). Find u, given that -u**w - 448*u + 444*u + 2*u**4 + u**3 - 10*u**2 + 24 = 0.
-3, -2, 2
Suppose -1687*c - 21 = 5*t - 1684*c, 14 = -2*t - 2*c. Factor 0 + 0*o**2 + t*o + 2*o**3 + 2/3*o**5 + 8/3*o**4.
2*o**3*(o + 1)*(o + 3)/3
Let m(l) be the first derivative of -l**4/14 - 68*l**3/7 + 15*l**2 + 412*l/7 + 3321. Determine f so that m(f) = 0.
-103, -1, 2
Let n(i) = -4*i**3 + 310*i**2 + 10950*i - 11250. Let u(g) = -3*g**3 + 308*g**2 + 10950*g - 11250. Let l(b) = -5*n(b) + 6*u(b). Factor l(r).
2*(r - 1)*(r + 75)**2
Let w(t) be the third derivative of t**5/510 + t**4/102 - 5*t**3 - 1784*t**2 + 2*t + 2. Factor w(o).
2*(o - 15)*(o + 17)/17
Let j(m) be the third derivative of 37*m**5/510 - 35*m**4/204 + 9380*m**2. Factor j(i).
2*i*(37*i - 35)/17
Let a(x) be the first derivative of 4*x**5/5 - 13*x**4 + 224*x**3/3 - 160*x**2 + 1562. Factor a(m).
4*m*(m - 5)*(m - 4)**2
Suppose 2*k + 67 = f, -9 = 3*f + 6. Let g be (-106)/(-8) + k/(-48). Solve -4*o**2 - 2 + 16*o + 0 - g = 0.
2
Suppose -s = -6*o + 2*o + 10, -2*s = 4*o + 20. Let m be (16/s)/(16/(-40)). Suppose -58*c + 54*c + 4*c**4 + m*c**3 - 2*c**4 + c**2 - 3*c**2 = 0. Calculate c.
-2, -1, 0, 1
Let t(l) = 71*l - l**2 + 28 + 107 + 87*l + 76*l - 205*l. Let k be t(33). Factor -9/4 - 9/4*r**2 - 33/8*r - 3/8*r**k.
-3*(r + 1)*(r + 2)*(r + 3)/8
Suppose 2*r + 3*g = -38, 4*g + 52 = 1829*r - 1831*r. Find t such that 10/3*t**3 + 2*t**r - 8/3*t**4 + 2/3 - 10/3*t = 0.
-1, 1/4, 1
Let n(q) be the third derivative of -q**5/240 + q**4/24 + q**3/2 - 6378*q**2. Determine i so that n(i) = 0.
-2, 6
Let z(g) be the first derivative of -3*g**5/20 - 125*g**4/16 - 105*g**3/4 - 115*g**2/8 + 39*g/2 - 377. Determine b so that z(b) = 0.
-39, -2, -1, 1/3
Let d(k) be the second derivative of 0*k**2 + 2*k**5 + 0*k**3 + 2 + 0*k**4 - k - 2/15*k**6. Determine q, given that d(q) = 0.
0, 10
Find g, given that -3*g**5 + g**5 - 18*g**4 + 110*g + 274*g + 144*g**2 - 123*g**2 + 139*g**2 - 24*g**3 = 0.
-4, 0, 3
Suppose -25*w = -20*w - 10. Suppose s**4 - 48*s**w - 16189*s + 3*s**4 + 16109*s + 36*s**3 = 0. Calculate s.
-10, -1, 0, 2
Factor 0 - 2000*f - 920*f**2 - 2/5*f**4 + 196/5*f**3.
-2*f*(f - 50)**2*(f + 2)/5
Factor -29/4*k + 0 - 7*k**2 + 1/4*k**3.
k*(k - 29)*(k + 1)/4
Let d(p) = p**3 + p - 1. Suppose -11*k = -17 + 6. Let q(x) = -6*x**3 + 35*x**2 - 31*x + 1. Let i(s) = k*q(s) + d(s). Suppose i(c) = 0. Calculate c.
0, 1, 6
Let h(c) be the second derivative of c**7/21 - 14*c**6/15 + 9*c**5/2 - 26*c**4/3 + 20*c**3/3 + 2306*c. What is o in h(o) = 0?
0, 1, 2, 10
Let o(w) be the second derivative of -2*w**6/165 + 41*w**5/220 - 47*w**4/66 + 7*w**3/22 + 1072*w. Solve o(u) = 0.
0, 1/4, 3, 7
Determine v so that 51 + 19 + 315*v**2 + 235 + 370*v + 106*v + 5*v**3 + 139*v = 0.
-61, -1
Factor 1/3*p**2 + 67/3*p - 46.
(p - 2)*(p + 69)/3
Let f = 2269413/407323 - 6/58189. Factor 240/7*g**2 + f*g**3 + 54/7 + 387/7*g.
3*(g + 3)**2*(13*g + 2)/7
Let p(r) be the third derivative of r**7/420 - 7*r**6/16 - 107*r**5/120 + 35*r**4/16 + 53*r**3/6 - 82*r**2 + 9. Factor p(x).
(x - 106)*(x - 1)*(x + 1)**2/2
Let b = 1/430320 + 765013/143440. Factor -b*y - 1/3*y**2 - 64/3.
-(y + 8)**2/3
Let a be 2*6*((-100)/9 + 11) + (9 - 7). Factor a*h**3 + 0*h + 8/3 - 2*h**2.
2*(h - 2)**2*(h + 1)/3
Let j be (-2)/(4/(-108)*6). Suppose 4 = j*z - 7*z. Let 2/3*s**4 - 2/3*s + 2/3 + 4/3*s**3 - 2/3*s**5 - 4/3*s**z = 0. What is s?
-1, 1
Suppose 5*c = 4*w + 3 - 11, -3*c - 2 = -2*w. Let m(a) = -a**3 + 2*a**2 + 35*a + 3. Let s be m(w). Factor -2/9*y**5 + 0 + 0*y - 2/3*y**4 - 2/9*y**2 - 2/3*y**s.
-2*y**2*(y + 1)**3/9
Suppose 16*j - 617 = -a + 20*j, 3*a - 3*j = 1806. Let g = -594 + a. Let 2/3*h**2 - 5/3 + g*h = 0. Calculate h.
-5, 1/2
Let g = 189566 - 1706090/9. Let -2/9*d**3 + 0 + g*d**4 + 0*d**2 + 0*d + 2/3*d**5 = 0. What is d?
-1, 0, 1/3
Let r(w) be the 