**4/6 + 5*d**3/3 - d**2 + d - 19. Let i(b) = a*v(b) + 6*u(b). Factor i(h).
-2*(h + 1)**2*(h + 2)
Let x(b) = 6*b**4 - b**2 - b. Let t(v) = -35*v**4 - 16*v**3 + 2*v**2 + 70*v. Let h(i) = -t(i) - 6*x(i). What is u in h(u) = 0?
-2, 0, 2, 16
Let o(r) be the first derivative of -4/21*r**3 + 2/7*r + 2/35*r**5 + 30 + 1/21*r**6 - 1/7*r**4 + 1/7*r**2. What is d in o(d) = 0?
-1, 1
What is s in -108*s**2 - 1400*s - s**3 - 2*s**3 + s**3 + 444*s + 466*s = 0?
-49, -5, 0
Let u(o) be the second derivative of 1/2*o**4 + 12*o + 0*o**2 - 1/21*o**7 + 11/45*o**6 - 1 - 1/2*o**5 - 2/9*o**3. Factor u(n).
-2*n*(n - 1)**3*(3*n - 2)/3
Let d(y) be the first derivative of 5*y**3/3 + 175*y**2/2 + 480*y - 674. Solve d(n) = 0.
-32, -3
Let f(k) be the third derivative of k**5/300 - k**4/40 + k**3/15 + 4*k**2 + 391*k. Factor f(g).
(g - 2)*(g - 1)/5
Find t such that -8 + 8*t**2 + 177*t**3 - 69*t**3 - t - 107*t**3 = 0.
-8, -1, 1
Let j = 145244/83 + -1750. Let o = 184/249 + j. Suppose -3*h**2 + o*h - 11/3*h**4 + 0 + 5*h**3 + h**5 = 0. Calculate h.
0, 2/3, 1
Let k(j) be the third derivative of -j**6/150 - 851*j**5/75 + 341*j**4/6 - 1706*j**3/15 + 980*j**2. Factor k(a).
-4*(a - 1)**2*(a + 853)/5
Suppose -r = 3*r, -3*q + 3*r = -0*r - 51. Let o(z) be the second derivative of -4/3*z**3 + 0 + 1/6*z**4 + 4*z**2 + q*z. Factor o(i).
2*(i - 2)**2
Factor -8/17*z**3 + 0 - 2/17*z**4 + 0*z - 8/17*z**2.
-2*z**2*(z + 2)**2/17
Let b(t) be the third derivative of -1/36*t**5 + 2/3*t**3 + 1/120*t**6 - 3 + 0*t + 7*t**2 - 2/9*t**4. Factor b(d).
(d - 3)*(d + 2)*(3*d - 2)/3
Let h(j) be the second derivative of j**4/16 + 5*j**3/2 + 24*j**2 + 412*j. Suppose h(z) = 0. Calculate z.
-16, -4
Suppose 4*b - 40 = 22*c - 23*c, -105 = -5*c - b. Suppose 0 = r - 4*n - n + 25, 4*n = c. Solve 0*l - 2/5*l**3 + 2/5*l**5 + r*l**2 + 0*l**4 + 0 = 0.
-1, 0, 1
Find z such that -2/13*z**2 - 270/13*z + 1692/13 = 0.
-141, 6
Suppose -1686*o = 1684*o - 3388*o + 612. What is r in o*r**4 + 15236/7*r**2 + 4394/21 + 6/7*r**5 + 9126/7*r + 9596/21*r**3 = 0?
-13, -1/3
Let g be (-4 - -1)*(205/30 - 7). Let u(x) be the second derivative of g*x**2 - 31*x + 0 - 1/3*x**3 + 1/12*x**4. Factor u(v).
(v - 1)**2
Let q(h) = 20*h + 48. Let w be q(-2). Factor -1548 + l + 1540 - 5*l + 0*l**3 + 4*l**3 + w*l**2.
4*(l - 1)*(l + 1)*(l + 2)
Let l(g) be the third derivative of 0*g**3 - 180*g**2 - 1/525*g**7 + 0*g + 19/300*g**6 + 0*g**4 + 0 + 0*g**5. Factor l(x).
-2*x**3*(x - 19)/5
Let l(b) be the third derivative of b**2 - 23 + 0*b - 1/480*b**5 - 5/192*b**4 + 7/24*b**3. Solve l(f) = 0 for f.
-7, 2
Let h be (25/(-3))/(1 - 16/12). Let g be (-5)/h*-2*(-15)/(-24). Factor 3/4 + 5/4*b + g*b**5 - 1/4*b**4 - 1/2*b**2 - 3/2*b**3.
(b - 3)*(b - 1)*(b + 1)**3/4
Let b = 4465659/7 + -637951. Let -64/7 + 64/7*x**2 - 2/7*x**3 + b*x = 0. What is x?
-1, 1, 32
Let q(b) be the second derivative of b**4/3 - 22*b**3/3 - 120*b**2 - 1734*b + 4. Factor q(c).
4*(c - 15)*(c + 4)
Let q be (-3)/18*-2 - (4/48)/(3/(-42)). Determine o so that -15*o + q*o**2 - 36 = 0.
-2, 12
Suppose -33 = -k - 2*g, 0 = -2*k + 2541*g - 2543*g + 60. Let p(y) be the third derivative of -5/9*y**3 + 1/36*y**5 - 5/72*y**4 + 0*y + k*y**2 + 0. Factor p(n).
5*(n - 2)*(n + 1)/3
Let d(n) be the third derivative of -3/8*n**4 - 1/64*n**8 - 292*n**2 - 131/160*n**6 + 0 + 27/140*n**7 - 2*n**3 + 7/5*n**5 + 0*n. Let d(o) = 0. What is o?
-2/7, 1, 2, 4
Let m(w) = -13*w**2 - 5986*w - 1794009. Let f(j) = -11*j**2 - 5987*j - 1794008. Let l(z) = -4*f(z) + 3*m(z). Factor l(b).
5*(b + 599)**2
Let l(m) be the second derivative of 25/42*m**3 + 40 + 2*m - 13/7*m**2 + 1/84*m**4. Find j, given that l(j) = 0.
-26, 1
Let q = 1303/195 + -326/65. Determine z so that 5/3*z**4 + 0 + 0*z**2 + 0*z + q*z**3 = 0.
-1, 0
Let m(a) be the first derivative of 236 - 2*a**3 - 7/12*a**4 - 1/15*a**5 - 8/3*a - 10/3*a**2. Let m(j) = 0. Calculate j.
-2, -1
Let g(p) be the third derivative of -p**5/180 + 19*p**4/72 + 55*p**3/3 + 428*p**2. Factor g(a).
-(a - 30)*(a + 11)/3
Let q(i) be the second derivative of -i**6/40 - 219*i**5/8 + 733*i**4/4 - 367*i**3 - 413*i + 1. Solve q(v) = 0.
-734, 0, 2
Let 3*r**2 + 8231*r - 4752*r + 100*r = 0. What is r?
-1193, 0
Let r(s) be the first derivative of 27/4*s**4 - 6*s + 31/2*s**3 - 55 - 9*s**2. Suppose r(q) = 0. Calculate q.
-2, -2/9, 1/2
Let w(g) = 6*g**3 + 31*g**2 - 37*g - 70. Let y be w(-2). Factor -y*p + 16*p**2 + 4/3*p**3 + 256/3.
4*(p - 2)**2*(p + 16)/3
Let i(z) be the second derivative of 1/50*z**5 - 4/225*z**6 - 1/45*z**7 + 0*z**2 + 0*z**4 + 0*z**3 + 2*z + 1. Suppose i(o) = 0. Calculate o.
-1, 0, 3/7
Let d(p) be the second derivative of p**5/30 + 9*p**4/2 + 243*p**3 + 43*p**2 - 5*p + 9. Let b(j) be the first derivative of d(j). Factor b(c).
2*(c + 27)**2
Let l(d) be the first derivative of -d**6/180 - d**5/18 + 17*d**4/36 + 7*d**3/3 + 89*d**2/2 - 135. Let v(t) be the second derivative of l(t). Factor v(h).
-2*(h - 3)*(h + 1)*(h + 7)/3
Let t(x) = -x**3 - 2*x**2 - x + 1. Let w(q) = -13*q**3 - 8*q**2 + 13*q + 17. Let c be 12/(-32)*-4*12/(-9). Let n(g) = c*w(g) + 18*t(g). Solve n(f) = 0 for f.
-1, -1/2, 4
Let y = 603 + -4821/8. Let o be (4 - 1)*16/24. Solve y*f + 1/8*f**o - 1/2 = 0.
-4, 1
Let v be (-5)/(28*(-42)/(-147) - 132/14). Suppose v*r**4 - 45/8*r**3 - 5/8*r**5 - 3 + 13/2*r - 1/4*r**2 = 0. Calculate r.
-1, 3/5, 2
Let k = 1039302 - 1039300. Factor -14/3*a**3 + 32/3*a**5 + 16/3*a**4 + 2/3*a**k + 0 + 0*a.
2*a**2*(a + 1)*(4*a - 1)**2/3
Let j = -76/81 - -179/162. Let t(c) be the first derivative of -1/2*c - j*c**3 + 7 - 1/2*c**2. Factor t(z).
-(z + 1)**2/2
Suppose 2*c + r + 51 = 4*r, -135 = 5*c - 5*r. Let o = 219/7 + c. Factor 12/7*j - 4/7 + o*j**2 - j**3.
-(j - 2)*(j + 1)*(7*j - 2)/7
Let q(y) = -69*y**3 + 1560*y**2 + 1601*y + 35. Let a(t) = -35*t**3 + 777*t**2 + 803*t + 18. Let l(g) = 14*a(g) - 6*q(g). Find k, given that l(k) = 0.
-1, -1/38, 21
Let k(g) be the first derivative of 49/6*g**6 - 14 + 119/5*g**5 - 20*g**2 + 0*g + 292/3*g**3 - 285/2*g**4. Factor k(a).
a*(a - 2)*(a + 5)*(7*a - 2)**2
Let s(f) = -4*f**2 - 24*f - 22. Let p(h) be the second derivative of -h**4/12 + h**3/6 + h**2/2 + 227*h. Let v(i) = -4*p(i) + 2*s(i). Factor v(y).
-4*(y + 1)*(y + 12)
Let x(z) be the first derivative of z**4/12 - 2*z**3 + 59*z**2/6 + 66*z - 5244. Find a such that x(a) = 0.
-2, 9, 11
Let v(m) be the second derivative of -m**7/168 + 11*m**6/20 - 1413*m**5/80 + 891*m**4/4 - 2187*m**3/2 + 289*m + 1. Factor v(f).
-f*(f - 27)**2*(f - 6)**2/4
Suppose 0 = -15*g + 56 - 26. Determine o so that -49*o**2 + 128*o - 176*o + 40*o**3 + 36 + 6*o**5 + g*o**5 + 44*o**4 - 31*o**2 = 0.
-3, -1, 1/2, 1
Let z(a) be the first derivative of -3 - 6*a**2 + 3*a - 2*a**3 - 1/4*a**4. Let y(h) be the first derivative of z(h). Factor y(d).
-3*(d + 2)**2
Factor -104*i + 1/9*i**2 - 1260 + 1/9*i**3.
(i - 35)*(i + 18)**2/9
Let z(a) be the first derivative of 155 - 9261*a - 1414*a**3 + 10143/2*a**2 + 423/2*a**4 - 81/5*a**5 + 1/2*a**6. Factor z(g).
3*(g - 7)**3*(g - 3)**2
Factor -24/7*q**4 + 0*q + 1/7*q**5 + 0*q**2 + 0 + 44/7*q**3.
q**3*(q - 22)*(q - 2)/7
Let y(u) = -u**3 - 13*u**2 + u + 17. Let q be y(-13). Suppose -7 + 2*t**5 - 6*t**3 + 4*t + 6*t**4 + 7 - 2*t**2 - q*t**4 = 0. Calculate t.
-2, -1, 0, 1
Suppose 50410*w**2 + 14163*w**2 + 1092*w + 4 - 30717*w**2 + 40673*w**2 = 0. What is w?
-2/273
Let z(j) be the third derivative of j**5/450 + 25*j**4/18 + 496*j**3/45 + 7889*j**2. Solve z(w) = 0 for w.
-248, -2
Factor -75 + 23/2*z + 1/6*z**2.
(z - 6)*(z + 75)/6
Factor -29/3*o**2 + 0 + o**3 + 6*o.
o*(o - 9)*(3*o - 2)/3
Suppose s + 6*s = -5*s + 11*s. Let 0 - o + 3/4*o**3 + s*o**2 + 1/4*o**4 = 0. What is o?
-2, 0, 1
Suppose 22*q + 77*q = -60*q + 10*q. Let f(d) be the third derivative of 1/4*d**3 + 11/240*d**5 + 26*d**2 + 0 - 17/96*d**4 + q*d. Find x such that f(x) = 0.
6/11, 1
Let n = -17 - -30. Let l be ((-4)/16 - n/(-4)) + -1. Factor -16*q + 3*q**2 - 3*q**2 + 4*q**2 + 0*q**l.
4*q*(q - 4)
Let f(r) = -55*r**2 - 108 - 8*r + r**3 + 43*r - 3*r - 30*r. Let j be f(55). What is u in -14/15*u**4 - 18*u - 122/15*u**3 - 114/5*u**j + 36/5 = 0?
-3, 2/7
Let l = 6745/4 + -1686. Let j(v) be the first derivative of l*v**5 - 5/12*v**3 + 5/24*v**6 + 0*v**2 - 5/16*v**4 - 3 + 0*v. Solve j(y) = 0.
-1, 0, 1
Let w(l) be the third derivative of l**5/40 + 517*l**4/8 + 267289*l**3/4 + 1582*l*