
-5*j*(j - 30)*(j - 2)
Let b(h) be the first derivative of -h**5/5 + 4*h**4/3 + 10*h**3/3 - 98*h - 77. Let o(d) be the first derivative of b(d). Factor o(c).
-4*c*(c - 5)*(c + 1)
Factor -2/5*z**2 + 92/5*z - 208.
-2*(z - 26)*(z - 20)/5
Suppose -395 = -4*v + 5*o - 38, -3*v - 3*o + 261 = 0. Factor -8*l - 4 - v*l**2 + 48*l**2 + 36*l**2.
-4*(l + 1)**2
Let z(l) be the second derivative of -3*l**5/20 + l**4/2 + l**3/2 - 3*l**2 - 120*l + 1. Find t, given that z(t) = 0.
-1, 1, 2
Suppose 2*p - 37 = -31. Factor 1 + 25*a**4 - 24*a**4 - 16*a**p + 16*a**3 - 2*a**2.
(a - 1)**2*(a + 1)**2
Let f(j) be the first derivative of j**6 + 4*j**5/5 - 9*j**4 + 8*j**3 + 7*j**2 - 12*j - 3758. Factor f(m).
2*(m - 1)**3*(m + 3)*(3*m + 2)
Let t(d) be the first derivative of -d**5/20 + 7*d**4/12 - 5*d**3/2 + 9*d**2/2 - 33*d - 50. Let m(a) be the first derivative of t(a). What is y in m(y) = 0?
1, 3
Factor 187272 + 1/2*z**2 - 612*z.
(z - 612)**2/2
Let s(p) = 135*p - 15. Let a be s(2). Factor -5*h**2 - 57*h - 13*h - a + 10.
-5*(h + 7)**2
Let t = 97407/35 - 2783. Let z(k) be the first derivative of 0*k + 1/21*k**6 - 2/21*k**3 + 5 - 1/14*k**4 + 0*k**2 + t*k**5. Factor z(i).
2*i**2*(i - 1)*(i + 1)**2/7
Let 9580/9*z**3 + 103040/9*z + 1/9*z**5 + 53000/9*z**2 + 190/9*z**4 + 67712/9 = 0. Calculate z.
-92, -2
Let g = -70158/5 + 141021/10. Let 8 + g*x**2 - 40*x + 49/4*x**4 - 203/4*x**3 = 0. Calculate x.
4/7, 1, 2
Suppose 11*g**3 - 150*g**2 - 15*g**3 - 11232 - 2304*g + 31*g**3 - 16*g**3 - 14*g**3 = 0. What is g?
-26, -12
Let s(p) be the second derivative of p**6/195 + 129*p**5/130 - 87*p**4/26 + 131*p**3/39 + 3531*p. Suppose s(r) = 0. Calculate r.
-131, 0, 1
Suppose a - 4*a = -114. Suppose 0 = -a*o + 37 + 39. Factor -6*i + 3*i**3 - 3/2*i**4 - 6 + 9/2*i**o.
-3*(i - 2)**2*(i + 1)**2/2
Let q be (11730/(-1564))/((-15)/6). Factor 31250/3*j**q - 10750*j**2 + 336*j - 8/3.
2*(j - 1)*(125*j - 2)**2/3
Let m(b) be the third derivative of 119*b**5/40 - 179*b**4/4 + 3*b**3 + 3194*b**2. Let m(r) = 0. Calculate r.
2/119, 6
Let i be (-1)/(-9) - (-32)/(-288). Let y be -1 - i - (-91)/(-140)*-4. Let -4*q**2 - y*q + 12/5 = 0. Calculate q.
-1, 3/5
Factor 136 + 2/9*u**3 - 1216/9*u + 298/9*u**2.
2*(u - 2)**2*(u + 153)/9
Suppose -4 - 25 = -r - 9*u, -7*u + 6*u = -3. Solve 27/5*c**r + 56/5*c - 1/5*c**4 - 2/5*c**3 - 16 = 0 for c.
-4, 1, 5
Let n be 2/5 - (-936)/5460. Let f be -7 + (1 + 13)/2. Factor n*j**2 + f - 4/7*j**3 + 0*j.
-4*j**2*(j - 1)/7
What is q in 16/3*q + 17*q**3 + 0 + 19/3*q**4 + 1/3*q**5 + 49/3*q**2 = 0?
-16, -1, 0
Let c(i) be the first derivative of 2*i**3/21 - 6*i**2 + 874*i/7 - 2203. What is n in c(n) = 0?
19, 23
Let r(t) = -234*t + 1408. Let k be r(6). Factor -2/7*h**2 + k*h - 14.
-2*(h - 7)**2/7
Let y(l) be the second derivative of -9*l**5/25 - 61*l**4/5 + 259*l**3/6 - 55*l**2 + 941*l. Let y(w) = 0. What is w?
-22, 5/6
Let l(u) be the first derivative of 2*u**5/35 + 3*u**4 + 320*u**3/7 + 2150*u**2/7 + 6750*u/7 + 958. Find o such that l(o) = 0.
-27, -5
Factor 15/8*c**2 + 3/2 - 23/2*c.
(c - 6)*(15*c - 2)/8
Suppose -12*c + 17 = -26 - 5. Let y(s) be the first derivative of -15/14*s**2 + 3/28*s**c + 9/7*s + 1/7*s**3 + 18. Factor y(o).
3*(o - 1)**2*(o + 3)/7
Let q = 11/4614 - 7834627/23070. Let r = 340 + q. Factor -r + 1/5*x + 1/5*x**2.
(x - 1)*(x + 2)/5
Let k(x) = -29*x**3 + 1564*x**2 + 106*x + 111. Let a be k(54). Factor -1/2*y + 1/2*y**4 + 1 - 3/2*y**2 + 1/2*y**a.
(y - 1)**2*(y + 1)*(y + 2)/2
Let m(g) be the first derivative of -g**5 - 320*g + 174 - 360*g**2 - 45/2*g**4 - 485/3*g**3. Factor m(t).
-5*(t + 1)**2*(t + 8)**2
Suppose 3 - 457/2*l - 590*l**2 = 0. Calculate l.
-2/5, 3/236
Let p(k) be the first derivative of -k**6/18 + 8*k**5/15 - k**4/2 - 40*k**3/9 - 25*k**2/6 - 1144. Factor p(b).
-b*(b - 5)**2*(b + 1)**2/3
Let p(x) = 3*x**2 + 24*x - 25. Let m(v) = -v**3 + 3*v**2 + 2*v + 3. Let t be m(4). Let d(w) = 4*w**2 + 26*w - 26. Let y(q) = t*d(q) + 6*p(q). Factor y(f).
-2*(f - 5)*(f - 2)
Factor -2/3*w**4 + 0 - 130/3*w**3 + 0*w + 268/3*w**2.
-2*w**2*(w - 2)*(w + 67)/3
Suppose -4*b + 9885 - 9865 = b. Let x(q) be the second derivative of 0*q**2 - q + 1/9*q**3 + 0 - 1/18*q**b. Solve x(a) = 0 for a.
0, 1
Let i(j) = 30*j**4 - 27*j**3 - j**2 + 2*j. Let a(n) = -61*n**4 + 53*n**3 + 2*n**2 - 4*n. Suppose 6*o + 128 = 158. Let c(y) = o*i(y) + 2*a(y). Factor c(f).
f*(f - 1)*(4*f + 1)*(7*f - 2)
Let v(m) be the third derivative of -m**7/1575 - m**6/100 - 7*m**5/150 - 19*m**4/180 - 2*m**3/15 + 2274*m**2. Factor v(s).
-2*(s + 1)**3*(s + 6)/15
Suppose -6*c - 123 = -111. Let s be c/4 - 0 - (-99)/90. Factor 0 + s*r + 3/5*r**2.
3*r*(r + 1)/5
Solve -6*t**5 + 5167*t**3 + 1 - 5183*t**3 - 5*t**4 + 28*t**2 + 20*t**5 - 15*t**4 + 2*t - 9 = 0 for t.
-1, -4/7, 1
Let k(v) = 3*v**4 - 86*v**3 + 223*v**2 + 2*v + 2. Let g(m) = m**4 - 2*m**3 + m**2 - m - 1. Let l(r) = 2*g(r) + k(r). Find a, given that l(a) = 0.
0, 3, 15
Let q(v) = -6*v**3 + 18*v**2 - 23*v + 6. Let a(g) be the first derivative of -8 - 17*g**2 + 9*g**3 + 9*g - 9/4*g**4. Let t(z) = 5*a(z) - 7*q(z). Factor t(n).
-3*(n - 1)**3
Let y = 807 + -727. Suppose -93*a + 101*a = y. Factor -4*p + a + 2/5*p**2.
2*(p - 5)**2/5
Let q(w) be the second derivative of 0*w**2 - 16*w + 7/3*w**3 + 0 + 1/270*w**6 - 1/90*w**5 + 0*w**4. Let s(y) be the second derivative of q(y). Factor s(z).
4*z*(z - 1)/3
Factor g**2 - 2633/2*g + 658.
(g - 1316)*(2*g - 1)/2
Suppose 4831 = -4*q - 5*v, -2*q = -v + 1632 + 787. Let w be q/(-930) + (-1)/(-5). Determine s, given that 1/3 + 3/2*s**2 + w*s = 0.
-2/3, -1/3
Find m, given that -293*m**4 - 8*m**5 + 13*m**2 + 3*m**2 - 124*m**3 - 286*m**4 + 647*m**4 - m + 49*m = 0.
-1/2, 0, 1, 2, 6
Let u be -5 - -23 - (54 - 39). Let j(p) be the first derivative of u*p**5 - 25/4*p**4 + 0*p - 5 + 10*p**2 - 20/3*p**3. Determine r, given that j(r) = 0.
-1, 0, 2/3, 2
Let a(o) = -13187*o + 131870. Let h be a(10). Factor 48/11*b + h + 34596/11*b**3 + 2232/11*b**2 + 178746/11*b**4.
6*b*(31*b + 2)**3/11
Let h = -4580 + 7621. Determine m so that h + 36*m**3 + 72*m - 8*m - 96*m**2 - 4*m**4 - 3041 = 0.
0, 1, 4
Let s(r) be the third derivative of 13/180*r**5 - 1/6*r**4 - 21*r**2 - 1/60*r**6 + 1/630*r**7 + 0*r + 2/9*r**3 + 0. Factor s(x).
(x - 2)**2*(x - 1)**2/3
Let j(o) be the second derivative of -o**6/150 + 13*o**5/50 - 157*o**4/60 + 8*o**3 - 54*o**2/5 + 9*o + 142. Find z, given that j(z) = 0.
1, 6, 18
Solve -176/3 - 442/3*j - 1/3*j**4 - 119*j**2 - 92/3*j**3 = 0.
-88, -2, -1
Let i(o) = o**2 - 3*o - 7. Let l be i(5). Suppose 2*x - 2*z + 6 = 0, -l*x + 2*x + 3*z = 13. Factor -3/2 + 5/2*n + n**x.
(n + 3)*(2*n - 1)/2
Let d(x) be the second derivative of -x**4/4 - 7*x**3/2 + 21*x**2 - 5*x. Let l(j) = 2*j**2 + 11*j - 22. Let y(s) = -3*d(s) - 5*l(s). Factor y(k).
-(k - 4)**2
Let r(m) = -3*m**2 + 15*m - 9. Let v = 22 + -20. Let l(w) = 4*w - 2 + 5*w**2 + 6*w**2 + 2*w**v - 14*w**2. Let c(p) = -9*l(p) + 2*r(p). Factor c(b).
3*b*(b - 2)
Let l(h) be the third derivative of -4*h**2 + 5 + 1/80*h**6 - 1/840*h**7 + 0*h + 0*h**3 - 1/12*h**4 + 1/60*h**5 - 1/1344*h**8. Determine k, given that l(k) = 0.
-2, 0, 1, 2
Let -153/2*a + 345 + 3/2*a**2 = 0. Calculate a.
5, 46
Factor -3/7*m**3 - 162/7 - 117/7*m + 6*m**2.
-3*(m - 9)*(m - 6)*(m + 1)/7
Let w(u) be the second derivative of -u**5/4 + 1295*u**4/12 - 2575*u**3/6 + 1285*u**2/2 - 153*u - 1. Factor w(q).
-5*(q - 257)*(q - 1)**2
Let n = 69609/35 - 16782/7. Let l = n + 411. Factor l*o + 3/5*o**2 + 12/5.
3*(o + 2)**2/5
Find z, given that 4/7*z**2 + 0 + 0*z - 118/7*z**3 + 114/7*z**4 = 0.
0, 2/57, 1
Solve -87/4*n - 297/2 - 3/4*n**2 = 0 for n.
-18, -11
Let -4/3*s**5 + 2248/3*s**2 - 1148*s + 28*s**4 - 216*s**3 + 588 = 0. Calculate s.
1, 3, 7
Let s(r) be the second derivative of r**5/4 - 185*r**4/12 - 5*r**3/6 + 185*r**2/2 - 3*r - 1557. Let s(u) = 0. What is u?
-1, 1, 37
Let l(d) = d**2 + 40*d + 4. Let z be l(-40). Suppose 5*x = 3*x + z*x. Suppose -3/7*q**4 - 6/7*q + x*q**2 + 6/7*q**3 + 3/7 = 0. Calculate q.
-1, 1
Let o(d) be the first derivative of d**6/50 + d**5/100 - 17*d**4/60 + 19*d**3/30 - 3*d**2/5 + 22*d - 54. Let i(b) be the first derivative of o(b). Factor i(u).
(u - 1)**2*(u + 3)*(3*u - 2)/5
Let t = 41 - -15. Let b = t + -54. Determine u, given that -8 + 2*u**2 - 8 - 6*u**b - 18*u + 2*u**2 = 0.
-8, -1
Let s be (-9)/2*(-7 - (-133)/21). Let b(u) = -u**3 -