**3/3 + 5216*c. Suppose m(k) = 0. Calculate k.
-8, 0, 2/3, 2
Let y = 875 + -875. Let x(p) be the second derivative of 0 + 14*p + y*p**2 + 4/27*p**3 + 1/54*p**4. Factor x(g).
2*g*(g + 4)/9
Let q(p) be the second derivative of -p**10/6048 - p**9/756 - 5*p**8/1344 - p**7/252 - 3*p**4/2 + p - 1. Let l(r) be the third derivative of q(r). Factor l(b).
-5*b**2*(b + 1)**2*(b + 2)
Factor -939*w + 15*w - 369*w**2 - 375*w**2 + 742*w**2 + 926.
-2*(w - 1)*(w + 463)
Suppose -24*w + 42*w - 126 = 0. Suppose 5*b + 2*j = 0, 3*j = w*b - 3*b - 23. Suppose -3/8*t**b - 1/8*t**4 + 3/8*t**3 + 0 + 1/8*t = 0. Calculate t.
0, 1
Let u(a) be the third derivative of a**5/24 + 55*a**4/6 + 2420*a**3/3 + 1046*a**2. Factor u(f).
5*(f + 44)**2/2
Determine h, given that -1384/5*h + 461/5 - 464/5*h**3 + 1386/5*h**2 + 1/5*h**4 = 0.
1, 461
Factor -190/13*t - 42/13 + 28/13*t**2.
2*(t - 7)*(14*t + 3)/13
Let x(i) be the second derivative of i**7/147 - 101*i**6/105 + 575*i**5/14 - 16199*i**4/42 + 16168*i**3/21 + 35344*i**2/7 + 11349*i. Let x(n) = 0. What is n?
-1, 4, 47
Let m(a) = -4*a**2 + 152*a. Let t(r) = -12*r**2 + 456*r. Suppose 35*c + 26 = 33*c + 4*b, -b = 2*c + 36. Let p(g) = c*m(g) + 6*t(g). Find j such that p(j) = 0.
0, 38
Let q = -107029/4 - -26759. Factor l**2 + 1/8*l**3 - q + 5/8*l.
(l - 1)*(l + 2)*(l + 7)/8
Let u(q) be the second derivative of -4/9*q**3 + 0 + 158*q + 1/45*q**6 + 4/9*q**4 - 1/6*q**5 + 0*q**2. What is r in u(r) = 0?
0, 1, 2
Factor -18 - 109/4*q - 1/8*q**2 + 3/8*q**3.
(q - 9)*(q + 8)*(3*q + 2)/8
Suppose -48 = 4*o - 56. Find l such that -44*l**4 - 2*l**o - l**3 - l + 4 + 45*l**4 - 3 - l**5 + 3*l**3 = 0.
-1, 1
Let r(s) be the second derivative of s**6/180 + 2*s**5/15 - 3*s**4/4 - s**3/3 - 5*s**2/2 - 17*s. Let a(m) be the second derivative of r(m). Solve a(z) = 0.
-9, 1
Let s = -15274/3 + 5094. Let q be (-4 + 11/3)*-6. What is c in -2 - 2/3*c**q + s*c = 0?
1, 3
Let z(q) be the third derivative of 39/2*q**4 + 68/3*q**3 + 18*q**2 + q + 0 - 7/15*q**5. Factor z(o).
-4*(o - 17)*(7*o + 2)
Let h = 149 + -145. Suppose -30 = -h*f - 2*f. Let 4*d**4 - 5*d - 5*d**3 + d**4 + f*d = 0. What is d?
0, 1
Let q = -4400 - -4405. Let t(w) be the third derivative of 4*w**3 + 0 + 0*w - 5/6*w**4 + 38*w**2 + 1/15*w**q. Factor t(i).
4*(i - 3)*(i - 2)
Let k(q) = -3*q**4 - 1315*q**3 + 311*q**2 - 7*q + 7. Let g(n) = -2*n**4 - 1313*n**3 + 313*n**2 - 6*n + 6. Let j(t) = 7*g(t) - 6*k(t). Factor j(x).
x**2*(x - 325)*(4*x - 1)
Let j be ((-5)/7)/(600/(-350)). Let m(i) be the second derivative of 1/8*i**5 - 5/4*i**2 + 5/24*i**4 + 0 - 12*i - j*i**3. Let m(p) = 0. What is p?
-1, 1
Let k be -4 - (-9 + 1 - -2). Solve -49 + 344*l**2 - 175*l**k - 170*l**2 - 14*l = 0.
-7
Let h be (-84)/16*(-4)/3. Solve -15*p**4 + 2*p**2 + p**3 + 7*p**4 + h*p**4 = 0 for p.
-1, 0, 2
Let o(c) = -c**3 - 11*c**2 + 19*c + 333. Let r be o(-9). Let l(h) be the first derivative of -3/7*h**2 + r*h - 5/7*h**3 - 3. Solve l(v) = 0.
-2/5, 0
Let q be (-405)/63 - (-31 + 44 + -22). Find o such that q - 2/7*o**2 + 0*o = 0.
-3, 3
Let f(y) = -4*y**2 - 8*y - 92. Let o be f(-6). Let a = 944/5 + o. Find t, given that -4/5*t**4 + 0 + 0*t + 8/5*t**3 - a*t**2 = 0.
0, 1
Let q = 455 - 453. Suppose -3*z - 2*y + 4 = 0, 3*z + 11 - 43 = 5*y. Let -5/6*d - 7/6*d**3 - 1/6 - 1/3*d**z - 3/2*d**q = 0. Calculate d.
-1, -1/2
Let q = 196 - 193. Let i(p) = p**3 + p**2 - p - 1. Let d(u) = -7*u**3 + u**2 + 23*u + 15. Let n(l) = q*i(l) + d(l). Solve n(z) = 0 for z.
-1, 3
Suppose 5*l = 2*i + 3*l - 48, 2*i = l + 46. Suppose -11*n**2 - i + 30*n + 8 - 26 + 6*n**2 = 0. Calculate n.
2, 4
Let l(v) be the second derivative of -v**4/30 + 572*v**3/5 - 736164*v**2/5 + 542*v + 12. Solve l(g) = 0 for g.
858
Suppose -12 = -5*u + 3. Find v such that -12*v**4 + 276*v**2 - 15*v**4 + 103*v**3 - 283*v**u - 96*v = 0.
-8, 0, 2/3
Factor -7 - 20*c**2 + 7 + 99*c**4 - 16*c**3 + 109*c**4 - 212*c**4 - 8*c.
-4*c*(c + 1)**2*(c + 2)
Let r(g) be the third derivative of g**5/180 + 57*g**4/8 - 1287*g**2. Suppose r(v) = 0. Calculate v.
-513, 0
Let g = -338 - -362. Solve 11*l - 18*l**3 - 3*l**4 + 3*l + 8 - 53 + 4*l + 24*l**2 + g = 0 for l.
-7, -1, 1
Let p(w) be the second derivative of w**5/180 - 79*w**4/108 - 161*w**3/54 - 9*w**2/2 - 801*w. Factor p(l).
(l - 81)*(l + 1)**2/9
Let h be (-2)/(-19) - 15916/(-98610). Let q(t) be the second derivative of 1/15*t**4 + 0*t**2 + 0 - 5*t + h*t**3. Factor q(x).
4*x*(x + 2)/5
Let s(g) be the second derivative of 0*g**4 - 139*g + 0 + 0*g**2 + 2*g**3 - 3/20*g**5. Find l such that s(l) = 0.
-2, 0, 2
Suppose 7*j + 4*j = 0. Let i be ((-3)/(-42))/((-5)/(-20) - j). What is p in 2/7 + 0*p - i*p**2 = 0?
-1, 1
Let v be ((-540)/(-8))/(-1)*(-8)/3. Let q = 182 - v. Suppose -1/2*u**q + 1/2*u + 1 = 0. Calculate u.
-1, 2
Let m(s) be the third derivative of -s**5/360 - 13*s**4/48 - 35*s**3/9 + 2*s**2 - 140*s - 7. Solve m(f) = 0.
-35, -4
Suppose -3*r + 8 = r, -4*r = k - 11. Suppose 4*p + 72 = k*t, 96 = -t + 4*t + 4*p. Let -t*n - 128 + 136 + 2*n**4 + 36*n**2 + 2*n**4 - 20*n**3 = 0. What is n?
1, 2
Let z(y) be the second derivative of 5*y**7/42 - 4*y**5 + 95*y**4/6 - 55*y**3/2 + 25*y**2 + 653*y. Factor z(u).
5*(u - 2)*(u - 1)**3*(u + 5)
Suppose 40 = -4*z - z. Let i be 10*(28/z + 4). Suppose 20*x - 8 - 4 + 6 - 14 - i*x**2 = 0. Calculate x.
2
Let k be -8*(-9)/(-18) - -12. Let g(u) = 4*u**3 + 56*u**2 - 140*u + 64. Let z(f) = 3*f**3 + 37*f**2 - 93*f + 43. Let c(j) = k*z(j) - 5*g(j). Factor c(q).
4*(q - 1)**2*(q + 6)
Let u(m) = -m**2 + m + 20. Let y = -88 - -93. Let s be u(y). Find r, given that 0*r + s + 3/7*r**2 = 0.
0
Let r(f) be the third derivative of -f**8/672 - f**7/105 + 11*f**6/40 - 29*f**5/30 + 55*f**4/48 - 1296*f**2. Solve r(w) = 0.
-11, 0, 1, 5
Let h(o) be the third derivative of 2*o**7/315 + o**6/10 + 3*o**5/5 + 3*o**4/2 + 1062*o**2. Solve h(i) = 0 for i.
-3, 0
Let f(j) = 199*j**3 - 2080*j**2 + 2067*j - 138. Let k(p) = -66*p**3 + 693*p**2 - 690*p + 45. Let w(g) = 3*f(g) + 8*k(g). Factor w(i).
3*(i - 9)*(i - 1)*(23*i - 2)
Let b be 276/(-18)*(-18)/12. Suppose -29 = -5*x - 4*n, -19*x - 25 = -b*x - 5*n. Factor 0*q + 0 + 1/3*q**x - 1/3*q**3 + 1/3*q**4 - 1/3*q**2.
q**2*(q - 1)*(q + 1)**2/3
Let s = -2277 + 61481/27. Let n(f) be the third derivative of -10*f**2 + 0*f + 1/270*f**5 + s*f**3 - 1/36*f**4 + 0. Factor n(c).
2*(c - 2)*(c - 1)/9
Let v(p) = p**3 + 3*p**2 - 6*p + 1. Let o be v(4). Let a = -68 + o. Factor -8*k**3 - 21*k - 4 + 4*k**2 - a*k + 2*k**5 + 48*k + 0*k**5.
2*(k - 1)**3*(k + 1)*(k + 2)
Let b = 206901 - 206901. Suppose -4*y**2 + b*y**3 - 24/7*y + 4/7*y**4 + 0 = 0. What is y?
-2, -1, 0, 3
Suppose 61*w - 65 = 62 + 178. Let b(q) be the first derivative of -w*q**4 - 4/5*q**5 - 8*q - 14 - 12*q**3 - 14*q**2. Find k, given that b(k) = 0.
-2, -1
Let f(p) = p**2 + 1. Let q(k) be the first derivative of 2*k**3/3 - 15*k**2 - 24*k - 84. Let y(g) = -4*f(g) + q(g). Determine t so that y(t) = 0.
-14, -1
Let h(v) be the second derivative of v**5/5 - 11*v**4/3 + 32*v**3/3 + 168*v**2 - 780*v. Factor h(l).
4*(l - 7)*(l - 6)*(l + 2)
Let v be (-2)/(-3)*(-180)/(-40). Let d be ((-8)/(-10) - 182/195)*-21. Factor -6/5 - d*g - 2/5*g**v - 2*g**2.
-2*(g + 1)**2*(g + 3)/5
Let i be (-23)/5 - (-12 + 7)*(-187)/(-85). Let -14*n**2 + 2/5*n**4 + 0 + 36/5*n + i*n**3 = 0. Calculate n.
-18, 0, 1
Let a(s) = -20*s - 29. Let k(n) = -74*n - 118. Let o(x) = 11*a(x) - 3*k(x). Let w be o(-16). Factor -3/4*g**w - 5*g**2 + 9/4*g + 7/2.
-(g - 1)*(g + 7)*(3*g + 2)/4
Let j = 306 - 305. Let f be (-488)/(-305) - j/5. Find g such that 9/5*g**2 - 4/5 - 3/5*g**5 + f*g**3 - 4/5*g - g**4 = 0.
-2, -1, -2/3, 1
Factor -8*h - 2/7*h**2 + 186/7.
-2*(h - 3)*(h + 31)/7
Let t(m) be the second derivative of m**4/3 - 1540*m**3/3 + 296450*m**2 + 2102*m. Solve t(k) = 0 for k.
385
Let 1/3*f**2 + 160/3 - 26/3*f = 0. Calculate f.
10, 16
Let r = 401 - 456. Let h(p) = 80*p**2 - 240*p - 2375. Let z(a) = -3*a**2 + 9*a + 88. Let g(i) = r*z(i) - 2*h(i). Determine j so that g(j) = 0.
-3, 6
Let x(c) be the first derivative of 1369*c**5 - 10545*c**4 + 22770*c**3 - 5130*c**2 + 405*c + 841. Factor x(z).
5*(z - 3)**2*(37*z - 3)**2
Let j(f) be the second derivative of f**4/66 + 298*f**3/33 - 299*f**2/11 + 98*f. Factor j(r).
2*(r - 1)*(r + 299)/11
Let n(h) = 2*h**3 + 29*h**2 - 100*h + 93. Let y(r) = -3*r**3 - 31*r**2 + 102*r - 100. Let i(g) = -4*n(g