*s. Let r be n(6). Solve -1/2*p**3 + r*p + p**2 + 0 - 5*p**4 = 0.
-1/2, 0, 2/5
Suppose -2*w = -7*q + 4*q + 6, 4*q + 3*w - 25 = 0. Solve -45504*l**2 + 886*l**3 + 196608 + 548*l**3 - 22*l**4 + 4*l**4 + 473088*l + 3*l**q = 0.
-2/5, 32
Find n, given that -1/4*n**3 + 159/2*n**2 - 12800 - 6240*n = 0.
-2, 160
Let b(v) be the third derivative of v**7/70 + v**6/40 - 3*v**5/20 - v**4/8 + v**3 + 7*v**2 + 1. Factor b(j).
3*(j - 1)**2*(j + 1)*(j + 2)
Suppose 3*l + 5 = -5*o + 1, 4 = 5*l + 3*o. Suppose 5*s - 13 = l*b + 5, 0 = 2*s + 5*b + 16. Factor -28/3*v - 4*v**s - 8/3.
-4*(v + 2)*(3*v + 1)/3
Factor -641556*m**3 - 641557*m**3 + 1283115*m**3 - 288*m.
2*m*(m - 12)*(m + 12)
Let b(k) = -125*k**3 - 2785*k**2 - 27985*k - 25215. Let l(a) = -9*a**3 - 199*a**2 - 1999*a - 1801. Let i = 183 + -128. Let u(g) = i*l(g) - 4*b(g). Factor u(j).
5*(j + 1)*(j + 19)**2
Let q(w) be the third derivative of -w**8/4032 - w**7/336 + w**6/36 - 23*w**5/30 + 2*w**2 - 13. Let r(j) be the third derivative of q(j). Factor r(y).
-5*(y - 1)*(y + 4)
Let d(y) = -y**3 - y**2 + 2*y. Suppose 0 = 3*h - 15, 3*b + b + 5*h - 41 = 0. Let c(j) = 6*j**3 + 28*j**2 - 4*j. Let m(k) = b*d(k) - 2*c(k). Factor m(p).
-4*p*(p + 4)*(4*p - 1)
Let b(o) be the third derivative of -o**6/60 - 38*o**5/15 - 1517*o**4/12 - 2738*o**3/3 + 303*o**2. Factor b(w).
-2*(w + 2)*(w + 37)**2
Let x(v) be the second derivative of v**6/60 - 7*v**5/10 - 41*v**4/8 - 79*v**3/6 - 16*v**2 + 3739*v. Let x(u) = 0. Calculate u.
-2, -1, 32
Let b(p) be the third derivative of p**7/840 + p**6/240 - 23*p**5/240 - p**4/4 + 6*p**3 + 160*p**2. Factor b(r).
(r - 3)**2*(r + 4)**2/4
Let t(r) be the first derivative of 2*r**3/15 + 121*r**2/5 - 1318. What is s in t(s) = 0?
-121, 0
Solve -843*u**2 + 32 + 180*u**3 + 407*u - 3*u**4 + 771*u - 32 - 188*u = 0 for u.
0, 2, 3, 55
Suppose -k - 801 = a, -7*a + 2*k = -5*a + 1590. Let v be (-2)/6 - 494/a. Solve v*o + 0 - 1/7*o**2 = 0.
0, 2
Let h(p) = -2*p**3 + 92*p**2 - 87*p - 1. Let y be h(1). Factor -3/2*z - 1/2*z**2 + y.
-(z - 1)*(z + 4)/2
Factor 3/7*a**2 + 867/7*a - 2628/7.
3*(a - 3)*(a + 292)/7
Suppose 5*k + 109 = 53 + 66. Let v(a) be the first derivative of -12/5*a**k - 3/10*a**4 + 8/5*a - 23 + 22/15*a**3. Factor v(p).
-2*(p - 2)*(p - 1)*(3*p - 2)/5
Let g(k) be the first derivative of k**3/18 - 80*k**2/3 + 2191*k/6 + 12989. Solve g(q) = 0 for q.
7, 313
Let b be -15 + (1 - -24) + -10. Let k(j) be the second derivative of 32*j + 0 - 1/180*j**6 - 1/18*j**4 - 1/30*j**5 + b*j**2 + 0*j**3. Factor k(v).
-v**2*(v + 2)**2/6
Let g(v) be the third derivative of -v**5/120 + 169*v**4/16 - 253*v**3/6 - 10*v**2 + 43*v. Solve g(y) = 0 for y.
1, 506
Let n(s) = -2*s**3 + 2*s**2 + s - 1. Let d be n(-1). Factor -2*h**3 - 36*h**2 + 66*h**d - 22*h**2.
-2*h**2*(h - 4)
Let g = 177813/10 - 17781. Let t(y) be the first derivative of 2*y - 1/15*y**3 - 15 + g*y**2. Factor t(v).
-(v - 5)*(v + 2)/5
Let -23*j + 72 - 27/4*j**3 - 1/4*j**4 - 42*j**2 = 0. What is j?
-18, -8, -2, 1
Let z(v) be the third derivative of -v**6/1440 + v**4/24 - 17*v**3/6 + 65*v**2. Let j(n) be the first derivative of z(n). Factor j(b).
-(b - 2)*(b + 2)/4
Suppose 4*b = -b - s + 15, -4*s = 3*b - 9. Suppose -5*i + 0*f + 16 = -2*f, 4*i + b*f = -1. Factor 6*w - 4*w**2 - 2 + 2 + i*w.
-4*w*(w - 2)
Let q(d) be the third derivative of -d**5/210 + d**4/84 - 3067*d**2 + 2*d. Let q(a) = 0. What is a?
0, 1
Let l = -247321/3 + 82441. Determine z, given that -2/5*z**3 - 8/5 + 26/15*z**2 - 2/15*z**5 + 16/15*z - l*z**4 = 0.
-3, -2, 1
Let x(r) be the first derivative of r**5/60 + r**4/12 + r**2 + 21*r - 155. Let j(v) be the second derivative of x(v). Find o such that j(o) = 0.
-2, 0
Let h(m) = m - 4. Let w be h(7). Find b such that 6*b**2 + w + 6*b**3 + 15*b - 33*b + 0 - 9*b**4 + 9*b + 3*b**5 = 0.
-1, 1
Let u be (1*3/3)/((-18)/18). Let t be 35/(-49)*-7 + u. Factor 0 + 3*a**3 - 3/2*a**t + 0*a**2 + 0*a.
-3*a**3*(a - 2)/2
Factor 350*t - 404 - 27*t + 3*t**2 + 281*t + 0*t**2.
(t + 202)*(3*t - 2)
Let n(c) be the third derivative of c**5/75 - 127*c**4/30 + 607*c**2. Factor n(y).
4*y*(y - 127)/5
Let f be (1272/50350)/((-23)/10 + 2). Let r = 84/95 + f. What is z in 32/5*z - r - 39/5*z**2 = 0?
2/13, 2/3
Let l be ((-14)/3)/(2257/(-111)). Let g = l - -1366/427. Let 50/7*a**2 + g*a**3 + 0 - 2*a**4 + 12/7*a = 0. Calculate a.
-1, -2/7, 0, 3
Let j(x) be the second derivative of x**4/4 - 16*x**3 + 384*x**2 + 4*x - 115. Determine s so that j(s) = 0.
16
Let k(x) be the third derivative of 13*x**8/168 - 128*x**7/105 + 33*x**6/5 - 176*x**5/15 - 16*x**4/3 + 10*x**2 - 17*x. Find v, given that k(v) = 0.
-2/13, 0, 2, 4
Solve 27/4*z**3 - 5499/4*z**2 - 609/4 + 3657/4*z = 0.
1/3, 203
Suppose -3*q + 9 = -5*y, y = 41*q - 40*q - 3. Let c be ((-129)/(-126) - y) + (-22)/132. Factor -c*a**3 + 0 + 9/7*a**2 + 6/7*a.
-3*a*(a - 2)*(2*a + 1)/7
Let n(j) be the second derivative of 1/30*j**6 + 0*j**2 + 29/12*j**4 + 10/3*j**3 + 1/2*j**5 + 61*j + 1. Factor n(o).
o*(o + 1)*(o + 4)*(o + 5)
Let n(t) be the first derivative of -5*t**3/3 + 1605*t**2/2 + 1610*t + 492. Find a, given that n(a) = 0.
-1, 322
Let n(w) = 2*w**3 + 260*w**2 - 3833*w + 11527. Let y(u) = 3*u**3 + 260*u**2 - 3832*u + 11528. Let a(p) = 8*n(p) - 7*y(p). Let a(s) = 0. Calculate s.
4, 24
Let o(c) be the second derivative of -c**7/840 + c**6/160 + c**5/240 - c**4/32 - 88*c**2 - 2*c + 15. Let f(r) be the first derivative of o(r). Factor f(h).
-h*(h - 3)*(h - 1)*(h + 1)/4
Solve -206116*h + 4*h**4 + 130379*h**3 + 32781*h**2 + 175151*h**2 - 132199*h**3 = 0.
0, 1, 227
Let o(w) = -2*w**2 - 694*w - 916. Let q(d) = 2*d**2 + 696*d + 974. Let r(j) = 5*o(j) + 4*q(j). What is i in r(i) = 0?
-342, -1
Let c = 493810 - 493808. Let v = -109/3 + 37. Find d, given that -8/3*d - 8/3 - v*d**c = 0.
-2
Let o(d) = -9*d**2 - 7021*d - 3076636. Let l(x) = 8*x**2 + 7020*x + 3076612. Let f(a) = 5*l(a) + 4*o(a). Factor f(w).
4*(w + 877)**2
Suppose -55 = 28*i - 615. Let h be (-12)/i - (-13)/5. Factor -5/3*j - 1/3*j**h - 2.
-(j + 2)*(j + 3)/3
Let r be -33*(-2911)/32802 + (-2)/(-28). Factor 1/4*a**2 - 1/8*a**r - 1/4 + 1/8*a.
-(a - 2)*(a - 1)*(a + 1)/8
Let x = -61 - -61. Suppose -a + x = -2. Suppose -18*i**3 + 8*i**4 - 2*i**5 + 29*i**3 - 21*i**3 + 3*i**a + i**2 = 0. What is i?
0, 1, 2
Let a(m) be the third derivative of m**6/180 + m**5/15 - 3370*m**2 - 2. Factor a(y).
2*y**2*(y + 6)/3
Let q(l) be the third derivative of l**2 - 1/90*l**5 + 0*l**4 + 0*l**3 + 38 + 0*l. Suppose q(k) = 0. What is k?
0
Suppose 3*x = -64*o + 62*o, -x = 0. Suppose o = -59*b + 100*b - 82. Factor 1/4*f**4 + 0 + 3/4*f**b + 0*f - 5/4*f**3 + 1/4*f**5.
f**2*(f - 1)**2*(f + 3)/4
Let 0 + 0*u + 3/2*u**3 + 1/2*u**5 - 3/2*u**4 - 1/2*u**2 = 0. Calculate u.
0, 1
Let y(l) be the first derivative of -1/8*l**4 + 174 + 13/9*l**3 - 4/3*l - 5/4*l**2. Find o, given that y(o) = 0.
-1/3, 1, 8
Let n(h) be the first derivative of 3*h**4/4 + 127*h**3 - 582*h**2 + 780*h + 4043. Factor n(f).
3*(f - 2)*(f - 1)*(f + 130)
Suppose 10*l - 6*l - 88 = 0. Let i = -18 + l. Factor 2*g**4 - 18*g**4 + 6*g**3 + 9*g**4 + i*g**2 - 3*g**4.
-2*g**2*(g - 1)*(5*g + 2)
Let a be (92/(-10))/((-31)/155). Let d(t) be the first derivative of -55/4*t**4 - 16*t - 52*t**3 - a*t**2 + 5*t**5 + 7. Suppose d(f) = 0. What is f?
-1, -2/5, 4
Let a(r) be the first derivative of r**4/36 - 521*r**3/27 - 29*r**2 - 6249. Factor a(h).
h*(h - 522)*(h + 1)/9
Let k(y) be the second derivative of 5*y**7/126 + 29*y**6/12 - 23*y**5/12 - 145*y**4/24 + 55*y**3/9 - 3*y + 93. What is l in k(l) = 0?
-44, -1, 0, 1/2, 1
Let q(w) be the second derivative of 5/4*w**5 - 5/2*w**3 - 10*w**2 + 5/2*w**4 - 57*w + 2. Determine f, given that q(f) = 0.
-1, 4/5
Let t = 322029 + -322026. Factor 0 - 242/9*j**t + 44/3*j**2 - 2*j.
-2*j*(11*j - 3)**2/9
Suppose 0 = 3*b - 2*b - 5. Suppose f + 3*m - 16 = 0, -m - 17 + 1 = -b*f. Factor -8*r - 5*r**2 - 5*r - f*r + 2*r.
-5*r*(r + 3)
Let l(w) be the first derivative of -9 + 1/2*w**4 + 0*w + 0*w**2 - 2/5*w**5 - 1/4*w**6 + 0*w**3. Factor l(h).
-h**3*(h + 2)*(3*h - 2)/2
Let x be (0 - (-2 + 3))*1. Let t be (-2)/10 - (-2 - -3)/x. Factor -6/5*h + 2/5*h**2 + t.
2*(h - 2)*(h - 1)/5
Let i(g) = 82*g**2 + 207*g + 72. Let p(b) = -20*b**2 - 52*b - 18. Let x be 2 + (-596)/30 + (-24)/180. Let l(d) = x*p(d) - 4*i(d). Let l(u) = 0. Calculate u.
-3, -3/8
Solve 0 + 0*j**3 + 0*j - 3/7*