a**3 - 703*a**2 + 29159*a - 2. Let u(p) = 2*t(p) - 2*z(p). Factor u(w).
4*w*(w - 27)**2*(w + 20)
Suppose -79*f = -73*f + 1698. Let o = -281 - f. Suppose -1/7*p**o - 2/7*p + 0 = 0. What is p?
-2, 0
Let s = -14423 + 14426. Let t(v) be the second derivative of -23*v + 0 - 1/36*v**s + 1/24*v**2 + 1/144*v**4. Determine j, given that t(j) = 0.
1
Let c(z) be the second derivative of z**6/6 + 29*z**5/10 + 27*z**4/4 + 4*z**3/3 - 10*z**2 - 27*z - 7. Find j, given that c(j) = 0.
-10, -1, 2/5
Let w(z) be the first derivative of -1/3*z**6 - 6/5*z**5 - z**4 + 4/3*z**3 + 2*z + 55 + 3*z**2. What is l in w(l) = 0?
-1, 1
Let g(f) be the third derivative of f**8/168 - 101*f**7/35 - 61*f**6/4 - 917*f**5/30 - 51*f**4/2 + 2*f**2 + 68. Solve g(m) = 0 for m.
-1, 0, 306
Let a(d) = -3*d**2 + 8*d + 1. Let j(o) = 13*o**2 - 32*o - 3. Let z(i) = i + 35. Let q be z(-13). Let x(l) = q*a(l) + 6*j(l). Factor x(t).
4*(t - 1)*(3*t - 1)
Let w(i) be the second derivative of 135*i + 4*i**3 + 11/6*i**4 + 2/15*i**5 + 0 + 7/3*i**2. Determine q so that w(q) = 0.
-7, -1, -1/4
Factor -1018/5 + 2/5*c**2 - 1016/5*c.
2*(c - 509)*(c + 1)/5
Let b = -9095 + 9095. Let x(n) be the third derivative of b*n - 4/15*n**3 + 7/30*n**4 + 3/200*n**6 - 1/10*n**5 - 8*n**2 + 0. Factor x(o).
(o - 2)*(3*o - 2)**2/5
Let k(g) = 5*g**4 - 100*g**3 - 4*g - 4. Let z(d) = -11 - 299*d**3 + 12*d - 25*d + 2*d + 13*d**4. Let u(a) = 11*k(a) - 4*z(a). Let u(h) = 0. Calculate h.
-32, 0
Let k(a) = 16*a**3 - 432*a**2 - 3020*a + 28. Let x(z) = -3*z**3 + 79*z**2 + 549*z - 5. Let p(w) = -5*k(w) - 28*x(w). Factor p(t).
4*t*(t - 17)*(t + 4)
Let q(c) = c**3 - 7*c**2 - 16*c + 64. Let v be q(8). Let z be v*(2 - 9 - -8). Factor -1/2*l**2 - l**3 + 1/2*l**4 + l + z.
l*(l - 2)*(l - 1)*(l + 1)/2
Factor -43 - 108*w**2 - 8*w**3 - 27 + 2*w**4 - 10331*w + 2*w**4 - 42 + 10123*w.
4*(w - 7)*(w + 1)*(w + 2)**2
Let c be ((-52)/13 - -10)/(24*15/240). Factor 2*o**c - 2/3*o**5 + 0 + 0*o + 2/3*o**2 - 2*o**3.
-2*o**2*(o - 1)**3/3
Let x(p) be the second derivative of -p**9/945 + 19*p**8/3360 - p**7/210 - 209*p**4/12 + 74*p. Let z(t) be the third derivative of x(t). Factor z(b).
-2*b**2*(b - 2)*(8*b - 3)
Find n such that -2673/2*n + 267 + 15/2*n**2 = 0.
1/5, 178
Let t(u) be the second derivative of -9/16*u**2 + 1/96*u**4 + 0*u**3 - 2*u - 4. Find d, given that t(d) = 0.
-3, 3
Let q(m) be the first derivative of -m**3/6 + 75*m**2/2 - 45. Factor q(d).
-d*(d - 150)/2
Let j(a) be the first derivative of 0*a**2 + 1/4*a**5 + 0*a**3 + 5/6*a**4 + 1 + 21*a. Let o(r) be the first derivative of j(r). Factor o(i).
5*i**2*(i + 2)
Factor 4*c**3 + 24*c - 2*c**3 - 75 + 54*c**2 + c**3 - 21*c**2 + 15.
3*(c - 1)*(c + 2)*(c + 10)
Suppose 162*b + 363 = 165*b. Factor 54*a - 11*a**2 - b*a + 65*a.
-a*(11*a + 2)
Let h(y) = 3*y**2 + 64*y - 63. Let p be h(1). Let s(r) be the second derivative of -3/70*r**5 + 17*r - 3/7*r**3 + 3/7*r**2 + 0 + 3/14*r**p. Factor s(t).
-6*(t - 1)**3/7
Let h be (2/2)/(11085/924 + -12). Let k = -308 - h. Suppose k*l + 4/3 + 4/3*l**4 - 8/3*l**2 + 0*l**3 = 0. What is l?
-1, 1
Let -181*z**2 + z**4 - 39*z**2 + 17*z**3 - 90*z**3 - 47*z**3 - 6*z**4 = 0. What is z?
-22, -2, 0
Let -4900 - 1/9*f**2 + 140/3*f = 0. Calculate f.
210
Let z(x) = 3*x**3 - 3*x**2 - 2*x + 3. Let a be z(1). Let y(d) = d**2 - 15*d - 35. Let h(j) = j**2 - 3. Let t(n) = a*y(n) + h(n). Suppose t(c) = 0. Calculate c.
-2, 19/2
Let r(h) = -16*h**2 + 219*h - 126. Let y be r(13). Let n(c) be the first derivative of -y - c**2 + 5/8*c**4 + 0*c + 4/3*c**3. Factor n(b).
b*(b + 2)*(5*b - 2)/2
Let k = -3563781/5 + 712757. Factor k*q - 44/5*q**3 + 0 - 14/5*q**2.
-2*q*(2*q + 1)*(11*q - 2)/5
Let h = -37 + 19. Let v be (-111)/h - 5/30. Suppose v*y - 6 - 3/2*y**2 = 0. Calculate y.
2
What is g in -1/5*g**5 + 5*g**2 + 0*g - 1/5*g**4 + 0 + 5*g**3 = 0?
-5, -1, 0, 5
Let w be (18/98)/((-3447)/(-104559)). Find v, given that w*v**2 + 48/7*v + 15/7 + 6/7*v**3 = 0.
-5, -1, -1/2
Let i be (-10)/(-2) + 12954/(-2448) - ((-16)/6 + 2). Suppose -i*c**3 - 9/4 - 3/8*c + 3/2*c**2 = 0. What is c?
-1, 2, 3
Factor 97/8*q**2 + 69/8*q + 3/4*q**4 + 43/8*q**3 + 9/8.
(q + 1)*(q + 3)**2*(6*q + 1)/8
Let q(x) be the first derivative of -5*x**4/4 + 6535*x**3/3 - 2138575*x**2/2 + 2132045*x + 5428. Factor q(h).
-5*(h - 653)**2*(h - 1)
Let h = 122227 - 122225. Factor 8/9*s**3 - 28/3 + 4/9*s**4 + 184/9*s - 112/9*s**h.
4*(s - 3)*(s - 1)**2*(s + 7)/9
Suppose -104 = 12*s + 88. Let k(p) = 12*p**3 - 144*p**2 + 400*p - 416. Let b(a) = 4*a**3 - 48*a**2 + 134*a - 138. Let i(x) = s*b(x) + 5*k(x). Factor i(r).
-4*(r - 8)*(r - 2)**2
Let x(a) be the first derivative of -5/3*a**3 - 43 - 25/2*a**2 - 30*a. Suppose x(k) = 0. What is k?
-3, -2
Let l(b) be the first derivative of -2*b**6/9 - 8*b**5/5 + 21*b**4 - 48*b**3 + 1114. Find i, given that l(i) = 0.
-12, 0, 3
Let m(l) be the third derivative of -l**6/80 + 33*l**5/40 + 965*l**2. Solve m(f) = 0 for f.
0, 33
Let t = 525 - 462. Suppose 0 = 38*x - t - 127. Suppose 0*k + 0 + 4/17*k**2 + 2/17*k**x + 8/17*k**4 + 10/17*k**3 = 0. What is k?
-2, -1, 0
Let p(n) be the first derivative of -2/75*n**5 - 80 + 0*n**2 + 0*n**3 + 4/15*n**4 + 0*n. Let p(o) = 0. Calculate o.
0, 8
Let o = -2/82111 - -328462/738999. Find w, given that -4/3*w**3 - o*w**2 + 0 + 8/9*w + 4/9*w**4 + 4/9*w**5 = 0.
-2, -1, 0, 1
Suppose -2*g + 9 = 1. Let h(x) = x**4 + 13*x**2 - 10*x. Let m(c) = c**4 + 13*c**2 + 12*c**2 - c - 24*c**2. Let v(n) = g*m(n) - h(n). Factor v(u).
3*u*(u - 1)**2*(u + 2)
Solve -748/9*a**3 + 0 + 200/9*a**2 + 242/3*a**4 - 16/9*a = 0.
0, 2/11, 2/3
Let g be 18/2*(58 - 57) - 3. Let s(r) be the third derivative of -1/120*r**g + 0*r**3 + 6*r**2 + 0 - 1/24*r**4 - 1/30*r**5 + 0*r. Factor s(z).
-z*(z + 1)**2
Let g be (-1330)/(-434) + (-76)/1178. Solve -3/8*f**g + 3/2 + 3/4*f**2 + 21/8*f = 0.
-1, 4
Let h(l) be the first derivative of -l**3/3 - 169*l**2/2 - 334*l - 1294. Determine z so that h(z) = 0.
-167, -2
Let f(p) = -7*p**3 - 454*p**2 + 1260*p - 33. Let g(i) = -3*i**3 - 151*i**2 + 420*i - 12. Let d(h) = 4*f(h) - 11*g(h). Factor d(o).
5*o*(o - 28)*(o - 3)
Let i(k) = 12*k + 276. Let o be i(-29). Let d be (o/10 - -8) + (-2)/15. Determine l, given that -4/9*l**3 - 4/9*l**2 - 2/9 - 2/9*l**5 + 2/3*l**4 + d*l = 0.
-1, 1
Factor -246*j + 249/4*j**2 - 1/4*j**3 + 245.
-(j - 245)*(j - 2)**2/4
Let a(k) be the second derivative of 3*k**5/80 + 17*k**4/16 + 10*k**3 + 24*k**2 + 4*k. Factor a(b).
3*(b + 1)*(b + 8)**2/4
Let r = -53983/6 + 8998. Let c(j) be the second derivative of 0*j**3 - 33*j + 0 + r*j**4 + 0*j**2 - 1/16*j**5. Solve c(l) = 0.
0, 8
Let z be (-8)/604 - 113741/(-48471). Factor 16/3*j - z*j**4 + 1/3*j**5 + 19/3*j**3 - 4/3 - 25/3*j**2.
(j - 2)**2*(j - 1)**3/3
Let w(c) = 6*c**3 + 44*c**2 + 509*c + 3465. Let z be w(-7). Solve z + 2/5*d**2 - d**3 + 0*d - 3/5*d**4 = 0 for d.
-2, 0, 1/3
Let z = 814/23 - 2396/69. Let p(j) be the second derivative of -17*j - 1/3*j**4 + 0*j**2 + 0 + z*j**3. Factor p(x).
-4*x*(x - 1)
Let s(n) be the third derivative of -1/300*n**6 + 0*n + 7/60*n**4 + 1/75*n**5 + n**2 + 57 + 4/15*n**3. Factor s(o).
-2*(o - 4)*(o + 1)**2/5
Let l = 382 - 380. Factor -16 - 13*b**2 + 12*b + 0 + 11*b**l.
-2*(b - 4)*(b - 2)
Let -18*b**2 + 26*b**3 + 184*b**2 + 140 + 352*b - 268 - 11*b**2 + 45*b**2 = 0. What is b?
-4, 4/13
Let z(j) be the second derivative of -27/4*j**5 + 0*j**2 + 5/6*j**6 + 25/2*j**4 - 75*j + 0 - 20/3*j**3. Factor z(d).
5*d*(d - 4)*(d - 1)*(5*d - 2)
Let q(f) be the second derivative of -f**4/60 + 137*f**3/30 + 139*f**2/5 + 26*f - 3. Factor q(j).
-(j - 139)*(j + 2)/5
Let o be (851 - 842)/(2/4*(1 + 5)). Let n(k) be the first derivative of -2/3*k**o - 5 + 2*k**2 + 6*k. Factor n(a).
-2*(a - 3)*(a + 1)
Let z(d) be the third derivative of 4/15*d**5 + 0 - 7*d**2 - 1/3*d**4 - 1/10*d**6 - 1/672*d**8 + 0*d**3 + 2/105*d**7 + 0*d. Factor z(p).
-p*(p - 2)**4/2
Let c(y) = 2. Let w = 165 - 161. Let r(l) = 2*l**2 - 4*l - 4. Let z(p) = w*c(p) + 2*r(p). Factor z(d).
4*d*(d - 2)
Let m(j) be the third derivative of -11/75*j**5 + 7/100*j**6 - 187*j**2 - 8/525*j**7 + 0 + 0*j + 1/840*j**8 + 0*j**3 + 2/15*j**4. Suppose m(h) = 0. Calculate h.
0, 1, 2, 4
Let -1296/5 + 2/5*a**4 - 414/5*a - 154/5*a**3 + 726/5*a**2 = 0. What is a?
-1, 3, 72
Let y(x) be the first derivative of 21*x**4/8 - 159*x**3/2 + 729*x**2/2 + 228*x + 2022. Suppose y(c) = 0. Wh