b**3*(b + 1)*(b + 2)
Let d(a) be the third derivative of -a**6/150 + 8*a**5/25 + 26*a**4/15 + 1246*a**2. Factor d(w).
-4*w*(w - 26)*(w + 2)/5
Let l(f) be the first derivative of -7 - 1/40*f**5 - 1/120*f**6 + 1/12*f**3 - 11*f + 1/48*f**4 + 0*f**2. Let m(n) be the first derivative of l(n). Factor m(i).
-i*(i - 1)*(i + 1)*(i + 2)/4
Let s(a) be the third derivative of -1/44*a**4 + 10/33*a**3 - 1/30*a**5 + 0 + 0*a + 1/1155*a**7 - 80*a**2 + 1/220*a**6. Determine l, given that s(l) = 0.
-5, -1, 1, 2
Let y be -5 + (5 - -9 - (-10 + (7 - -9))). Factor -1/4*q**4 - q**y - 3/2*q**2 - 1/4 - q.
-(q + 1)**4/4
Let p be 8 - (391/(-115))/17*39/(-3). Suppose -31/5*k**2 + 0*k + p*k**4 + 27/5*k**5 - 27/5*k**3 + 4/5 = 0. Calculate k.
-1, -2/3, 1/3, 1
Suppose 27*p - 228 = 15*p. Let f be -14 - -13 - (-21)/p. Factor -294/19*m - f*m**3 + 686/19 + 42/19*m**2.
-2*(m - 7)**3/19
Let s be 5/(9 + -14) + 21/(168/40). Find f, given that 300*f - 1715*f**3 + 630*f**2 - 80 - 5145/2*f**s = 0.
-2/3, -4/7, 2/7
Let p(r) be the second derivative of -3/4*r**5 + 82*r - 175/12*r**4 + 0 - 35/2*r**3 + 55/2*r**2. Factor p(c).
-5*(c + 1)*(c + 11)*(3*c - 1)
Suppose -3*a - 49 = -36*a + 545. Let f(s) be the third derivative of 0*s + 1/240*s**6 + 1/120*s**5 - 5/48*s**4 + 0 - a*s**2 + 1/4*s**3. Factor f(w).
(w - 1)**2*(w + 3)/2
Let q = 299/94 + 479/470. What is h in -39/5*h + 9*h**2 + 3/5*h**4 - q*h**3 + 12/5 = 0?
1, 4
Factor -25*r**2 + 3*r**2 - 880*r + 20*r**2 - 96800.
-2*(r + 220)**2
Let g(o) be the second derivative of -40*o**2 + 150*o + 5/12*o**4 + 5*o**3 + 0. Suppose g(n) = 0. Calculate n.
-8, 2
Let c = -38 + 46. Let t(l) = -l**2 - 187*l - 2113. Let v(p) = 4*p**2 + 560*p + 6340. Let y(m) = c*t(m) + 3*v(m). Determine i so that y(i) = 0.
-23
Let x(k) be the first derivative of k**4/66 - 5*k**3/33 + 6*k**2/11 + 79*k - 27. Let j(q) be the first derivative of x(q). Find m, given that j(m) = 0.
2, 3
Determine f so that 356/9*f - 2/3*f**2 - 320/3 - 2/9*f**3 = 0.
-16, 3, 10
Let 82/7*z**3 + 1016/7*z**2 + 2592/7 + 2/7*z**4 + 504*z = 0. What is z?
-18, -4, -1
Let q(d) be the second derivative of 75*d**7/7 - 101*d**6/2 + 261*d**5/10 + 105*d**4 + 52*d**3 - 4*d + 35. What is u in q(u) = 0?
-2/5, 0, 2, 13/6
Suppose 2080 = 35*h + 1905. Let p(q) be the third derivative of 0*q - 1/132*q**4 - 1/660*q**h - 6*q**2 + 1/22*q**3 + 0. Let p(f) = 0. Calculate f.
-3, 1
Let w(i) be the second derivative of -i**6/2160 - i**5/180 + 5*i**4/144 + 34*i**3/3 - 115*i. Let d(k) be the second derivative of w(k). Factor d(b).
-(b - 1)*(b + 5)/6
Let g(a) = -a**4 + 10*a**3 + a**2 - 13*a + 3. Let w(p) = 12*p**4 - 110*p**3 - 12*p**2 + 144*p - 34. Let m(h) = -34*g(h) - 3*w(h). Factor m(j).
-2*j*(j - 1)*(j + 1)*(j + 5)
Suppose 1254/13 - 2/13*v**3 + 138/13*v**2 - 1390/13*v = 0. Calculate v.
1, 11, 57
Suppose 22*u**4 - 127*u**2 + 364*u**3 - 364*u + 368 - 18*u**4 - 129*u**2 - 116*u**2 = 0. What is u?
-92, -1, 1
Let o(j) be the third derivative of j**6/720 + 13*j**5/72 + 127*j**4/144 + 7*j**3/4 - 82*j**2 - 2*j - 6. Factor o(s).
(s + 1)**2*(s + 63)/6
Suppose -93*b - 182*b = -123*b - 304. Factor 0 - 1/7*a**3 + 1/7*a + 0*a**b.
-a*(a - 1)*(a + 1)/7
Let k(w) be the second derivative of w**5/4 - 220*w**4/3 + 17480*w**3/3 + 169280*w**2 - 127*w. Find h such that k(h) = 0.
-8, 92
Let u = 1/23260 + 18607/23260. Determine a, given that -5 - u*a**2 - 4*a = 0.
-5/2
Let w be (-40)/(-215)*(-430)/(-20). Determine t so that -2 + 20/3*t - 8*t**2 + 4*t**3 - 2/3*t**w = 0.
1, 3
Let x(w) = -8*w**4 - 1667*w**3 - 3040*w**2 + 864*w + 5. Let g(b) = 8*b**4 + 2501*b**3 + 4560*b**2 - 1296*b - 7. Let u(h) = -5*g(h) - 7*x(h). Factor u(y).
4*y*(y - 54)*(y + 2)*(4*y - 1)
Let a(i) be the third derivative of -i + 0 + 19/30*i**5 + 22*i**2 - 11/72*i**6 + 2/315*i**7 + 68/9*i**4 + 64/9*i**3. Factor a(z).
(z - 8)**2*(z + 2)*(4*z + 1)/3
Let j be (1 - (-413)/(-5))/((-1)/(-10)). Let v = 819 + j. Factor 0*d**2 - 2/9*d + 2/9*d**v + 0.
2*d*(d - 1)*(d + 1)/9
Let q = 1372 - 1372. Let r(j) be the first derivative of 0*j**2 - 25/3*j**3 + 5/4*j**4 + 14 + q*j. Determine d, given that r(d) = 0.
0, 5
Let g(h) = h**2 - 7*h + 12. Let r be g(5). Let f = 36215 - 181061/5. Find w, given that -32/5*w + 8/5 + 2*w**r + f*w**3 = 0.
-2, 2/7, 1
Let x(o) be the first derivative of 3*o**4/4 + 19*o**3/3 - 26*o**2 - 96*o - 1377. Let x(j) = 0. Calculate j.
-8, -4/3, 3
Find j such that j**3 + 20*j**2 - 40405*j - 3*j**3 - 92 + 40383*j - 48 = 0.
-2, 5, 7
Let a(q) = q**4 - q**3 - q**2 + 1. Let b be ((-5)/(-10))/((-3)/6). Let m(u) = -12*u**4 + 6*u**3 + 12*u**2 + 3*u - 9. Let s(r) = b*m(r) - 9*a(r). Factor s(o).
3*o*(o - 1)*(o + 1)**2
Let i = 6777/2 - 20329/6. Solve -i*g**2 + 1/2*g - 1/6*g**3 + 0 = 0.
-3, 0, 1
Let v = -15907/20 + 809. Let g = -67/5 + v. Factor g*y**4 + 0*y + 1/4*y**2 - 1/2*y**3 + 0.
y**2*(y - 1)**2/4
Let b(s) = -3*s**3 - 11001*s**2 - 10960*s + 2. Let o(l) = -20*l**3 - 77010*l**2 - 76705*l + 15. Let c(w) = -15*b(w) + 2*o(w). Let c(v) = 0. What is v?
-2198, -1, 0
Let j be (-63)/(-210)*(-2)/(-4). Let x(r) be the second derivative of j*r**5 - r + 0 + 1/4*r**4 + 0*r**2 - 1/10*r**6 - 1/2*r**3. What is t in x(t) = 0?
-1, 0, 1
Let g(u) be the first derivative of -u**4/24 + u**2/4 + u/3 + 601. Factor g(y).
-(y - 2)*(y + 1)**2/6
Let l(o) be the first derivative of -o**3 + 633*o**2/2 - 4375. Determine q, given that l(q) = 0.
0, 211
Let w be -2 + (-1)/1 + 7. Suppose 5 = -2*b - 3*q, 3*b - 9 = -11*q + 12*q. Factor w*j**b - 8*j + 7 + 12 - 19.
4*j*(j - 2)
Let c(t) be the second derivative of -t - 1/4*t**4 - 9/2*t**3 - 181 + 15*t**2. Factor c(x).
-3*(x - 1)*(x + 10)
Let x = -2/785 + 3933/3140. Let v(u) be the first derivative of 0*u - u**5 + 2 - x*u**4 + 5/2*u**2 + 5/3*u**3. Find s such that v(s) = 0.
-1, 0, 1
Let z = -77 + 80. Factor -2*p**2 - 13*p**3 + 59*p - 1 - 35*p + z*p**2 - 11*p**3.
-(p - 1)*(p + 1)*(24*p - 1)
Let c be (2 + (-98)/56)/3. Let d(w) be the third derivative of -c*w**8 + 0*w**5 + 0*w + 0*w**3 + 4/105*w**7 - 15*w**2 + 0 + 0*w**4 + 0*w**6. Factor d(f).
-4*f**4*(7*f - 2)
Let i(y) be the second derivative of y**5/40 + 11*y**4/12 - 23*y**3/12 - 7*y - 1. Find g, given that i(g) = 0.
-23, 0, 1
Let h(w) be the first derivative of w**4/16 - 661*w**3/4 + 984063*w**2/8 - 982081*w/4 + 4615. Factor h(o).
(o - 991)**2*(o - 1)/4
Let o be 2/4*8*1/2. Factor -9*n - 22*n**3 - 51*n**o + 15*n**4 - 9*n**3 + 32*n**3 - 28*n**3.
3*n*(n - 3)*(n + 1)*(5*n + 1)
Suppose 308 = 233*p - 158. Solve -8/3*d + 0 + 5/3*d**3 - 6*d**p = 0.
-2/5, 0, 4
Let g(u) be the third derivative of u**6/480 + 5*u**5/6 + 9797*u**4/96 - 10201*u**3/12 - 337*u**2 + 2. Solve g(n) = 0.
-101, 2
Let l(n) be the third derivative of n**7/315 - 17*n**6/30 + 2977*n**5/90 - 1598*n**4/3 + 35344*n**3/9 + 92*n**2 + 3. What is g in l(g) = 0?
4, 47
Suppose 213 = 34*m + 14*m + 23*m. Let y = -13 + 40/3. Determine a, given that -m*a**2 + 25/3 + 5*a + y*a**3 = 0.
-1, 5
Let r = -113 + 118. Suppose -2*d - 3*b + 10 = 13, 4 = -r*d - 4*b. Factor d*f + 2/5 - 2/5*f**2.
-2*(f - 1)*(f + 1)/5
Let l(t) = 3*t**2 + 3*t. Let j(g) be the third derivative of 0*g - 1/60*g**5 + 0*g**3 - 6*g**2 + 0 - 1/24*g**4. Let h(u) = -12*j(u) - 3*l(u). Factor h(c).
3*c*(c + 1)
Factor 1086332/15*g**2 + 144256/3*g**3 + 24010/3*g**4 + 2944/5*g + 6/5.
2*(g + 3)**2*(245*g + 1)**2/15
Suppose 167*q + 55 = 156*q. Let a be 3/4*(q - (-13 + 4)). Factor -3/4*j**2 - 3/4*j**3 + 3*j + a.
-3*(j - 2)*(j + 1)*(j + 2)/4
Let b(d) be the first derivative of -d**3/12 + 59*d**2/4 - 1064. Factor b(s).
-s*(s - 118)/4
Let f(z) be the first derivative of -z**7/210 + 31*z**6/480 - z**5/6 - z**4/8 + 39*z**2 - 97. Let x(w) be the second derivative of f(w). Factor x(a).
-a*(a - 6)*(a - 2)*(4*a + 1)/4
Let h be ((-6)/9)/((-20)/45)*10/9. Let m(q) be the first derivative of h*q**3 - 4 - 60*q + 5/2*q**2. Factor m(f).
5*(f - 3)*(f + 4)
What is z in 28*z**3 - 80/3*z - 4/3*z**4 + 0 - 4/3*z**5 + 4/3*z**2 = 0?
-5, -1, 0, 1, 4
Let u(b) be the second derivative of b**9/7560 - b**8/168 + 5*b**7/63 + 11*b**4/12 + 2*b**3/3 - 9*b. Let s(p) be the third derivative of u(p). Factor s(g).
2*g**2*(g - 10)**2
Let t be (0 - (-36)/(-77))/((-202)/((-114534)/(-243))). Factor 2/11*k**4 + t*k**3 + 18/11*k**2 + 0*k + 0.
2*k**2*(k + 3)**2/11
Let s(v) be the first derivative of -3*v**4/16 - 225*v**3/4 - 1341*v**2/8 - 669*v/4 - 146. Let s(q) = 0. Calculate