)*(b + 2)/3
Let c(f) = -f**2 - 3*f + 1. Let g(k) = -k**3 + 44*k**2 - 167*k + 103. Let q(y) = 35*c(y) - 5*g(y). Factor q(d).
5*(d - 48)*(d - 2)*(d - 1)
Solve -1/2*i**2 - 1/4*i**3 + 0*i + 0 = 0 for i.
-2, 0
Let o(y) be the third derivative of y**6/660 - 7*y**5/330 + 4*y**4/33 - 4*y**3/11 + 322*y**2. Determine h, given that o(h) = 0.
2, 3
Let n = -1316 + 1321. Let z(g) be the second derivative of 0 + 0*g**3 - 1/27*g**4 + 0*g**2 - 1/135*g**6 + 7*g + 1/30*g**n. Solve z(u) = 0.
0, 1, 2
Let j(z) = -z**3 + 6*z**2 + 8*z - 20. Let m be j(6). Solve 6*q**3 - 70*q**3 + m*q**2 + 5*q**4 + 4*q**3 + 27*q**2 = 0 for q.
0, 1, 11
Factor -4052*k + 6157014 + 2/3*k**2.
2*(k - 3039)**2/3
Let u be -15 - (335265/(-720))/31. Let b(v) be the second derivative of -u*v**4 + 0 + 1/8*v**3 - 1/4*v**2 + 16*v. Find o, given that b(o) = 0.
1, 2
Let m(a) = a**3 + 113*a**2 + 2825*a + 988. Let h be m(-76). Solve h + 2/5*q**5 + 2/5*q**4 - 2/5*q**3 - 2/5*q**2 + 0*q = 0 for q.
-1, 0, 1
Suppose 84*y - 133 - 166 + 47 = 0. Let n(k) be the third derivative of 0*k**y + 0*k - 1/12*k**4 - 1/15*k**5 + 1/48*k**6 + 0 + 9*k**2. Solve n(v) = 0.
-2/5, 0, 2
Let c(z) be the second derivative of -z**7/231 + 9*z**5/110 - 2*z**4/33 - 4*z**3/11 + 144*z - 2. Solve c(r) = 0 for r.
-3, -1, 0, 2
Suppose 14 = 3*y - 4*w + 2*w, 2*w + 4 = -2*y. Suppose -5*c - 4*z = -10, -5*c + y*z + 10 = z. Find a such that 8*a + 4*a**c - 759 + 759 = 0.
-2, 0
Solve 1/3*r**5 - 19/6*r**3 + r**2 + 0 + 1/2*r**4 + 4/3*r = 0 for r.
-4, -1/2, 0, 1, 2
Suppose -13*p + 80 - 15 = 0. Let w(t) be the first derivative of 10*t**4 - 3*t**p + t**3 - 4 + 3*t**3 - 2*t**5 - 9*t**3. Determine k, given that w(k) = 0.
0, 3/5, 1
Let g = -318449 - -3502953/11. Find p such that 0 - 10/11*p**5 - 14/11*p**2 + 4/11*p + g*p**4 + 6/11*p**3 = 0.
-1, 0, 2/5, 1
Let t = 3443 - 44757/13. Let q be 1/(-2) + (-170)/(-260). Factor t*p**3 + q*p**2 - 10/13*p + 6/13.
2*(p - 1)**2*(p + 3)/13
Let i be 8289/(-90)*(-5)/90. Let y = -9/20 + i. Factor -8/3*h**2 + y*h**3 - 4/3*h**4 - 2/3*h**5 + 0*h + 0.
-2*h**2*(h - 1)**2*(h + 4)/3
Factor 360/17 - 4/17*a**2 + 234/17*a.
-2*(a - 60)*(2*a + 3)/17
Factor -19/2*g**3 + 0 + 9*g + 1/2*g**2.
-g*(g - 1)*(19*g + 18)/2
Let a(h) be the third derivative of h**7/126 + 17*h**6/45 - 14*h**5/15 - 55*h**4/8 + 8*h**2. Let k(c) be the second derivative of a(c). Factor k(i).
4*(i + 14)*(5*i - 2)
Let a be 8/(-14) + (-15776)/(-119). Let b = -123 + a. Factor 12 + b*o + 3/2*o**2.
3*(o + 2)*(o + 4)/2
Let n(b) = 3*b + 92. Let x be n(48). Let i = 241 - x. Factor 0 - 4/11*a**4 + 0*a**3 - 2/11*a**i + 2/11*a + 4/11*a**2.
-2*a*(a - 1)*(a + 1)**3/11
Let j be 17/5 + (-2)/5 + -7. Let c(s) = -s**2 - 39*s + 40. Let r(m) = -40*m + 40. Let z(l) = j*r(l) + 5*c(l). Find t such that z(t) = 0.
-8, 1
Let h(y) = -y**2 + 25*y + 74. Let s be h(38). Let t be s/(-180)*(-9)/(-42). Factor 27/2 - 9*d**2 + 4*d**3 - t*d**4 + 0*d.
-(d - 3)**3*(d + 1)/2
Suppose 2*c - 2*k - 13 = c, -5*k = -5*c + 45. Let d = 9 + -5. Factor -c + 1 + d*y**2 - 339*y + 339*y.
4*(y - 1)*(y + 1)
Suppose 51 = 4*x + 35. Solve -462*v**2 + 2*v**3 + 461*v**2 - 2*v + 2*v**3 - v**5 - v**3 + v**x = 0.
-1, 0, 1, 2
Suppose 15*w + 23 = 83. Factor -23*j**3 + 13*j**3 - 2*j**w + j**5 + 7*j**3.
j**3*(j - 3)*(j + 1)
Suppose 32/17*l**2 - 1264/17*l + 12482/17 = 0. What is l?
79/4
Let z(r) = r**2 + r + 6. Let s(f) = f**4 + 3*f**3 - 4*f**2 - 14*f - 20. Let c(n) = -s(n) - 2*z(n). Factor c(d).
-(d - 2)*(d + 1)*(d + 2)**2
Let r = -12777 + 12782. Let q(t) be the second derivative of 0*t**2 + 0 - 1/10*t**r + 1/30*t**6 + 0*t**3 + 10*t + 1/12*t**4. Find x such that q(x) = 0.
0, 1
Let s(d) be the first derivative of -29 + 13/14*d**2 - 22/7*d - 1/21*d**3. Factor s(f).
-(f - 11)*(f - 2)/7
Let a(p) be the third derivative of p**5/300 + 751*p**4/20 + 1692003*p**3/10 + 16*p**2 - 18*p. Factor a(o).
(o + 2253)**2/5
Let k(h) = -8*h**2 + 141*h - 270. Let o(g) = 3*g**2 - 70*g + 136. Let l(p) = -2*k(p) - 5*o(p). Let l(x) = 0. What is x?
-70, 2
Let r be -16 - 32/(-36) - -18. Let k = -962/153 - -122/17. Factor -k - 4/3*n**3 - r*n**2 - 2/9*n**4 - 8/3*n.
-2*(n + 1)**2*(n + 2)**2/9
Let a(k) be the second derivative of 25*k**7/252 + 3*k**6/2 + 829*k**5/120 + 15*k**4/2 + 25*k**3/9 - 1511*k. Solve a(i) = 0.
-5, -2/5, 0
Let z(i) be the third derivative of i**8/448 - i**7/40 + i**6/80 + 7*i**5/20 - 3*i**4/4 + 846*i**2. Determine g so that z(g) = 0.
-2, 0, 1, 2, 6
Factor -6962/3 - 1/6*x**2 - 118/3*x.
-(x + 118)**2/6
Determine f, given that -164*f**2 - 447 + 52*f**4 + 29 + 4*f**5 + 139*f**3 + 98 + 9*f**3 - 584*f = 0.
-8, -5, -1, 2
Let l(w) be the second derivative of -w**8/1512 - 4*w**7/945 + w**6/108 + 171*w**2/2 + 173*w. Let k(b) be the first derivative of l(b). Solve k(u) = 0 for u.
-5, 0, 1
Let s be 300/(-1500)*187/(-16) + (-1)/(-16). Factor 3/5*y**4 + 44/5*y + 26/5*y**3 + 11*y**2 + s.
(y + 1)**2*(y + 6)*(3*y + 2)/5
Let a(k) be the first derivative of -8/9*k**2 + 4/27*k**3 + 0*k - 127. Factor a(n).
4*n*(n - 4)/9
Let c(h) be the first derivative of 1/42*h**4 - 2/9*h**3 - 211 + 0*h + 4/7*h**2. Factor c(m).
2*m*(m - 4)*(m - 3)/21
Let z(u) be the second derivative of -4/57*u**3 + 4 - 1/114*u**4 - 10*u + 0*u**2. Factor z(o).
-2*o*(o + 4)/19
Let v(d) be the first derivative of d**6/900 + d**5/300 + d**3/3 + 35*d + 2. Let u(c) be the third derivative of v(c). Factor u(s).
2*s*(s + 1)/5
Suppose n - 22 = -4*l, -45 = -32*n - l + 532. Suppose n + 1/8*f**2 + 3*f = 0. Calculate f.
-12
Let s be ((-252)/(-3654))/(-2*(-2)/116). Factor -32/13*r + 0 - 2/13*r**s.
-2*r*(r + 16)/13
Factor 300 - 1/6*u**4 + 129/2*u**2 - 4*u**3 - 785/3*u.
-(u - 5)**2*(u - 2)*(u + 36)/6
Suppose 941*f = 926*f + 45. Let b(j) = j**2 - 3*j - 7. Let v be b(5). Solve -107*n**2 - 3*n**f + 113*n**2 + 0*n**v - 3*n = 0 for n.
0, 1
Factor 2057*p**3 + 145863*p - 19108 + 6*p**4 - 10133 - 17097*p**2 + 37594*p**2 + 156658*p**2.
(p + 1)*(p + 171)**2*(6*p - 1)
Let m(q) be the second derivative of 27 + 8/3*q**4 + 4*q + 20*q**2 + 1/5*q**5 - 38/3*q**3. Factor m(l).
4*(l - 1)**2*(l + 10)
Let z(j) be the third derivative of 108*j**2 + 37/108*j**4 - 4/3*j**3 + 0*j + 0 - 1/270*j**5. Factor z(w).
-2*(w - 36)*(w - 1)/9
Let u(j) be the second derivative of 3/4*j**5 + 0*j**2 + 4 + 0*j**3 - 3*j - 1/4*j**4 - 2/5*j**6. Factor u(x).
-3*x**2*(x - 1)*(4*x - 1)
Let q be 2968/1908*3/(-49) + 0 + 4/42. Determine h so that 2/9*h**3 + q + 0*h + 8/9*h**2 = 0.
-4, 0
Suppose 41/2*x**3 - 37/2*x**2 - 7/2*x**4 + 22 - 1/2*x**5 - 20*x = 0. What is x?
-11, -1, 1, 2
Let q(j) be the first derivative of -j**6/15 - j**5 - 37*j**4/6 - 20*j**3 - 36*j**2 - 175*j + 130. Let b(d) be the first derivative of q(d). Factor b(n).
-2*(n + 2)**2*(n + 3)**2
Let z = 2/753 + 2255/1506. Factor -z + 1/4*y**2 - 1/4*y.
(y - 3)*(y + 2)/4
Let u be (-3 - (1 + -5))/(-2)*(-22 - -22). Let q(s) be the third derivative of 27*s**2 + 1/6*s**4 + u + 0*s - 5/3*s**3 - 1/150*s**5. Factor q(z).
-2*(z - 5)**2/5
Let l(y) be the second derivative of y**7/14 - 41*y**6/5 + 7023*y**5/20 - 6765*y**4 + 54450*y**3 + 314*y + 3. Let l(c) = 0. What is c?
0, 11, 30
Let t be (34/(-10) - -5) + (-1804)/1230. Factor t*l**5 + 0 - 32/5*l**2 + 0*l - 32/15*l**4 + 104/15*l**3.
2*l**2*(l - 12)*(l - 2)**2/15
Suppose 1467/8 + 60*p - 3/8*p**2 = 0. What is p?
-3, 163
Let g(w) = 30*w**2 - 65*w + 380. Let s(i) = i**2 + i - 1. Let z(t) = t**2 + t - 1. Let u(d) = -4*s(d) + 3*z(d). Let b(f) = g(f) + 25*u(f). Factor b(c).
5*(c - 9)**2
Let i(p) be the first derivative of p**5/40 - 31*p**4/12 + 154*p + 233. Let a(w) be the first derivative of i(w). Factor a(n).
n**2*(n - 62)/2
Let m(o) = -14*o**2 + 20*o + 192. Let w(i) = -15*i**2 + 22*i + 184. Let y(d) = -5*m(d) + 6*w(d). Solve y(l) = 0 for l.
-2, 18/5
Let n be ((658/63)/(-47) - 25/9)*(-12)/7. Suppose 6*p**2 + 0 - 6/7*p**3 - n*p = 0. Calculate p.
0, 1, 6
Let s(q) be the second derivative of 25/8*q**3 + 11/16*q**5 + 0 + 5/4*q**2 - 60*q + 5/2*q**4. Factor s(c).
5*(c + 1)**2*(11*c + 2)/4
Let y(s) be the second derivative of s**7/105 + s**6/5 + 59*s**5/50 + 97*s**4/30 + 24*s**3/5 + 4*s**2 - 1899*s. Suppose y(o) = 0. What is o?
-10, -2, -1
Suppose 7*w - 659 + 540 = 0. Let x(b) be the second derivative of w*b + 25/4*b**2 + 0 + 5/6*b**3 + 1/24*b**4. Determine j, given that x(j) = 0.
-5
Suppose -3*z + 15 = 0, -3*f - 37 = -z - 2. Let m be (10/2)/f*-24. Factor 12 + 4*x*