*2 + 75/4*g.
-3*(g - 3)*(g + 2)*(4*g + 1)/4
Let r be ((-8)/18)/(4/(-6)). Let x = 2 + -4/3. Factor 2*s**2 - 2*s + r - x*s**3.
-2*(s - 1)**3/3
Let r(f) be the third derivative of 1/945*f**7 - 10*f**2 + 0 + 0*f**3 + 1/270*f**5 + 1/270*f**6 + 0*f + 0*f**4. Find w, given that r(w) = 0.
-1, 0
Factor 3*u + 17*u - 14*u - 16 - 4*u**2 + 10*u.
-4*(u - 2)**2
Suppose -15*p + 11*p + 68 = 0. Let v(g) = g - 15. Let u be v(p). Let -2*r**2 - r**5 + 6*r**5 + 3*r**4 - 1 - 3*r - 4*r**5 + u*r**3 = 0. What is r?
-1, 1
Let s = 4411/3 - 1470. Let x(o) be the third derivative of s*o**3 + 0*o**5 + 0*o + 0 - 6*o**2 + 1/120*o**6 - 1/8*o**4. Factor x(g).
(g - 1)**2*(g + 2)
Let c(d) be the second derivative of -d**4/12 + 55*d**3/3 - 3025*d**2/2 + 60*d - 3. Solve c(p) = 0 for p.
55
Let c(n) be the first derivative of -3*n - 3/2*n**4 + 3*n**2 + 0*n**3 + 3/5*n**5 + 37. Suppose c(d) = 0. What is d?
-1, 1
Let u(b) be the second derivative of -5*b**4/12 + 230*b**3/3 - 5290*b**2 - 23*b + 5. Suppose u(m) = 0. Calculate m.
46
Let y(z) be the third derivative of -5*z**8/336 + z**7/42 + z**6/24 - z**5/12 + 5*z**2. What is w in y(w) = 0?
-1, 0, 1
Let c be 5/(10/(-6))*3/(-9). Let r(h) be the first derivative of 1/18*h**3 + c + 1/3*h - 1/4*h**2. Factor r(y).
(y - 2)*(y - 1)/6
Let d(p) = 3*p**2 + 13*p + 32. Let s(l) = 2*l**2 + l. Let h(r) = -2*d(r) + 2*s(r). Factor h(u).
-2*(u + 4)*(u + 8)
Let g(h) be the first derivative of 0*h + 0*h**2 + 4*h**3 - 7 - 3*h**4 + 3/5*h**5. Factor g(v).
3*v**2*(v - 2)**2
Let h = 16177/4 - 4042. Suppose 3/4*n**3 + 0*n + 0 - h*n**2 = 0. What is n?
0, 3
Let -163*t**2 + 171*t**2 + 4*t - 7*t = 0. Calculate t.
0, 3/8
Let k be (-8868)/1478 - 102/(-16). Solve 3/8*w + 9/8 - 9/8*w**2 - k*w**3 = 0.
-3, -1, 1
Suppose 229*s + 20 = 233*s. Suppose -s*i - 8 = 2*o, i + o = -0*o - 4. Find j such that 1/2*j**3 - 1/4*j**2 + 0 + i*j - 1/4*j**4 = 0.
0, 1
Let b(j) = 4*j**3 + 204*j**2 + 14697*j + 343006. Let o(g) = 3*g**3 + 206*g**2 + 14698*g + 343004. Let u(i) = 2*b(i) - 3*o(i). Suppose u(v) = 0. Calculate v.
-70
Let y(s) be the second derivative of 8*s - 3 + 80/3*s**3 - 640*s**2 - 5/12*s**4. Find r such that y(r) = 0.
16
Suppose -4*l = -3*k - k + 400, -3*l = -2*k + 295. Let i = l - -97. Solve 8/5*h**3 - 2/5*h**5 + 0*h**4 - 4/5*h**i - 6/5*h + 4/5 = 0 for h.
-2, -1, 1
Let c be (-8)/26 + 5310/2301. Suppose -4/21*q - 2/7*q**c + 2/7*q**4 + 2/21*q**3 + 0 + 2/21*q**5 = 0. Calculate q.
-2, -1, 0, 1
Suppose 0 = -4*v - 0*v. Let g = v - -2. Factor -3/5*b - 3/5 + 6/5*b**g.
3*(b - 1)*(2*b + 1)/5
Suppose -8*t + 7*t + 5 = 0. Suppose -l - 29 = -3*l + 5*y, t*l - 30 = 4*y. Factor 12/5*f**3 + 0*f - 2/5*f**4 + 0 - 18/5*f**l.
-2*f**2*(f - 3)**2/5
Let k(o) = -7*o - 2. Suppose 3*p - 3*n = -9, 4*p + 2*n - 4*n = -8. Let v be k(p). What is x in 0 - 6/11*x**3 - 2/11*x**2 + 2/11*x**4 + 2/11*x**v + 4/11*x = 0?
-2, -1, 0, 1
Let j(u) be the second derivative of u**9/113400 - u**7/18900 - 5*u**4/6 - 3*u. Let s(v) be the third derivative of j(v). Factor s(q).
2*q**2*(q - 1)*(q + 1)/15
Let k(b) = -5*b**2 - 13*b + 18. Let t(q) = -65*q**2 - 170*q + 235. Let y be (6/(-4)*4)/(2 + -4). Let n(z) = y*t(z) - 40*k(z). Suppose n(x) = 0. What is x?
-3, 1
Let v = -1151/2442 - -18/37. Let l(t) be the second derivative of -v*t**4 + 8*t + 0*t**2 + 2/33*t**3 + 0. Determine w so that l(w) = 0.
0, 2
Determine v, given that -116/9*v**2 + 0 - 2/3*v**3 + 80/9*v = 0.
-20, 0, 2/3
Let c(x) be the first derivative of 2*x**3/21 + 3*x**2 + 39. Factor c(l).
2*l*(l + 21)/7
Let k(j) be the second derivative of -j**7/420 + j**6/30 - 3*j**5/20 + j**4/3 + 5*j**3/6 + 6*j. Let g(c) be the second derivative of k(c). Factor g(p).
-2*(p - 4)*(p - 1)**2
Let m(w) be the second derivative of -w**5/30 - w**4/3 - 4*w**3/3 + 11*w**2/2 - 23*w. Let z(b) be the first derivative of m(b). Factor z(f).
-2*(f + 2)**2
Let i(f) be the second derivative of -9*f**7/140 + 11*f**6/80 - f**5/20 - 3*f**2 + f. Let y(u) be the first derivative of i(u). Factor y(s).
-3*s**2*(s - 1)*(9*s - 2)/2
Let s(z) be the second derivative of -z**7/5880 + z**5/280 - z**4/84 - 7*z**3/3 - 3*z. Let m(p) be the second derivative of s(p). Factor m(q).
-(q - 1)**2*(q + 2)/7
Let n(f) = -9*f - 42. Let y(a) = -a**2 + 14*a - 38. Let j be y(11). Let u be n(j). Suppose 5/4*g + g**2 + 1/4*g**u + 1/2 = 0. Calculate g.
-2, -1
Let c(l) = 4*l**2 - 11*l - 4. Let n = 59 - 63. Let m(b) = -b**2 + 4*b + 1. Let v(t) = n*c(t) - 11*m(t). Suppose v(o) = 0. Calculate o.
-1, 1
Let y be ((0 + -1)/(-1))/(94/470). Let a(m) be the first derivative of 4*m + 3/10*m**y + 3*m**2 - 7/8*m**4 - m**3 - 4. Solve a(l) = 0.
-1, -2/3, 2
Suppose -82*n**3 + 2/3*n**5 + 0 + 388/3*n**2 + 32/3*n**4 - 176/3*n = 0. What is n?
-22, 0, 1, 4
Factor 31*m**2 - m**3 - 33*m**2 + m + 4 - 2.
-(m - 1)*(m + 1)*(m + 2)
Suppose 11*h = h - 5*h. Let f(k) be the second derivative of 1/100*k**5 + 0*k**4 + 7*k + h + 0*k**3 + 0*k**2 + 1/150*k**6. Factor f(c).
c**3*(c + 1)/5
Let m(t) be the third derivative of 2*t**7/35 + t**6/40 - 101*t**5/40 + 73*t**4/16 - 3*t**3 - 270*t**2. Find y such that m(y) = 0.
-4, 1/4, 1/2, 3
Factor 1/2*y**2 - 21/2 - 2*y.
(y - 7)*(y + 3)/2
Let b(j) be the first derivative of -13/300*j**5 + 0*j**2 + 1/180*j**6 + 1 + 0*j - 1/10*j**4 - 2/3*j**3. Let n(s) be the third derivative of b(s). Factor n(r).
2*(r - 3)*(5*r + 2)/5
Let l(h) be the first derivative of -h**6/16 + 9*h**5/40 + 3*h**4/32 - 7*h**3/8 + 3*h/2 + 529. Determine j, given that l(j) = 0.
-1, 1, 2
Suppose 261*d + 2*d**2 + 246*d - 734*d + 247*d - 7*d**2 = 0. Calculate d.
0, 4
Suppose 2/3*k**3 + 384 - 94/3*k**2 + 352*k = 0. Calculate k.
-1, 24
Suppose -64*l + 69*l = 10. Factor 9*w**3 + 0*w**5 - 3*w**5 - 24*w**3 + 20*w**4 - l*w**5.
-5*w**3*(w - 3)*(w - 1)
Let f(h) = h**3 + 3*h**2 - 4*h. Let u be f(-4). Let r = 4215 + -4210. Factor -1/2*d**3 + d**4 - d**2 + u*d + 1/2*d**r + 0.
d**2*(d - 1)*(d + 1)*(d + 2)/2
Let b = 233 - 234. Let y be ((-2)/3 - b)/(12/9). Determine g so that 0 - 3/8*g**2 + 1/8*g**3 + y*g = 0.
0, 1, 2
Suppose 0 = 2*m - 2*j + 2, -4*m + 16 + 4 = 4*j. Factor 5*h**m - 2/3 + 19/3*h**3 + 7/3*h**4 + 1/3*h.
(h + 1)**3*(7*h - 2)/3
Let t be (-60)/9*(-336)/560. Solve 5/3*a**t - 5/3*a + 5/3*a**3 - 5/3*a**2 + 0 = 0 for a.
-1, 0, 1
Suppose -5*m + 5*s = -20, -5*s = -3*m + 6 + 6. Factor -y**3 + 119*y**2 - y**4 - 117*y**2 - 2*y**m.
-y**2*(y + 1)*(3*y - 2)
Let d = 198/7 - 28. Suppose 5*l = -n + 9 - 2, -2*l + 8 = 3*n. Factor -d - 72/7*i**n + 24/7*i.
-2*(6*i - 1)**2/7
Suppose 2*h + 9 = 5*h. Let f(v) = -2*v**2 + 4*v + 9. Let b be f(3). Factor t**5 + 0*t**2 + 3*t - 5*t**2 + t**b + 3*t**2 + 2 - 5*t**h.
(t - 2)*(t - 1)*(t + 1)**3
Let y(b) be the third derivative of -5*b**8/112 + 4*b**7/21 + b**6/4 - 2*b**5/3 - 5*b**4/8 - 2*b**2 + 156*b. Suppose y(t) = 0. What is t?
-1, -1/3, 0, 1, 3
Determine v, given that -108*v**3 - 9*v + 30*v**2 + 38*v**3 + 61*v**3 = 0.
0, 1/3, 3
Let i(s) be the third derivative of -1/72*s**4 + 0*s**3 - 1/630*s**7 + 0 + 0*s + 1/360*s**6 + 1/180*s**5 + 6*s**2. Determine g, given that i(g) = 0.
-1, 0, 1
Let h = 7 + 0. Suppose 3*p + 102 = 37*p. Factor -5*l**3 - 3*l**5 + 2*l**4 + 2*l**4 - 4*l**2 + h*l**5 + l**p.
4*l**2*(l - 1)*(l + 1)**2
Let u(t) be the third derivative of -t**6/90 + t**5/5 - 7*t**3/2 + 7*t**2. Let m(l) be the first derivative of u(l). Suppose m(v) = 0. What is v?
0, 6
Let s be 48/8 - 8/2. Suppose -4 = -s*v - 0*v. Determine r, given that 57*r**v + r - 59*r**2 - 3*r**3 + 0*r = 0.
-1, 0, 1/3
Let r(s) be the second derivative of -10*s**2 + 15/4*s**4 + 6*s + 0 - 40/3*s**3. Find q such that r(q) = 0.
-2/9, 2
Let z be ((-160)/(-100))/((-210)/(-75)). Find l such that -z*l**2 - 80/7*l - 400/7 = 0.
-10
Let 27/7*k**3 - 162/7*k + 0 + 3*k**4 + 3/7*k**5 - 81/7*k**2 = 0. Calculate k.
-3, 0, 2
Let v(m) = m**2 + 3*m + 8. Let z(j) = -j**2 - j - 1. Let d(h) = v(h) + 2*z(h). Let c be d(0). Factor 6*q + 8*q - 9 + 3*q**4 + c*q + 4*q - 18*q**2.
3*(q - 1)**3*(q + 3)
Factor 16/3*l**2 + 13/3*l - 1.
(l + 1)*(16*l - 3)/3
Factor -16 - 10*a - a**2 + 18 - 11.
-(a + 1)*(a + 9)
Let k(o) be the second derivative of o**5/20 - o**4/4 - 3*o**3/2 - 5*o**2/2 - 174*o. Factor k(r).
(r - 5)*(r + 1)**2
Let x = 1576 - 20482/13. Factor -4/13*m**2 + x*m + 0 - 2/13*m**3.
-2*m*(m - 1)*(m + 3)/13
Let z be (1*(-2)/5)/(760/(-950)). Let x(m) be the first derivative of 0*m + 1/10*m**5 - 7 + 5/6*m**3 