3 + 16*r**2 + 4. Suppose s(t) = 0. What is t?
-1, -1/3, -2/7, 6
Let c be 22/(-2) - (-5382)/442. Factor -10/17*b**4 - c*b**2 + 10/17*b - 2/17 + 2/17*b**5 + 20/17*b**3.
2*(b - 1)**5/17
Let l(w) = 5*w**2 - 90*w + 1762. Let j(h) = -27*h**2 + 453*h - 8809. Let s(r) = -6*j(r) - 33*l(r). Factor s(c).
-3*(c - 42)**2
Let c be 2/3*(-900)/(-24). Factor -2 - 29*q**2 + 8*q - 4*q - c*q - 10*q.
-(q + 1)*(29*q + 2)
Solve 23814 - 378*h + 3/2*h**2 = 0.
126
Let x(n) be the third derivative of 5/192*n**8 - 7/96*n**6 - 1/84*n**7 - 6*n**2 + 1/24*n**5 + 0 + 0*n**4 + 0*n**3 + 0*n. Let x(t) = 0. Calculate t.
-1, 0, 2/7, 1
Let r = 3886 - 19364/5. Factor -3*u**3 - r*u**2 - 24/5 - 84/5*u.
-3*(u + 2)**2*(5*u + 2)/5
Let m be 6/42 - 2/(-14). Let g = 471 - 468. Find v such that 4/7 - 4/7*v**2 - 2/7*v**g + m*v = 0.
-2, -1, 1
Let f(i) = i**2 + 5*i + 6. Let c be f(-4). Let y(q) = q**2 + 16*q + 31. Let w be y(-14). Factor s**4 + c*s - s**5 - 8 + w*s**3 + 8 - 5*s**2.
-s*(s - 1)**3*(s + 2)
Find k, given that 5*k**4 + 4*k**4 - 52*k**2 - 2*k**4 - 18*k**4 - 8*k + 58*k**3 - 4*k**4 = 0.
-2/15, 0, 2
Let q = 516 + -19609/38. Let i = q + 79/114. Factor i + 1/3*x**2 + x.
(x + 1)*(x + 2)/3
Let c(x) = 144*x**4 + 64*x**3 - 7*x**2 + 8. Let m(n) = -96*n**4 - 43*n**3 + 4*n**2 - 5. Let z(v) = 5*c(v) + 8*m(v). Factor z(a).
-3*a**2*(4*a + 1)**2
Let i(t) be the first derivative of -2/39*t**3 - 6/13*t**2 + 1/26*t**4 - 8 + 0*t. Find q, given that i(q) = 0.
-2, 0, 3
Let y be -3 + (197/56 - 10/70). Let x(h) be the second derivative of 0 - 9*h - 9/4*h**3 - 1/40*h**5 - y*h**4 - 27/4*h**2. Factor x(j).
-(j + 3)**3/2
Let q be (-86)/(-102) - (245/21 + -12). What is b in 20/17*b**3 - 2/17 - q*b**2 + 2/17*b**5 - 10/17*b**4 + 10/17*b = 0?
1
Let k(x) = -x**2 + 2*x. Let l(z) = 3*z**2 + 66*z + 1225. Let m(r) = -6*k(r) - 3*l(r). Factor m(h).
-3*(h + 35)**2
Let k = -40997 - -164356975/4009. Let l = 256570/12027 + k. Let -l - 4/3*t**2 - 32/3*t = 0. What is t?
-4
Let j = 56/131 + -261/917. Factor 0 - 3/7*b**3 + j*b**2 + 1/7*b**5 + 2/7*b - 1/7*b**4.
b*(b - 2)*(b - 1)*(b + 1)**2/7
Let u(o) be the third derivative of -1/4*o**4 + 0*o - 5*o**2 + 0*o**3 + 0 - 1/20*o**5. Determine g so that u(g) = 0.
-2, 0
Suppose -2*v - 2*d = 2*d - 24, 2*v - 4*d = 0. Let i be v*((-20)/(-12) - 1). What is a in -3*a**3 + 4*a**2 - 7*a + 11*a - a**3 - i = 0?
-1, 1
Let c(w) = -w**3 + w**2 + w. Let r(u) = -7*u**3 + 4*u**2 + 13*u + 4. Let f(g) = -15*c(g) + 3*r(g). Factor f(l).
-3*(l - 2)*(l + 2)*(2*l + 1)
Let q(t) = -t**3 - 7*t**2 - 17*t - 11. Let c(r) = r - 1. Let a = 48 + -43. Let w(x) = a*q(x) + 5*c(x). Factor w(y).
-5*(y + 2)**2*(y + 3)
Let r = -8633 - -86333/10. Factor 0 + 1/5*n**2 + 0*n + 1/10*n**4 + r*n**3.
n**2*(n + 1)*(n + 2)/10
Suppose 2*h = -2*w + 14, 2*w = 6*h - 2*h - 40. Suppose -3*b + 3 + h = 0. Suppose -3*v**3 - 2*v**b + 0 - 1/2*v - 2*v**2 - 1/2*v**5 = 0. Calculate v.
-1, 0
Suppose -5*a + 4 - 5 = -j, 3*j + 5*a - 23 = 0. Let s = -4 + j. Factor 0 + 4/3*d - s*d**2 + 2/3*d**3.
2*d*(d - 2)*(d - 1)/3
Let z(s) be the third derivative of -3/100*s**5 + 0*s**3 + 0*s + 15*s**2 - 1/300*s**6 + 0 + 1/60*s**4 + 3/350*s**7. Determine t so that z(t) = 0.
-1, 0, 2/9, 1
Suppose 0 = -3*q - p - 4, -22 + 6 = 4*q + 4*p. Let l(d) be the first derivative of q*d + d**4 + 11 + 4/3*d**3 - 4*d**2. Let l(t) = 0. Calculate t.
-2, 0, 1
Let k(u) be the third derivative of -u**6/1260 + u**4/21 + 7*u**3/3 - 10*u**2. Let s(p) be the first derivative of k(p). Factor s(t).
-2*(t - 2)*(t + 2)/7
Let b(w) be the first derivative of 9*w**2 - 27 - 2/3*w**3 - 16*w. What is o in b(o) = 0?
1, 8
Let p(v) be the third derivative of -v**6/1200 + v**5/75 - v**4/12 + 4*v**3/15 + 2*v**2 - 21*v. Factor p(h).
-(h - 4)*(h - 2)**2/10
Let g be 8/4 - (7 - 7). Let r(f) be the first derivative of -5/4*f**g + 3/2*f - 3 - 1/3*f**3. Solve r(o) = 0 for o.
-3, 1/2
Let a(w) = -14*w - 2067. Let m be a(-148). Suppose -40*j + 20*j**4 - 5/2*j**m + 0 - 60*j**3 + 80*j**2 = 0. Calculate j.
0, 2
Factor 1 + 225*y**2 + 120*y + 16 - 11 + 14 + 125*y**3.
5*(y + 1)*(5*y + 2)**2
Let p = 11889/7930 + 3/3965. What is t in 0 - p*t**2 + 15/8*t - 3/8*t**3 = 0?
-5, 0, 1
Let h(n) be the third derivative of -3/2*n**3 + 11/240*n**5 - 1/4*n**4 - 1/480*n**6 + 0*n + 8*n**2 + 0. Solve h(u) = 0.
-1, 6
Let 122*d**2 + 4 + 84*d**3 + 8*d + 34*d - 4*d + 72*d**4 + 76*d**3 = 0. What is d?
-1, -1/2, -2/9
Let b(v) be the second derivative of v**6/6 + 31*v**5/4 + 145*v**4/4 + 425*v**3/6 + 70*v**2 + 160*v. Factor b(t).
5*(t + 1)**3*(t + 28)
Let q(m) be the first derivative of -5*m**3/12 - 9*m**2 - 7*m - 229. What is d in q(d) = 0?
-14, -2/5
Suppose -116 = 203*l - 232*l. Let f(i) be the second derivative of 3*i + 0*i**2 + 0 + 0*i**5 + 1/35*i**6 - 2/21*i**l + 0*i**3 - 1/147*i**7. Factor f(d).
-2*d**2*(d - 2)**2*(d + 1)/7
Let q(a) = -20*a - 20. Let y(c) = c**2 - 1. Let t(p) = q(p) - 5*y(p). Suppose t(b) = 0. Calculate b.
-3, -1
Let c = -65/3 + 22. Suppose 3*d - 12 = 5*n, -n + 2*d + 16 = 6*d. Solve -c*x**5 + n + 0*x + 1/3*x**2 + 1/3*x**3 - 1/3*x**4 = 0.
-1, 0, 1
Suppose 11*c + 18*c - 9*c - 40 + 58 + 2*c**2 = 0. What is c?
-9, -1
Let f(b) be the first derivative of 2*b**4 - 9*b + 12*b**2 - 22/3*b**3 + 24 - 1/5*b**5. Factor f(q).
-(q - 3)**2*(q - 1)**2
Let v(i) = 3*i**4 - 21*i**3 + 15*i**2 + 3*i. Let p(d) = -2*d**4 + 11*d**3 - 8*d**2 - d. Let o(y) = 9*p(y) + 5*v(y). Factor o(j).
-3*j*(j - 1)*(j + 1)*(j + 2)
Suppose 17*z = 20*z - 12. Suppose 2*d = -z + 10. Factor 0*o + d*o**4 - o**4 + 6*o**2 - 6*o**3 - 2*o.
2*o*(o - 1)**3
Let s(r) = r**3 + 2*r**2 - 2*r. Let c be s(-2). Suppose x - 3*x = -2*w - 34, -c*x - 4*w = -28. Factor -x*n - 1 - 2*n**3 - 5 - 8*n**2 + 2 - n**2.
-(n + 2)**2*(2*n + 1)
Let v(q) be the third derivative of -q**9/6048 - 17*q**8/10080 - q**7/420 - 2*q**5/5 - 14*q**2. Let o(w) be the third derivative of v(w). Solve o(f) = 0.
-3, -2/5, 0
Let c be 913/(-1782)*-6 - 4/54. Factor -4/11*l - 6/11*l**c + 0 + 2/11*l**4 + 2/11*l**5 - 10/11*l**2.
2*l*(l - 2)*(l + 1)**3/11
Let p(k) be the second derivative of k**4/24 - 3*k**3/2 - 19*k**2/4 - 24*k - 3. Factor p(o).
(o - 19)*(o + 1)/2
Let d(x) = x**2 + 3. Let v be d(0). Determine j so that 8 - j**2 - 4 + j**2 - v*j - j**2 = 0.
-4, 1
Determine g, given that -1/6*g**4 - g**3 - 11/6*g**2 - g + 0 = 0.
-3, -2, -1, 0
Suppose 150 - 15*q**2 - 14 + 7*q + 12*q**2 + 53*q - q**2 = 0. What is q?
-2, 17
Factor -6 + 3/2*j**3 + 0*j + 9/2*j**2.
3*(j - 1)*(j + 2)**2/2
Let y(w) be the second derivative of -w**7/5040 + w**6/720 + w**5/80 - w**4/2 + 15*w. Let v(j) be the third derivative of y(j). Factor v(h).
-(h - 3)*(h + 1)/2
Let z(n) be the second derivative of n**8/336 + n**7/70 + n**6/60 + 3*n**2 - 2*n. Let v(x) be the first derivative of z(x). Determine s, given that v(s) = 0.
-2, -1, 0
Let q(o) be the first derivative of -o**5/20 + 9*o**4/8 - 121*o**3/12 + 45*o**2 - 100*o - 11. Factor q(d).
-(d - 5)**2*(d - 4)**2/4
Let l(k) be the first derivative of -k**3 + 21*k**2 - 120*k - 262. Factor l(i).
-3*(i - 10)*(i - 4)
Suppose -36 = -15*d - 6. Let f(a) be the first derivative of -3 + 4/5*a**5 - 4/3*a**3 + d*a**2 + 0*a - a**4. Find g such that f(g) = 0.
-1, 0, 1
Let d(i) = -i - 19. Let a be d(-14). Let l(b) = 7*b**2 + 12*b + 5. Let k(s) = 8*s**2 + 12*s + 4. Let p(x) = a*l(x) + 4*k(x). Factor p(g).
-3*(g + 1)*(g + 3)
Let x = -143 - -81. Let j = x - -64. Factor 1/3*u**4 + 1/3*u**5 - 1/3*u**j + 0 - 1/3*u**3 + 0*u.
u**2*(u - 1)*(u + 1)**2/3
Suppose -m - 9*m - 2420 = 0. Let i = m + 245. Factor -i*q + 3/2*q**2 + 0.
3*q*(q - 2)/2
Suppose 0 = -98*m + 99*m - 3*c - 3, -2*c = 0. Determine f, given that 40*f**5 + 0*f**2 + 0 - 20*f**4 + 0*f - 15/2*f**m = 0.
-1/4, 0, 3/4
Let p be (40 - 5)/(0 + 0 + 1). Let k = 38 - p. Determine u, given that -4/5*u**k + 0 + 4/5*u - 2/5*u**4 + 2/5*u**2 = 0.
-2, -1, 0, 1
Let g(t) be the second derivative of -t**6/4320 + t**5/288 - t**4/48 + 22*t**3/3 - 12*t. Let m(k) be the second derivative of g(k). Factor m(u).
-(u - 3)*(u - 2)/12
Determine u, given that -1872*u - 64 - 22749*u**3 - 18252*u**2 - 37775*u**3 + 1205*u**3 = 0.
-4/39
Let s(x) = -x**2 + 13*x - 12. Let i be s(11). Solve -15*f**2 + 25 - 25 - 10*f + i*f**3 = 0 for f.
-1/2, 0, 2
Let a be (-6)/140 - (27/(-5) - -5). Let c = a + -4/21. Determine s, given that 0 + c*s - 1/6*s**2 = 0.
0, 1
Let z(l) be the first derivative of 1/24*l**4 + 0*l 