et n(t) = -t**5 + t**3 + 1. Let o(r) = a(r) - 11*n(r). Let o(s) = 0. Calculate s.
-2, -1, 0, 17
Suppose -6 = 22*j - 24*j. Factor 60*n**j - 10*n + 452*n**4 - 417*n**4 + 2*n**2 + 13*n**2.
5*n*(n + 1)**2*(7*n - 2)
Let w be (1 - (1 - 1))*(12 + -12). Let t be w + 2/12 + (-10595)/(-6846). Find n, given that -t*n**3 + 8/7 + 2/7*n**4 + 26/7*n**2 - 24/7*n = 0.
1, 2
Let b(o) = 7*o**4 + o**3 - 18*o**2 + 33*o - 9. Let p(a) = 2*a**4 + a**3 - a**2 - a - 3. Let h(k) = -2*b(k) + 6*p(k). Find z such that h(z) = 0.
-4, 0, 3
Let i(g) = -84*g + 88. Let y be i(0). Let v be -2 - (-52)/15 - y/66. Factor -4/5*z**4 - 8/5*z**3 + 0 - 16/15*z**2 + 0*z - v*z**5.
-2*z**2*(z + 2)**3/15
Let j(s) = -s + 13. Let a be j(7). Suppose 2*o - 5*o = -a. Solve -90 - 184*x**o - 50*x**4 - 29*x**2 + 285*x + 190*x**3 + 5*x**5 - 127*x**2 = 0 for x.
1, 2, 3
Let w be 6*6/36*3. Factor 1 - 10*d + 2*d**w - 7 + 3*d - d**3.
(d - 3)*(d + 1)*(d + 2)
Let i = -89 + 92. Let 11*y**2 - 165*y**i + 72*y - 36 + 36*y**4 + 124*y**2 + 48*y = 0. What is y?
-2/3, 1/4, 2, 3
Let t(h) be the first derivative of -h**3/2 + 915*h**2/2 - 279075*h/2 + 827. Factor t(n).
-3*(n - 305)**2/2
Determine h so that 6*h**2 + 0 - 16/7*h**3 + 18/7*h = 0.
-3/8, 0, 3
Let a(c) be the second derivative of -c**5/50 + 21*c**4/5 - 41*c**3/5 - 50*c**2 - 7*c + 100. Factor a(z).
-2*(z - 125)*(z - 2)*(z + 1)/5
Let y be ((-4)/7)/((-14)/112*(-2)/(-3)). Suppose 0 - y*p**2 - 72/7*p - 6/7*p**3 = 0. Calculate p.
-6, -2, 0
Let g = -212693/3 + 70905. Let 28/3*o - g - 2*o**2 = 0. What is o?
1, 11/3
Let k(d) = 3*d**3 - 96*d**2 + 390*d + 11598. Let l(o) = 3*o**3 - 94*o**2 + 389*o + 11595. Let j(m) = -7*k(m) + 6*l(m). Factor j(z).
-3*(z - 22)**2*(z + 8)
Suppose -68*s - 207 = -3*z - 71*s, 2*s + 822 = 13*z. What is o in -72/5*o**2 + z*o**3 - 324/5*o**5 + 4/5*o + 0 + 72/5*o**4 = 0?
-1, 0, 1/9, 1
Let w(f) be the first derivative of -3*f**5/40 - 25*f**4/24 - 2*f**3/3 + 207*f - 161. Let k(s) be the first derivative of w(s). Factor k(p).
-p*(p + 8)*(3*p + 1)/2
Let s(u) = u**3 + 5*u**2 - 16*u - 10. Let o be s(-7). Factor -8*v**4 + 0*v**o + 13*v**4 + 60*v**3 + 180*v**2.
5*v**2*(v + 6)**2
Let m(u) be the second derivative of -u**6/60 + 103*u**5/4 - 87719*u**4/8 - 266255*u**3/3 - 267289*u**2 + 251*u + 14. Solve m(k) = 0.
-2, 517
Find s, given that -s**2 + 4*s**2 + 178282*s + 84050 - 177462*s + s**2 - 2*s**2 = 0.
-205
Factor 54*d**3 + 32259*d**2 - 4*d**5 - 6*d**3 - 32323*d**2.
-4*d**2*(d - 2)**2*(d + 4)
Let j(b) = b**5 - 2*b**3 - b**2 + b - 1. Let u(s) = -15*s**5 + 2*s**4 + 32*s**3 + 3*s**2 - 9*s + 13. Let g(v) = 26*j(v) + 2*u(v). Factor g(c).
-4*c*(c - 1)**3*(c + 2)
Let f(c) = c**2 - 309*c - 9016. Let y be f(-27). Factor y*u**2 - 48*u - 32/3 + 980/3*u**3.
4*(5*u - 2)*(7*u + 2)**2/3
Factor -428*n**2 + 39*n + 576 - 19*n + 210*n**2 + 217*n**2.
-(n - 36)*(n + 16)
Factor 77/4 - 1/8*g**2 - 153/8*g.
-(g - 1)*(g + 154)/8
Let g be 2/22*((6 - 24) + 414/(8 + 15)). Solve -2/3*u**2 + 2/3*u**4 - 8*u**3 + 8*u + g = 0.
-1, 0, 1, 12
Let u(f) be the third derivative of -f**6/360 + 19*f**5/180 - 13*f**4/9 + 88*f**3/9 + 1509*f**2. Solve u(n) = 0 for n.
4, 11
Let c(x) be the first derivative of 9 - 8/3*x**3 + 2*x + 1/3*x**4 + 6*x**2. Let j(t) be the first derivative of c(t). Factor j(q).
4*(q - 3)*(q - 1)
Let h be (-245)/280*-48*2/18. Solve -h + 3*a - 1/3*a**2 = 0 for a.
2, 7
Let r = 2 - -2. Let x(y) = 519*y + 5194. Let l be x(-10). Factor 6*w**4 - 4*w**r - 6*w**l - 8 + 12*w**2 + 4*w**3 - 4*w.
-4*(w - 2)*(w - 1)*(w + 1)**2
Let n = 3117 + -3114. Let z(w) be the first derivative of -4/5*w**5 + 4/3*w**3 + 0*w + 7 + n*w**4 - 6*w**2. What is x in z(x) = 0?
-1, 0, 1, 3
Let r(k) be the third derivative of -k**5/18 + 23*k**4/18 - 104*k**3/9 - 10555*k**2. Factor r(s).
-2*(s - 4)*(5*s - 26)/3
Let f(t) = t**2 - 63*t - 128. Let v be f(65). Let y(x) be the second derivative of -1/6*x**4 + 1/6*x**3 + x**v - 1/20*x**5 + 0 + 7*x. Factor y(w).
-(w - 1)*(w + 1)*(w + 2)
Find f such that 2/3*f**2 - 2/3*f**3 + 40/3*f + 0 = 0.
-4, 0, 5
Let c(f) be the third derivative of 71*f**5/90 + 5*f**4/18 + 6707*f**2. Factor c(n).
2*n*(71*n + 10)/3
Let z(d) = -d**3 - 6*d**2 - 6*d + 2. Let s(r) = 2*r**3 - 4 + 1 + 9*r**2 + 57*r - 46*r + 2*r**2. Let n(g) = -3*s(g) - 5*z(g). Factor n(w).
-(w + 1)**3
Let u(r) = 4*r**2 + 70*r - 11. Let c be u(-18). Let b be 1 - ((-85)/c - (-8 + 4)). Factor -2*t**3 + 4/5 - b*t - 16/5*t**2.
-2*(t + 1)**2*(5*t - 2)/5
Let j(v) be the third derivative of -v**5/150 + 17*v**4/60 - 14*v**3/3 + 2002*v**2. Factor j(b).
-2*(b - 10)*(b - 7)/5
Let u(n) = -n**2 + 24*n + 15. Let q be u(11). Suppose 316 - 2*k**3 - 157 + 2*k - q - k**4 = 0. What is k?
-1, 1
Let g(x) be the first derivative of 0*x - 1/3*x**2 - 8/15*x**5 - 16 - 1/9*x**6 - x**4 - 8/9*x**3. Factor g(v).
-2*v*(v + 1)**4/3
Let d be -3*2*1*((-44)/6 + 7). Let x(a) be the third derivative of 0 - 1/360*a**6 + 0*a + a**d - 1/60*a**5 + 1/72*a**4 + 1/630*a**7 + 1/9*a**3. Factor x(w).
(w - 2)*(w - 1)*(w + 1)**2/3
Let s(k) be the third derivative of k**5/270 - k**4/108 - 4*k**3/9 - 53*k**2 + 17. Solve s(u) = 0.
-3, 4
Let n(x) be the first derivative of -5*x**4/2 - 265*x**3/3 + 1035*x**2/2 - 450*x + 124. Determine d, given that n(d) = 0.
-30, 1/2, 3
Let t(h) be the third derivative of 0*h**6 - 2 + 0*h**4 - 1/10*h**5 + 0*h + 1/70*h**7 + 1/2*h**3 + 13*h**2. Factor t(k).
3*(k - 1)**2*(k + 1)**2
Let u(k) be the first derivative of 5/3*k**3 + 283 + 13005*k - 255*k**2. Factor u(y).
5*(y - 51)**2
Let c be -11*34/44 - -14. Determine f so that -16*f + c*f**2 + 14 - 1/2*f**3 = 0.
2, 7
Let z(a) be the third derivative of -a**7/525 - a**6/150 + a**5/150 + a**4/30 + 1406*a**2. Factor z(k).
-2*k*(k - 1)*(k + 1)*(k + 2)/5
Let w be 12/(-8)*(-465)/135 + 5/15. Let m(y) be the first derivative of 1/6*y**3 - 34 + 5/2*y**2 - w*y. Factor m(n).
(n - 1)*(n + 11)/2
Suppose -12*o = -8*o - 420. Suppose 0 = -2*u + 9*u - o. Factor 2 - 2 + 19*q**4 - u*q**4.
4*q**4
Let h(k) = 5*k**3 - 3602*k**2 + 14671*k - 14770. Let d(p) = -2*p**3 + 1200*p**2 - 4890*p + 4924. Let f(m) = 17*d(m) + 6*h(m). Suppose f(u) = 0. Calculate u.
-307, 2
Let a(k) = -2*k**3 - k**2 - 4*k - 4. Let i be a(-5). Let -20*z + 4 + 237*z**2 - i*z**2 - 28 = 0. Calculate z.
-3, -2
Let x(g) = -g**2 - 11*g - 12. Let z be x(-9). Let t = z + 2. Let t*h**5 + 10*h**3 - 5*h**2 + 16*h**3 - 26*h**4 - 2*h**5 - h**2 = 0. What is h?
0, 1/3, 1, 3
Let a(j) = -9*j - 5. Let o be a(-1). Suppose -o*q + 8 = d - 7*q, 2*d - 4*q = 12. Factor -6*h - h**4 + 20*h**d + 2*h**5 + 2 + 20*h**3 + 16*h + 11*h**4.
2*(h + 1)**5
What is h in 36/13*h - 16/13 + 10/13*h**2 = 0?
-4, 2/5
Factor -3/2*y**3 - 171/2*y**2 + 171/2 + 3/2*y.
-3*(y - 1)*(y + 1)*(y + 57)/2
Find w, given that 20/9*w**3 + 64/9*w**2 + 0 + 2/9*w**4 + 64/9*w = 0.
-4, -2, 0
Let z(h) be the first derivative of -h**4/18 + 136*h**3 - 124848*h**2 + 50937984*h - 3094. Find n, given that z(n) = 0.
612
Factor 80/3*i + 6*i**3 - 31*i**2 - 1/3*i**4 + 64.
-(i - 8)**2*(i - 3)*(i + 1)/3
Let k = 3 - 0. Suppose -g - 4*g + q + 16 = 0, -k*g = 2*q - 20. Suppose -2*p**5 - 4*p**3 - 2*p**g + 6*p**3 - 2*p**3 = 0. Calculate p.
-1, 0
Let g(f) be the second derivative of f**5/190 - f**4/6 + 88*f**3/57 + f + 296. Factor g(p).
2*p*(p - 11)*(p - 8)/19
Let s(o) be the third derivative of 5*o**8/336 + o**7/14 - o**6/24 - o**5/4 + 4452*o**2. What is x in s(x) = 0?
-3, -1, 0, 1
Let 506 + 2/3*z**2 - 160/3*z = 0. Calculate z.
11, 69
Let w(t) be the second derivative of 0*t**2 - 8/5*t**5 - 2*t + 0*t**4 - t**6 + 0*t**3 + 25 + 1/21*t**7. Factor w(q).
2*q**3*(q - 16)*(q + 1)
Let p(r) be the third derivative of -r**5/72 - 163*r**4/144 + 11*r**3/6 - 169*r**2 - 2. Find k such that p(k) = 0.
-33, 2/5
Factor -164/3*y**2 + 682/3*y - 2/3*y**3 - 172.
-2*(y - 3)*(y - 1)*(y + 86)/3
Let f(c) be the first derivative of -c**5/40 + 11*c**4/16 + 3*c**3 - 12*c**2 + 60. Let g(k) be the second derivative of f(k). Determine h so that g(h) = 0.
-1, 12
Let a(l) be the third derivative of l**6/420 - 18*l**5/35 - 225*l**4/28 - 342*l**3/7 + 12231*l**2. Suppose a(o) = 0. What is o?
-3, 114
Let x = 557/349 - 1805/2443. Factor 0 - x*z**2 + 6*z.
-6*z*(z - 7)/7
Let g = -18 - -44. Suppose -96 = -4*t - 4*y + 2*y, -6 = 3*y. Find m, given that -32*m**3 - g*m**3 - 12*m**4 + 3*m + 89*m**3 + 12*m**2 - t*m**3 - 9*m**5 = 0.
-1, -1/3, 0, 1
Let d(m) be the first deriva