et h(m) = -m**3 + 5*m**2 + 7*m - 4. Let r be h(6). Factor r*y + d*y**2 + 4/3.
2*(y + 1)*(y + 2)/3
Factor 24/11*c + 6/11*c**3 + 0 - 24/11*c**2.
6*c*(c - 2)**2/11
Suppose 4*n + 2 = -18. Let t(x) = -x**2 - 5*x + 1. Let i be t(n). Factor j - i + 3 + 2*j**2 + 3*j.
2*(j + 1)**2
Suppose -2 = 3*a - a + p, 4*a + 8 = -4*p. Let y be a/(3*3/9). Find r, given that y + 2*r**3 + 4/3*r - 14/3*r**2 - 10/3*r**5 + 14/3*r**4 = 0.
-1, 0, 2/5, 1
Let b(g) = 2*g - 1. Let p be b(5). Suppose 0 = -i - 3*x - 2, -4*x - 3 = -i + p. Factor -3*u**2 + u - u + i*u**2 + 2*u.
u*(u + 2)
Let p(t) be the first derivative of -4*t**5 + 3*t**4 + 16*t**3 + 8*t**2 + 6. Factor p(u).
-4*u*(u - 2)*(u + 1)*(5*u + 2)
Let x be (-1 + -1)/(112/(-21)). Let p = x + 23/24. Factor p*n**4 + 2*n**3 + 1/3*n + 1/3*n**5 + 4/3*n**2 + 0.
n*(n + 1)**4/3
Let s = 40 + -36. Factor 0*p + 0*p**2 - 1/3*p**3 + 4/3*p**5 + 0 + p**s.
p**3*(p + 1)*(4*p - 1)/3
Let q = 37 - 109/3. Factor q*b**4 + 8/3 - 2*b**2 - 4/3*b**3 + 8/3*b.
2*(b - 2)**2*(b + 1)**2/3
Let q be (-16)/9 - (-2 - 0). Let w be (-16)/(-7) - 10/35. Factor -q*l**w - 2/9 + 4/9*l.
-2*(l - 1)**2/9
Let j(s) be the first derivative of 8*s**3/3 - 3*s**2/2 - 8. Solve j(y) = 0 for y.
0, 3/8
Suppose 14 + 9*d**3 + 2*d**4 - 6*d - 16*d**2 + 3*d**3 - 6*d = 0. Calculate d.
-7, -1, 1
Let j(k) be the first derivative of k**4/5 + 56*k**3/5 + 1176*k**2/5 + 10976*k/5 - 60. Find m, given that j(m) = 0.
-14
Factor 2*t**3 + 8*t**2 + 7*t + t**4 + 2 - t**5 - 2*t**4 - t**4.
-(t - 2)*(t + 1)**4
Let y be (30/(-40))/(2 - (-339)/(-120)). Find q, given that -4/11*q**3 - 8/11*q - 2/11 - y*q**2 = 0.
-1, -1/2
Let p(s) be the first derivative of -4*s**3 - 3*s**2/2 + 26. Factor p(m).
-3*m*(4*m + 1)
Let u be 886/(-232) - 44/(-11). Let y = 2/29 + u. Factor -y*c**5 - 3/2*c**3 - c**2 + 0 - 1/4*c - c**4.
-c*(c + 1)**4/4
Let j = -11 + 14. Let p(t) be the first derivative of 10/3*t**j - 1 + t**2 - 4*t - 1/2*t**4 - 6/5*t**5. Find d such that p(d) = 0.
-1, 2/3, 1
Let m(k) be the second derivative of k**4/3 + 2*k**3 + 20*k. Factor m(b).
4*b*(b + 3)
Factor -9*h**4 - 244*h + 123*h + 121*h + 3*h**5 + 9*h**3 - 3*h**2.
3*h**2*(h - 1)**3
Let k = 43/62 + -6/31. Factor -1/2*f**4 - 1/2 + f**3 + f**2 - k*f - 1/2*f**5.
-(f - 1)**2*(f + 1)**3/2
Let m = 26/15 - 14/15. Factor -6/5*s + m - 2*s**2.
-2*(s + 1)*(5*s - 2)/5
Let s(z) be the third derivative of z**7/105 - z**6/30 + z**5/30 - 4*z**2. Factor s(g).
2*g**2*(g - 1)**2
Suppose -35 - 2 = -3*v - j, 5*j = 5. Let c = v - 1. Factor -2 - 3 + 15*o + 32*o**2 - 1 - c*o**2.
3*(o + 1)*(7*o - 2)
What is i in -3*i + 12*i**3 + 2*i**2 + 7*i**2 + 7*i**2 + 7*i = 0?
-1, -1/3, 0
Let p(a) be the second derivative of -9*a**7/70 - 11*a**6/40 - a**5/10 - 2*a**2 + 2*a. Let q(d) be the first derivative of p(d). Factor q(t).
-3*t**2*(t + 1)*(9*t + 2)
Let j(d) be the third derivative of -d**5/20 - 5*d**4/24 + d**3/3 + d**2 - 17*d. Factor j(i).
-(i + 2)*(3*i - 1)
Suppose -20*w**3 + 26*w**2 + 4*w**2 - 56*w**3 + 15*w**4 - 5*w**3 = 0. Calculate w.
0, 2/5, 5
Factor 9*g - 5*g**2 - 2*g + 10 + 0*g - 2*g.
-5*(g - 2)*(g + 1)
Let h be ((-3 - -1) + 0)*(-1)/6. Determine s so that 0 - s**3 + 1/3*s**4 - h*s + s**2 = 0.
0, 1
Let u(w) be the second derivative of -w + 0*w**2 + 3/4*w**4 + 0 + 3/4*w**5 - w**3. Factor u(z).
3*z*(z + 1)*(5*z - 2)
Let n be 2/12*15/10. Let g(s) be the second derivative of -s - 1/6*s**3 - n*s**2 + 1/8*s**4 - 1/15*s**6 + 1/10*s**5 + 0. Factor g(a).
-(a - 1)**2*(2*a + 1)**2/2
Solve -44 + o - 6*o**2 + 47 - 4*o = 0 for o.
-1, 1/2
Let j(f) be the first derivative of 1/4*f**4 + 0*f**3 - f**2 + 3 + 0*f + 1/20*f**5. Let m(b) be the second derivative of j(b). Factor m(k).
3*k*(k + 2)
Let k = 66 + -62. Let i(t) be the second derivative of -1/24*t**k + 0*t**3 + 0*t**2 + 1/40*t**5 + 0 - t. Let i(s) = 0. What is s?
0, 1
Let n(c) be the first derivative of -c**6/39 + 34*c**5/65 - 53*c**4/13 + 580*c**3/39 - 25*c**2 + 250*c/13 - 4. Let n(a) = 0. Calculate a.
1, 5
Let c(n) = 3*n**2 - 2. Let u be c(2). What is o in -5*o**2 - 4*o + u*o**5 - 2*o**2 - o**2 - 6*o**3 - 6*o**2 + 14*o**4 = 0?
-1, -2/5, 0, 1
Let x = -7 + 5. Let y be ((-8)/(-20))/(x/(-10)). Solve -11 + 11 - 4*b - b**y - 4 = 0 for b.
-2
Let t = -54 - -59. Suppose 0 + 4/7*n**4 - 4/7*n**2 - 2/7*n**t + 0*n**3 + 2/7*n = 0. Calculate n.
-1, 0, 1
Let i(j) be the first derivative of -j**4/4 + j**3/6 + j**2/4 + 7. Let i(u) = 0. Calculate u.
-1/2, 0, 1
Suppose 5*w - 10 = -4*o, 3*w - o - 2 = 2*w. Factor 0 + 1/2*s + 1/4*s**3 + 3/4*s**w.
s*(s + 1)*(s + 2)/4
Let f(p) be the third derivative of p**8/2856 - p**7/595 - p**6/510 + p**5/85 + p**4/204 - p**3/17 - 9*p**2. Find w such that f(w) = 0.
-1, 1, 3
Suppose 3*z + 22 = 5*z + 4*o, -19 = -z + 2*o. Solve z*j - 21*j**4 - 7 - 1 - 15*j**3 + 27*j**2 + 2 = 0.
-1, 2/7, 1
Find n such that 0*n**3 - 1/3 - 1/3*n**4 + 0*n + 2/3*n**2 = 0.
-1, 1
Let y = 5 + 14. Suppose -114*r**2 + 24 + y*r**3 + 14*r**3 - 72*r + 84*r + 45*r**4 = 0. Calculate r.
-2, -2/5, 2/3, 1
Let x(c) be the third derivative of -c**5/30 + c**4/6 - 5*c**2. Factor x(l).
-2*l*(l - 2)
Let m(s) be the second derivative of s**4/30 - s**3/5 + 2*s**2/5 + 10*s. Suppose m(o) = 0. Calculate o.
1, 2
Let v(g) be the first derivative of -g**5/20 + g**3/12 - 17. Find n, given that v(n) = 0.
-1, 0, 1
Let q(y) be the second derivative of y**6/30 + y**5/5 + y**4/3 + 7*y**2/2 + 8*y. Let i(n) be the first derivative of q(n). Find s such that i(s) = 0.
-2, -1, 0
Let h(t) be the first derivative of 2*t**3/3 + 42*t**2 + 882*t - 57. Suppose h(p) = 0. Calculate p.
-21
Let q(z) be the third derivative of z**6/24 - z**5/3 + 25*z**4/24 - 5*z**3/3 - 12*z**2. Factor q(l).
5*(l - 2)*(l - 1)**2
Let o(f) be the second derivative of -f**5/160 - f**4/32 + f**2/4 + 12*f. Factor o(d).
-(d - 1)*(d + 2)**2/8
Let i be (70/(-24))/(3/(-4)). Let g = i + -11/3. Factor 0*k**2 + 2/3*k**5 + 0 - 4/9*k**3 - g*k**4 + 0*k.
2*k**3*(k - 1)*(3*k + 2)/9
Let t = 992/9 - 110. Factor t - 2/3*d**4 + 4/9*d**2 + 2/9*d**5 - 2/3*d + 4/9*d**3.
2*(d - 1)**4*(d + 1)/9
Let j = -1 - -5. Let -j*x**2 - 220*x + 220*x = 0. Calculate x.
0
Factor -1/4*n - 1/2 + 1/2*n**2 + 1/4*n**3.
(n - 1)*(n + 1)*(n + 2)/4
What is k in -16/5*k**4 + 0*k**2 - 4/5*k**5 + 0*k - 16/5*k**3 + 0 = 0?
-2, 0
Let x(t) be the first derivative of -7*t**4/22 + 4*t**3/33 + 7*t**2/11 - 4*t/11 + 6. Determine b, given that x(b) = 0.
-1, 2/7, 1
Let k(g) = g**2 + 11*g + 4. Let c be k(-11). What is t in 3 + 2*t**3 - 3 + 6*t**2 - 4*t**3 - c*t = 0?
0, 1, 2
Suppose -3*k = -5*t + 10*t + 6, 0 = -2*t + 5*k + 10. Suppose 0*w**2 + 6/5*w**4 + 3/5*w**3 + t + 0*w + 3/5*w**5 = 0. What is w?
-1, 0
Let h(u) = u**2 + u - 1. Let k(t) = 6*t**2 - 6*t - 2. Let w(r) = -2*h(r) + k(r). Solve w(p) = 0 for p.
0, 2
Let b(g) be the second derivative of -g**6/6 + g**5/4 + 5*g**4/4 - 5*g**3/6 - 5*g**2 + 34*g. Factor b(c).
-5*(c - 2)*(c - 1)*(c + 1)**2
Let m be 9*(-4)/(-108) - (1 - 1). Let 1/3*f**2 + m - 2/3*f = 0. Calculate f.
1
Factor 0 - 4/5*a**2 + 8/5*a.
-4*a*(a - 2)/5
Let c(y) be the second derivative of 7*y**6/30 + 4*y**5/5 - 2*y**4 - 32*y**3/3 - 8*y**2 - 14*y. What is j in c(j) = 0?
-2, -2/7, 2
Let b(k) be the second derivative of 0 + 0*k**3 - k + 0*k**2 - 1/100*k**5 + 1/60*k**4. Factor b(l).
-l**2*(l - 1)/5
Factor -6 + 3 - 3*s**2 + 6.
-3*(s - 1)*(s + 1)
Let g = 12 + -12. Suppose -3*s**2 + g - 1 - 2 - 6*s + 0 = 0. Calculate s.
-1
Let w(l) = 9*l**3 - 33*l**2 + 24*l - 5. Let k(z) = -8*z**3 + 32*z**2 - 24*z + 4. Let v(r) = -5*k(r) - 4*w(r). Factor v(o).
4*o*(o - 6)*(o - 1)
Let g(r) = 3*r**2 - 6*r + 1. Let n be g(4). Let k = n - 23. Factor -2/9*c**k - 4/9 + 2/3*c.
-2*(c - 2)*(c - 1)/9
Let s(m) = m**3 + m**2 + m. Let k(c) = -c**4 + c**3 - 10*c**2 - 8*c + 8. Let b(x) = -5*k(x) - 20*s(x). Find g such that b(g) = 0.
-1, 2
Suppose 13*q - 2*q**2 + 6*q**2 - 19*q + 2*q**3 = 0. What is q?
-3, 0, 1
Let i(f) = -24*f**3 + 10*f**2. Suppose 7 - 1 = 2*q. Let y(o) = 4*o**2 - 5*o**3 - o**2 - o**2. Let j(m) = q*i(m) - 14*y(m). Factor j(t).
-2*t**2*(t - 1)
Let -18/5*j**2 + 12/5*j + 0 = 0. What is j?
0, 2/3
Suppose -290 = 3*d - 299. Factor -2/7*u**d + 2/7*u + 2/7*u**4 - 2/7*u**2 + 0.
2*u*(u - 1)**2*(u + 1)/7
Let c(i) = -3*i**2 + 3*i - 4. Let k(o) = -4*o**2 + 4*o - 4. Let j(m) = 6*c(m) - 5*k(m). Factor j(f).
2*(f - 2)*(f + 1)
Let j(c) be the third derivative of c**6/540 - c**4/108 - 3*c**2. Factor j(