3, 1
Suppose -2*u - 2 = -6. Suppose 30 = 5*w - 5*a, -2*w - 2 - 2 = u*a. Find v, given that 18/5*v**w + 2/5 - 12/5*v = 0.
1/3
Factor -75*f**3 + 25*f**3 - 20*f**4 - 2*f**5 - f + f.
-2*f**3*(f + 5)**2
Let t(p) = -81*p**3 - 48*p**2 + 96*p. Let l = -8 + 11. Let k(s) = 0*s + 6*s - l*s**2 + 0*s**2 - 5*s**3. Let w(m) = -33*k(m) + 2*t(m). Factor w(u).
3*u*(u - 1)*(u + 2)
Let g(c) be the second derivative of -1/4*c**4 + 3/2*c**3 + 0 + 3*c - c**2 - 1/5*c**5. Factor g(k).
-(k - 1)*(k + 2)*(4*k - 1)
Let w be 1/(-4) - 33/6. Let z = 6 + w. Factor 0*f + 0 + z*f**2.
f**2/4
Let a(m) be the third derivative of m**8/2184 - 4*m**7/1365 + m**6/156 - m**5/195 - 48*m**2. Factor a(z).
2*z**2*(z - 2)*(z - 1)**2/13
Let i(o) = 4*o**5 + 8*o**4 + 6*o**3 + 4*o**2 + 2. Let t(w) = -13*w**5 - 25*w**4 - 18*w**3 - 13*w**2 - 7. Let b(s) = -7*i(s) - 2*t(s). Factor b(v).
-2*v**2*(v + 1)**3
Factor 4*g**3 - 3*g**2 - 8*g - 2*g**2 + 6*g**2 + 3*g**2.
4*g*(g - 1)*(g + 2)
Suppose -72*z + 39/2*z**2 - 3/2*z**3 + 54 = 0. Calculate z.
1, 6
Let a = -242 + 971/4. Find g such that -1/4*g**4 - 1/2*g**2 + 0*g + a*g**3 + 0 = 0.
0, 1, 2
Let s(q) = q**4 + q**2 - 1. Let h(x) = 4*x**4 + 5*x**3 + 12*x**2 + 7*x - 1. Let d(a) = 2*h(a) - 6*s(a). Suppose d(g) = 0. Calculate g.
-2, -1
Let d be 40/15 - 2/3. Let m(z) = -z**3 + 4*z**2 - 3*z + 1. Let s be m(d). Let 0 + 2/3*o**4 + 2/3*o**s - 2/3*o - 2/3*o**2 = 0. What is o?
-1, 0, 1
What is b in 0*b - 2/3*b**2 + 2/3 = 0?
-1, 1
Let h(n) be the second derivative of -n**7/147 + 2*n**6/105 + 3*n**5/70 - 2*n**4/21 - 4*n**3/21 - 35*n. Find c such that h(c) = 0.
-1, 0, 2
Factor -64*b**3 + 5 + 9*b + 89*b**3 + 5 - 34*b - 10*b**2.
5*(b - 1)*(b + 1)*(5*b - 2)
Let g(l) be the first derivative of l**4/5 - 8*l**3/15 - 6*l**2/5 - 17. Factor g(f).
4*f*(f - 3)*(f + 1)/5
Let w be 4/14*(-182)/(-39). Let g = w - 5/6. Factor 0*i + 0 - i**4 - g*i**3 + 0*i**2 - 1/2*i**5.
-i**3*(i + 1)**2/2
Let b be ((-21)/(-6) + -1)*1/5. Factor -g**2 - b*g - 1/2*g**3 + 0.
-g*(g + 1)**2/2
Let s be 2/(-11) - 32/(-55). Factor 2/5*t**3 - s*t - 2/5*t**4 + 0 + 2/5*t**2.
-2*t*(t - 1)**2*(t + 1)/5
Determine n so that 5*n**3 + 5/3*n**5 + 20/3*n**4 - 20/3*n + 0 - 20/3*n**2 = 0.
-2, -1, 0, 1
Let b(r) be the third derivative of r**5/120 + r**4/48 - r**3/6 + r**2. Factor b(g).
(g - 1)*(g + 2)/2
Factor 0*g - 1/2*g**3 + 0 - 1/2*g**4 + 1/2*g**5 + 1/2*g**2.
g**2*(g - 1)**2*(g + 1)/2
Let p(n) be the first derivative of -n**9/6048 - n**8/1680 + n**6/360 + n**5/240 - 2*n**3/3 + 4. Let l(w) be the third derivative of p(w). Factor l(d).
-d*(d - 1)*(d + 1)**3/2
Suppose 3*d = -3*l + 18, 4*l = 8*l - 20. Let a be (-2)/12*(-1 - d). Determine o, given that 1/3*o**3 + o - a - o**2 = 0.
1
Let k(b) be the third derivative of -b**7/840 + b**6/120 - b**5/40 - b**4/6 + 2*b**2. Let p(y) be the second derivative of k(y). Suppose p(u) = 0. Calculate u.
1
Let v(b) be the first derivative of -4*b**3 + 1/2*b**4 - 16*b - 3 + 12*b**2. Factor v(t).
2*(t - 2)**3
Let h(c) = c**2 + 2*c - 5. Let n be h(-4). Determine u, given that -u - 2/3 + 1/3*u**2 + 1/3*u**4 + u**n = 0.
-2, -1, 1
Suppose 2*k + h - 5 = 0, 0*h + 4*h = 3*k + 20. Let g(v) be the first derivative of -4*v + v**3 + 1/4*v**4 + 4 + k*v**2. Suppose g(u) = 0. What is u?
-2, 1
Let n = 39 + -37. Factor 2/3*s**n + 4/3 + 2*s.
2*(s + 1)*(s + 2)/3
Let n(g) be the first derivative of 5*g**4/12 - 5*g**3/9 - 5*g**2/6 + 5*g/3 - 2. Find m, given that n(m) = 0.
-1, 1
Let t = -554/5 - -111. Let v(z) be the first derivative of -3/5*z**2 + 3/5*z + 3 + t*z**3. Find q, given that v(q) = 0.
1
Let c(m) be the third derivative of m**5/12 + 5*m**4/12 - 6*m**2. Factor c(k).
5*k*(k + 2)
Let -3*w**4 + w**4 + 2*w**2 + 3*w**4 - 3*w**2 = 0. What is w?
-1, 0, 1
Let k(h) = h. Let u(g) = -3*g**2 - 26*g - 18. Let x(i) = 5*k(i) + u(i). Factor x(y).
-3*(y + 1)*(y + 6)
Let k(q) = -q**3 - 16*q**2 + q + 18. Let h be k(-16). Let p(u) = u + 7. Let v be p(-5). Factor 2*m**2 - 4 - 2*m**2 - 6*m - h*m**v.
-2*(m + 1)*(m + 2)
Let y(n) be the second derivative of n**4/6 + 4*n**3/3 + 3*n**2 - 32*n. Solve y(x) = 0 for x.
-3, -1
What is t in 0*t - 1/5*t**2 + 0 - 3/5*t**3 - 1/5*t**5 - 3/5*t**4 = 0?
-1, 0
Let m(l) be the third derivative of 4*l**2 - 1/840*l**8 + 0*l**5 + 0 + 1/150*l**6 - 1/60*l**4 + 0*l + 0*l**7 + 0*l**3. Factor m(t).
-2*t*(t - 1)**2*(t + 1)**2/5
Find a, given that 1 - 3/2*a + 1/2*a**2 = 0.
1, 2
Let i(t) be the third derivative of t**8/56 - t**7/70 - 3*t**6/20 + 7*t**5/20 - t**4/4 - 6*t**2. Determine c, given that i(c) = 0.
-2, 0, 1/2, 1
Let t = -1140 - -3484/3. Factor -154/3*o**3 - 98/3*o**4 - 8/3*o + 0 - t*o**2.
-2*o*(o + 1)*(7*o + 2)**2/3
Suppose 18*b - 23*b = -25. Let x(r) be the third derivative of 2*r**2 + 1/48*r**4 + 0*r + 0 - 1/120*r**b + 0*r**3. Solve x(q) = 0 for q.
0, 1
Suppose 7*k - 3*k - 16 = 0. Suppose 20 = 5*q, -4*l - 3*q + 18 = -2*l. Factor -l*f**2 - f**3 - f**k + 3*f**2.
-f**3*(f + 1)
Find d such that -11*d**4 + 45*d**3 + 19*d**4 - 49*d**3 = 0.
0, 1/2
Solve 21*r**2 - 15*r**5 - 12*r**4 + 24*r**3 + 33*r - 3 + 9 + 6*r**5 + 33*r**2 = 0.
-1, -1/3, 2
Let m = -572/105 + 40/7. Determine i so that -m - 2/5*i + 0*i**2 + 2/15*i**3 = 0.
-1, 2
Let s(p) be the first derivative of 12*p**2 + 1/8*p**4 + 7 + 32*p + 2*p**3. Let s(w) = 0. Calculate w.
-4
What is d in 57/7*d**2 - 12/7*d**4 + 18/7 - 24/7*d**3 + 69/7*d = 0?
-3, -1/2, 2
Let t(d) be the second derivative of -d**6/45 - d**5/30 + d**4/18 + d**3/9 + 3*d. Factor t(m).
-2*m*(m - 1)*(m + 1)**2/3
Let o be (-4)/(-14) - (2 + 368/(-84)). Factor 6*f + 4/3 + o*f**2.
2*(f + 2)*(4*f + 1)/3
Let q(p) be the second derivative of 2*p**5/15 - p**4/2 + 2*p**3/3 + 4*p**2 - p. Let b(l) be the first derivative of q(l). Factor b(w).
4*(w - 1)*(2*w - 1)
Let u(o) be the first derivative of -o**3/12 + 5*o**2/8 - 3*o/2 - 1. Let u(l) = 0. Calculate l.
2, 3
Let i(p) be the second derivative of 4*p**7/35 - 4*p**6/15 + 7*p**5/30 - p**4/12 - 3*p**2/2 - 3*p. Let x(h) be the first derivative of i(h). Factor x(y).
2*y*(2*y - 1)**2*(3*y - 1)
Let h = -58/13 + 200/39. Factor -h*l**2 - 1/3*l + 2/3 + 1/3*l**3.
(l - 2)*(l - 1)*(l + 1)/3
Suppose -3*r + 2*m + 10 = 0, -3*m - 18 + 1 = -5*r. Determine t so that 0 + 16*t**3 - r*t**2 + 1/4*t = 0.
0, 1/8
Let r(d) be the third derivative of d**7/1785 - d**6/340 + d**5/170 - d**4/204 + 21*d**2. Suppose r(u) = 0. Calculate u.
0, 1
Let l(q) = 7*q**5 - 16*q**4 + 8*q**3 + 4*q**2 + 4*q. Let h(n) = 6*n**5 - 15*n**4 + 9*n**3 + 3*n**2 + 3*n. Let g(j) = 4*h(j) - 3*l(j). Factor g(w).
3*w**3*(w - 2)**2
Let d(s) = s**5 - s**3 + s**2 + s - 1. Let t(q) = 9*q**5 + 24*q**4 + 51*q**3 + 69*q**2 + 41*q + 3. Let c(w) = -5*d(w) + t(w). Factor c(h).
4*(h + 1)**4*(h + 2)
Let c(k) = -14*k**5 + 8*k**4 + 10*k**3 - 18*k**2 + 4*k - 10. Let v(d) = -d**5 + d**3 - d**2 - 1. Let w(u) = -c(u) + 10*v(u). What is z in w(z) = 0?
-1, 0, 1
Let z be (-3 - -3)/(-1 - 1). Find b, given that z*b + 0 + 2/7*b**2 = 0.
0
Let q(m) be the first derivative of -m**4/12 - 2*m**3/9 + 2*m**2/3 + 8*m/3 + 7. Factor q(w).
-(w - 2)*(w + 2)**2/3
Factor 4*a**2 + 4*a**3 - 5*a**3 - 7*a**2.
-a**2*(a + 3)
Let q(j) be the second derivative of j**6/60 + j**5/10 + 5*j**4/24 + j**3/6 - 10*j + 3. Determine k, given that q(k) = 0.
-2, -1, 0
Solve 8/17*j - 2/17*j**2 + 0 = 0.
0, 4
Let g(v) be the first derivative of -2*v**3/3 - v**2/2 + 17. Factor g(c).
-c*(2*c + 1)
Let w(f) be the first derivative of 2*f**5/5 - f**4/2 - 2*f**3/3 + f**2 - 10. Factor w(t).
2*t*(t - 1)**2*(t + 1)
Let v be ((-15)/20)/(45/(-24)). Let a(j) be the first derivative of 2*j**4 - 2*j - v*j**5 - 4*j**3 + 4*j**2 - 4. Factor a(l).
-2*(l - 1)**4
Suppose 2*y + 10 = 7*y. Factor 1/3*q**y - q + 2/3.
(q - 2)*(q - 1)/3
Factor 0 + 9/8*a**4 + 0*a**2 + 3/4*a**3 + 0*a + 3/8*a**5.
3*a**3*(a + 1)*(a + 2)/8
Let b = 461 - 456. Let -1/3*u**4 - 1/6*u**b + 2/3*u**2 - 1/3 - 1/6*u + 1/3*u**3 = 0. What is u?
-2, -1, 1
Let a(j) be the first derivative of -6/5*j**5 + 2*j - 1/3*j**6 + 4/3*j**3 + 3*j**2 - j**4 - 5. Factor a(q).
-2*(q - 1)*(q + 1)**4
Let f(p) be the first derivative of 3*p**5/5 - 3*p**4/4 - 5*p**3 - 9*p**2/2 - 1. Determine c so that f(c) = 0.
-1, 0, 3
Suppose 2*i - 4 = 2. Solve -d**i + d**2 + 1/2 - 1/2*d**5 + 3/2*d - 3/2*d**4 = 0.
-1, 1
Factor 0*g + 2/13*g**2 + 0.
2*g**2/13
Let v(z) = -z**4 - z**3 - 4*z**2 - 4*z + 4. Let l(g) = 2*g**4 + 3*g**3 + 9*g**2 + 8*g - 7. Let 