1, 0
Let w(r) be the first derivative of 3/2*r**2 - 7/16*r**4 - 3/4*r**3 + r - 7. Determine k so that w(k) = 0.
-2, -2/7, 1
Let z(o) = 5*o**3 + o**2 - 6*o + 1. Let d(b) = -b**2 + b - 1. Let x(a) = -d(a) - z(a). Factor x(p).
-5*p*(p - 1)*(p + 1)
Let i be (1 - 0) + 2/(-6). Suppose 3*y = -y - 20, 4*y = 2*p - 24. Solve -q**p + q**4 - i*q + 2/3*q**3 + 0 = 0 for q.
-1, -2/3, 0, 1
Let j(g) be the first derivative of 2*g**3/21 + 3*g**2/7 + 4*g/7 - 4. Factor j(a).
2*(a + 1)*(a + 2)/7
Let n = 4 - 2. Let q = 9 - 6. Factor -2*d + q*d**n + 0*d - 2*d**2 + 1.
(d - 1)**2
Let b(s) be the second derivative of 1/9*s**3 + 0 + 0*s**4 + 0*s**2 - 1/180*s**6 - 1/40*s**5 + 8*s. Solve b(z) = 0.
-2, 0, 1
Solve 0*j - 1/3*j**3 + 0 + 0*j**2 - 4/3*j**4 = 0 for j.
-1/4, 0
Suppose 0 = 4*q - 12, 7*y - 3*y + 43 = 5*q. Let u(z) = z + 9. Let l be u(y). Factor -1/3*b**l - b - 2/3.
-(b + 1)*(b + 2)/3
Let u(c) = 2*c**3 + 10*c**2 + 10*c + 10. Let w be u(-4). Factor 6/7 - 8/7*g + 2/7*g**w.
2*(g - 3)*(g - 1)/7
Let v be ((-98)/4)/((-1)/2). Let r be 13/14 - 21/v. Suppose 0 - 1/4*w**4 + 1/4*w**2 + 1/2*w - r*w**3 = 0. Calculate w.
-2, -1, 0, 1
Let t be (-6 - (-133)/21)*9. Factor -3/7*k**4 + 9/7*k**2 + 0*k**t + 0 - 6/7*k.
-3*k*(k - 1)**2*(k + 2)/7
Let f(p) = -p**2 - 3*p + 57. Let i be f(-9). Factor -i*u - 9/2 - 1/2*u**2.
-(u + 3)**2/2
Let b(d) be the third derivative of d**6/120 + d**5/60 - d**4/12 - 5*d**2. Factor b(w).
w*(w - 1)*(w + 2)
Let r = -4 + -5. Let k be (-39)/r - 2/6. Determine w so that 0 + 1/4*w**3 + 0*w + 1/4*w**5 + 0*w**2 + 1/2*w**k = 0.
-1, 0
Factor -3/2*f**4 - 3*f**3 + 9/2*f**2 - 6 + 6*f.
-3*(f - 1)**2*(f + 2)**2/2
Let w(d) be the first derivative of d**6/12 - 3*d**5/10 + d**4/8 + d**3/2 - d**2/2 - 49. Factor w(s).
s*(s - 2)*(s - 1)**2*(s + 1)/2
Determine g, given that 6*g**3 + 4*g**4 + 2*g + 15*g**2 - 10*g + 2*g**3 - 3*g**4 - 16 = 0.
-4, -1, 1
Let b(s) = -8*s**3 + 2*s**2 - 10*s + 4. Let x(w) = 24*w**3 - 5*w + 35*w - 7*w**2 - 12 - w**3. Let p(d) = -17*b(d) - 6*x(d). Factor p(t).
-2*(t - 2)*(t - 1)**2
Factor 4*t**3 - 2*t**3 + 0*t**2 - t**2 + 3*t**2 - 2 - 2*t.
2*(t - 1)*(t + 1)**2
Let p(h) be the second derivative of -h**8/1680 + h**7/420 - h**6/360 + h**3/2 - h. Let z(c) be the second derivative of p(c). Factor z(j).
-j**2*(j - 1)**2
Factor -3*k**3 - 2*k**5 - 2*k**5 + k**5 + 6*k**3.
-3*k**3*(k - 1)*(k + 1)
Let i(s) = -s**4 + 9*s**3 - 41*s**2 - 40*s + 29. Let d(n) = -2*n**3 + 8*n**2 + 8*n - 6. Let o(w) = 22*d(w) + 4*i(w). Find x such that o(x) = 0.
-2, 1
Let a(i) = i**3 - 3*i**2 - 2*i - 4. Let b be a(4). Factor 5*w - w**b - 5*w - 1 + w**2 + w**2.
-(w - 1)**2*(w + 1)**2
What is z in 0*z + 1/5*z**5 - 3/5*z**4 - 1/5*z**3 + 7/5*z**2 - 4/5 = 0?
-1, 1, 2
Let s(r) be the first derivative of -4 + 2/7*r + 5/7*r**2 + 8/21*r**3. Let s(d) = 0. Calculate d.
-1, -1/4
Determine k so that k + 0 + 1/3*k**3 - 4/3*k**2 = 0.
0, 1, 3
Let w(r) be the third derivative of -r**5/40 + r**4/4 - 3*r**2. Suppose w(x) = 0. What is x?
0, 4
Let n(p) be the first derivative of -4*p**2 - p - 1. Let k be n(-2). Let -k*i**3 + 6*i**2 - 4*i**2 - 8*i**2 + 21*i**4 = 0. Calculate i.
-2/7, 0, 1
Suppose 4/3*n + 4/3*n**4 + 4*n**3 + 4*n**2 + 0 = 0. Calculate n.
-1, 0
Suppose 0 - 8/5*h**2 + 8/5*h**4 - 4/5*h**5 + 4/5*h + 0*h**3 = 0. Calculate h.
-1, 0, 1
Factor 0*d + 1/4*d**4 + 0 + 3/4*d**3 + 1/2*d**2.
d**2*(d + 1)*(d + 2)/4
Suppose 3*r + 8 = 7*r. Let j(g) be the first derivative of -19/8*g**4 - r - 6*g**2 - 2*g + 7/12*g**6 - 41/6*g**3 + 9/10*g**5. Factor j(d).
(d - 2)*(d + 1)**3*(7*d + 2)/2
Let n(t) be the second derivative of t**4/12 + t**3 + 5*t**2/2 - 7*t. Factor n(p).
(p + 1)*(p + 5)
Suppose -5 = 4*r - 3*r, 0 = -3*j - 2*r - 10. Let t = j + 1/3. Let 0*n + 0 - t*n**4 + 0*n**3 + 1/3*n**2 = 0. What is n?
-1, 0, 1
Let t(i) be the third derivative of 2*i**2 + 0 + 0*i + 1/60*i**5 - 1/4*i**4 + 3/2*i**3. Factor t(s).
(s - 3)**2
Let q(s) be the third derivative of 0*s + 6*s**2 + 8/7*s**3 + 0 + 1/7*s**4 + 1/140*s**5. Factor q(i).
3*(i + 4)**2/7
Let s(q) = -14*q**3 - 16*q**2. Let j(x) = -9*x**3 - 11*x**2. Let o(t) = 8*j(t) - 5*s(t). Factor o(b).
-2*b**2*(b + 4)
Let f(y) be the third derivative of y**8/12 + 4*y**7/105 - 7*y**6/30 - 2*y**5/15 - y**2. Find r such that f(r) = 0.
-1, -2/7, 0, 1
Let j(z) = -6*z**2 - 7*z + 4. Suppose -a + 5*a + 5*o = -40, 4*o = 0. Let h(v) = 3*v**2 + 3*v - 2. Let q(n) = a*h(n) - 4*j(n). Factor q(u).
-2*(u + 1)*(3*u - 2)
Find u, given that -5/2*u**4 - 25/2*u**5 - 8*u + 1/2*u**2 + 41/2*u**3 + 2 = 0.
-1, 2/5, 1
Let t(r) be the second derivative of -1/10*r**5 + 0 + 1/3*r**3 - 1/6*r**4 + 1/15*r**6 + 4*r + 0*r**2. Factor t(u).
2*u*(u - 1)**2*(u + 1)
Let k(t) be the first derivative of 3*t**5/10 - 3*t**4/2 + 5*t**3/2 - 3*t**2/2 + 6. Factor k(x).
3*x*(x - 2)*(x - 1)**2/2
Let f be 4/34 + 1200/204. Suppose -3 = f*n - 27. Factor -2/7*x**3 + 2/7*x**n + 0*x**2 + 0*x + 0.
2*x**3*(x - 1)/7
Let m(x) = x**4 - x**3 + x**2 + 4*x - 4. Let l(w) be the third derivative of -w**6/120 - w**5/60 - w**3/6 + 3*w**2. Let s(i) = 10*l(i) - 2*m(i). Factor s(b).
-2*(b + 1)**4
Let c(i) = i**3 - 9*i**2 + 5. Let q be c(9). Factor -7*g**3 + q*g**3 + 4*g - 2*g.
-2*g*(g - 1)*(g + 1)
Suppose 16*z = 2*z + 12*z. Let 1/4*w**2 + z + 1/4*w**5 + 0*w - 1/4*w**4 - 1/4*w**3 = 0. What is w?
-1, 0, 1
Find t, given that 40 - 15*t**2 + 5*t**4 + 0*t**4 - 1130*t + 20*t**3 + 1080*t = 0.
-4, -2, 1
Suppose 2/17*i**5 - 2/17*i**4 + 2/17*i**2 + 4/17*i - 6/17*i**3 + 0 = 0. Calculate i.
-1, 0, 1, 2
Let o be (-8)/(-20)*(-1)/(-24). Let n(r) be the third derivative of 3*r**2 + 2/15*r**3 - 1/150*r**5 - o*r**4 + 0 + 0*r. Factor n(a).
-2*(a - 1)*(a + 2)/5
Factor -6/7*w**4 - 3/7*w**3 + 0*w + 0 + 0*w**2 - 3/7*w**5.
-3*w**3*(w + 1)**2/7
Let x(z) = -z**4 + z**3 + z**2 + z - 1. Let m(c) = -16*c**4 + 16*c**3 + 26*c**2 + 6*c - 30. Let u(q) = -2*m(q) + 28*x(q). What is j in u(j) = 0?
-2, -1, 2
Let q(b) be the second derivative of -b**6/15 - 3*b**5/10 + b**4/2 + 7*b**3/3 - 6*b**2 + 18*b. Factor q(g).
-2*(g - 1)**2*(g + 2)*(g + 3)
Let f = -16 - -49/3. Let g(o) be the second derivative of -1/6*o**4 + 0 + f*o**3 + 2*o - 1/10*o**5 + o**2. Factor g(n).
-2*(n - 1)*(n + 1)**2
Determine v, given that -v**3 + v**5 - 4*v**5 - 2*v**3 - 6*v**4 = 0.
-1, 0
Let t(d) be the first derivative of -d**6 - 16*d**5/5 - 7*d**4/2 - 4*d**3/3 - 14. Factor t(p).
-2*p**2*(p + 1)**2*(3*p + 2)
Factor -13 - 4 + 1 - z**2 + 8*z.
-(z - 4)**2
Suppose -2*l = l. Let q(z) = -z**2 - z + 2. Let y be q(l). Factor t + 1 + 1/4*t**4 - 3/4*t**y - 1/2*t**3.
(t - 2)**2*(t + 1)**2/4
Let g(f) be the third derivative of -f**6/720 + f**5/360 + 5*f**4/144 + f**3/12 - 4*f**2. Suppose g(b) = 0. What is b?
-1, 3
Let k(a) be the third derivative of a**6/240 - a**5/30 + 5*a**4/48 - a**3/6 - 26*a**2. Let k(y) = 0. Calculate y.
1, 2
Suppose k = -3*y - y + 4, -3*y = 3*k + 6. Suppose y*f - 6 = -2. Suppose -4/5*q + 2/5*q**f + 2/5 = 0. What is q?
1
Let p(z) = 3*z**4 + 105*z**3 + 261*z**2 + 255*z + 105. Let i(h) = -h**4 - 26*h**3 - 65*h**2 - 64*h - 26. Let o(g) = 9*i(g) + 2*p(g). Factor o(k).
-3*(k + 1)**2*(k + 2)*(k + 4)
Find s such that 3*s**4 - 12*s**2 - 50 + 8*s**3 + s**4 + 50 = 0.
-3, 0, 1
Let a(r) = -4*r**5 - 2*r**4 + 3*r**2 - 3. Let n be -1*-1*(1 - -1). Let j(p) = -5 + 1 - p**5 + p**n + 3 - p**4. Let s(v) = a(v) - 3*j(v). Factor s(h).
-h**4*(h - 1)
Determine z so that 0*z + 4*z**3 - 64/5*z**4 + 36/5*z**5 + 0 + 8/5*z**2 = 0.
-2/9, 0, 1
Determine z so that -2*z**3 + 3*z - 1 + z**4 + 2 + z**5 + 0 - 2*z - 2*z**2 = 0.
-1, 1
Let o(a) be the second derivative of -7*a**7/30 - 21*a**6/25 - 11*a**5/100 + 59*a**4/30 + 2*a**3 + 4*a**2/5 + 20*a. Determine f, given that o(f) = 0.
-2, -1, -2/7, 1
Let r(n) be the third derivative of n**5/30 + 2*n**4/3 + 16*n**3/3 - 19*n**2. Factor r(x).
2*(x + 4)**2
Suppose 6*y - 5*y = 0. Suppose 0 = -o - y + 2. Factor 2/3*p**3 + 10/3*p + 8/3*p**o + 4/3.
2*(p + 1)**2*(p + 2)/3
Let a(m) = -m. Let v be a(-2). Let y be (-8)/(-6) - 4/(-6). Factor -r - 2*r + r + y*r**v.
2*r*(r - 1)
Let r(b) be the first derivative of -3 - 1/8*b**4 - 1/12*b**6 + 1/4*b**5 + 1/2*b**2 - 1/3*b**3 - 1/4*b. Let r(a) = 0. Calculate a.
-1, 1/2, 1
Let o(b) be the second derivative of 4*b**7/147 + b**6/35 + b**5/140 + 6*b. Factor o(w).
w**3*(2*w + 1)*(4*w + 1)/7
Let t(n) = n + 2. Let b be t(-8). Let g(y) = -y**2 - 6*y + 7. Let a be g(b). Factor