1
Let d(m) = m**2 + 18*m + 58. Let f be d(-14). Factor 0 + 3/2*c - 1/2*c**f.
-c*(c - 3)/2
Factor s - 2*s - 2*s**2 - 2 - 5*s + 2*s.
-2*(s + 1)**2
Suppose 5 = 4*d + 1. Let o be -3 - (-2 + -24 - d). Factor 4*r**4 + 4*r**2 + 0*r + 23*r**5 + 3*r - o*r**5 - 6*r**3 - 4*r.
-r*(r - 1)**4
Let t(k) = -17*k**4 - 3*k**3 + 7*k + 7. Let c(j) = 8*j**4 + 2*j**3 - 3*j - 3. Let z(q) = -7*c(q) - 3*t(q). Factor z(v).
-5*v**3*(v + 1)
Let c(h) be the third derivative of h**8/112 + 3*h**7/70 + h**6/20 - h**5/10 - 3*h**4/8 - h**3/2 - h**2 + 17. Determine f, given that c(f) = 0.
-1, 1
Let j = 4 + 1. Factor -2*i**3 - 1 + 2*i**2 - 6*i**5 + 0*i**3 + 7*i**j - i**4 + i.
(i - 1)**3*(i + 1)**2
Let q be ((-3)/(-21)*-4)/((-150)/35). Factor 2/15*n**2 - q*n - 2/15 + 2/15*n**3.
2*(n - 1)*(n + 1)**2/15
Let k(p) = -p**3 - p**2 - 6*p - 2. Let m(s) = -3*s**3 - 3*s**2 - 12*s - 5. Let g(a) = -10*k(a) + 4*m(a). Factor g(y).
-2*y*(y - 2)*(y + 3)
Let a(u) be the second derivative of -u**7/21 - 4*u**6/15 - 3*u**5/5 - 2*u**4/3 - u**3/3 + 13*u. Let a(b) = 0. Calculate b.
-1, 0
Suppose -2*i + i = -0*i. Factor 0*t**4 + 0*t**2 + 0*t + 0*t**3 + 1/4*t**5 + i.
t**5/4
Let p(x) be the second derivative of -x**8/4200 - x**7/1575 - x**6/1800 - x**4/2 - x. Let s(g) be the third derivative of p(g). Let s(i) = 0. What is i?
-1/2, 0
Determine g, given that 16/3 - 238/3*g**3 - 1960/9*g**4 + 686/9*g**5 - 472/9*g + 1412/9*g**2 = 0.
-1, 2/7, 3
Suppose -17*n**3 - 2*n**4 - 64*n - 9*n**2 + n**3 - 32 - 32*n**2 - 7*n**2 = 0. What is n?
-2
Let h(n) be the first derivative of n**4 - 2*n**3 - 15*n**2/8 - n/2 + 3. Factor h(g).
(g - 2)*(4*g + 1)**2/4
Let w = 8 + -6. Suppose g**3 - w*g**3 - 2*g**2 - 19 + 19 - g = 0. Calculate g.
-1, 0
Factor -2*k**2 + 3*k + k**2 - 6*k + 0*k**2.
-k*(k + 3)
Suppose -3*m - 4*q + 10 = -2*q, 2*q + 6 = 5*m. Suppose -6*i = -4*i - 10. Let -2/3*f + 0 - 4/3*f**i - 2/3*f**m + 2/3*f**4 + 2*f**3 = 0. Calculate f.
-1, -1/2, 0, 1
Suppose 4*p + 1 - 9 = 0. Solve 17/4*r**4 + r**5 + 7*r**3 + 11/2*r**p + 1/4 + 2*r = 0 for r.
-1, -1/4
Factor -2*b**2 + 2/3*b**4 + 2/3*b**3 - 10/3*b - 4/3.
2*(b - 2)*(b + 1)**3/3
Factor 8*g - 10*g - 3*g**2 + 4*g**2.
g*(g - 2)
Let q = 13 - 9. Determine s, given that s + 6*s**3 - 4*s**q - 4*s + 2*s**4 - 5*s = 0.
-1, 0, 2
Solve 1 + 1 + 31*o**2 - 4 + 15*o + 4 + 12*o**3 = 0 for o.
-2, -1/3, -1/4
Let a = -7 + 35. Determine q so that -a*q + 4 + 39*q**2 + 2*q + 0 - 17*q**2 = 0.
2/11, 1
Let v(i) = -2*i + i + i**2 + 4*i**5 - 5*i**5 - i**4 + 1. Let c(d) = -14*d**5 + 16*d**4 - 27*d**3 + 20*d**2 - 9*d + 7. Let a(n) = -4*c(n) + 28*v(n). Factor a(r).
4*r*(r - 1)**3*(7*r - 2)
Suppose 4 = 3*z - 2. Let l = 6 - z. Factor 0*x + 0*x**2 + 2/5*x**l + 0 - 2/5*x**3.
2*x**3*(x - 1)/5
Let h(q) be the third derivative of q**7/2520 - q**5/120 - q**4/12 - 5*q**2. Let g(v) be the second derivative of h(v). Factor g(f).
(f - 1)*(f + 1)
Suppose -3*i - 3*z = -69, 0 = 5*i + 5*z - z - 113. Solve i*h**4 - 27*h**2 - 20*h**3 + 10*h**2 + 2 + 20*h - 6 = 0.
-1, 2/7, 2/3, 1
Solve 0 - p**2 + 5/2*p**3 + 0*p - p**4 = 0 for p.
0, 1/2, 2
Let n(o) be the third derivative of 0*o**4 + 1/525*o**7 + 0*o**3 + 2*o**2 - 1/300*o**6 + 0 - 1/150*o**5 + 1/840*o**8 + 0*o. Factor n(b).
2*b**2*(b - 1)*(b + 1)**2/5
Find r such that 3*r**2 + 87*r + 62*r - 30 - 122*r = 0.
-10, 1
Suppose 0 = 7*r + 7 - 28. Let a(p) be the first derivative of -1/5*p**5 + 0*p - 1 - 1/3*p**r + 0*p**2 - 1/2*p**4. Let a(s) = 0. Calculate s.
-1, 0
Factor -4/7*d**2 + 0 + 16/7*d.
-4*d*(d - 4)/7
Suppose -147/2*k - 343/2 - 21/2*k**2 - 1/2*k**3 = 0. What is k?
-7
Let u = 1 + -2. Let p be 4*(u/(-2) - 0). Suppose 2*q**4 + 4 - p*q**2 - 4 = 0. What is q?
-1, 0, 1
Let r(c) = c**2 - 5*c + 4. Let m be r(6). Let g = 13 - m. Find l, given that 3*l**2 + 3*l**3 + 4*l - l**2 - 5*l**g + 0*l**2 = 0.
-1, 0, 2
Solve 0 - 2/5*j**4 - 3/5*j**5 + 0*j - 2/5*j**2 + 7/5*j**3 = 0.
-2, 0, 1/3, 1
Let 2*f - 5*f - 3*f**2 + 9 + 5*f + 4*f = 0. Calculate f.
-1, 3
What is t in 36*t**4 - 4*t**2 + 44*t**3 - 35*t**3 + 21*t**5 - 2*t**2 = 0?
-1, 0, 2/7
Suppose 3/2*j + 1/2*j**2 + 0 = 0. Calculate j.
-3, 0
Suppose -9/7*p**4 + 3*p**3 + 0 - 15/7*p**5 - 6/7*p + 9/7*p**2 = 0. What is p?
-1, 0, 2/5, 1
Let y = 42 + -39. Let c(g) be the third derivative of -g**2 - 2/525*g**7 + 0*g**4 + 0*g**y + 0*g**5 + 1/840*g**8 + 0 + 0*g + 1/300*g**6. Factor c(f).
2*f**3*(f - 1)**2/5
Let y(r) = 5*r - 8*r**2 - 7*r + 7*r**2 + 6*r + 5. Let d(v) = -v - 1. Let a(h) = -28*d(h) - 4*y(h). Suppose a(c) = 0. What is c?
-2, -1
Let o(t) be the second derivative of -t**5/10 + t**4/2 - t**3 + t**2 - 6*t. Factor o(g).
-2*(g - 1)**3
Let t(i) be the third derivative of -i**7/420 + i**6/90 - i**5/60 - i**3/6 + 2*i**2. Let v(u) be the first derivative of t(u). Solve v(s) = 0 for s.
0, 1
Let m = 16 - -23. Let d be m + 6*(-1)/(-2). Suppose -5 - 4*z**3 - 16*z - 5 + d*z**2 - 10*z**4 - 4*z**4 + 2 = 0. What is z?
-2, -2/7, 1
Let p(x) be the third derivative of -x**6/180 + 4*x**5/45 - 13*x**4/36 + 2*x**3/3 + 9*x**2. Solve p(b) = 0.
1, 6
Let s(o) = -12*o**4 + 66*o**3 + 90*o**2 - 39*o - 51. Let x(z) = -z**4 + 5*z**3 + 7*z**2 - 3*z - 4. Let t(w) = 2*s(w) - 27*x(w). Solve t(l) = 0.
-1, 1, 2
Let c(l) be the third derivative of -l**7/2520 + l**5/120 + l**4/3 + 7*l**2. Let o(h) be the second derivative of c(h). Factor o(y).
-(y - 1)*(y + 1)
Suppose 4*d + 4*g + 4 = g, -4*d - g = -4. Factor -i**2 + 3*i**5 - 3*i**3 - 3*i**4 + 3*i**2 + 0*i**4 + i**d.
3*i**2*(i - 1)**2*(i + 1)
Let n(u) be the second derivative of -2/21*u**7 + 0 + 11/18*u**4 + 7*u - 13/45*u**6 - 1/10*u**5 + u**3 + 2/3*u**2. Solve n(o) = 0 for o.
-1, -2/3, -1/2, 1
Let i(q) = -4*q**4 - q**2 + 2*q**3 + 2*q**3 - 3*q**2. Suppose 3 = 2*h - 7. Let j(x) = 9*x**4 - 7*x**3 + 7*x**2 + x. Let s(d) = h*i(d) + 2*j(d). Factor s(r).
-2*r*(r - 1)**3
What is n in -1/5*n**3 + 1/5*n**5 + 0*n - 1/5*n**4 + 1/5*n**2 + 0 = 0?
-1, 0, 1
Let l = 6357/4 - 1589. Factor 1/8*u**3 - l*u**2 + 0 + 0*u.
u**2*(u - 2)/8
Let n(y) = -2*y - 2. Let l be n(-4). Let f be (4/(-3))/((-4)/l). Factor -2*v**3 + 2*v**2 + 5*v**2 + 3*v**2 - 6*v**4 + f*v - 4*v**2.
-2*v*(v - 1)*(v + 1)*(3*v + 1)
Let y(i) = 2*i**5 + 6*i**4 + 3*i**3 - 6*i**2 - 5*i + 5. Let r(b) = b**5 + 3*b**4 + 2*b**3 - 3*b**2 - 3*b + 3. Let m(d) = 10*r(d) - 6*y(d). Solve m(o) = 0.
-3, -1, 0, 1
Suppose -81 + 77 = -2*c. Let h(w) be the first derivative of 0*w**c + 7/15*w**3 - 4/5*w - 3/20*w**4 + 3. Determine k, given that h(k) = 0.
-2/3, 1, 2
Factor -2*s**4 + s**2 - 3*s**3 + 5*s**3 - s**4 + 0*s**3.
-s**2*(s - 1)*(3*s + 1)
Let r be (-3)/(-24)*-6*-4. Let t(q) be the second derivative of 0*q**2 - 2*q - 1/24*q**r + 0 + 1/48*q**4. Factor t(z).
z*(z - 1)/4
Find w such that 3/2*w**3 + 0 - 2*w + 2*w**2 = 0.
-2, 0, 2/3
Let l = 1 + 2. Let b(f) = -1 + l*f**2 - 5 + 2 + 0*f + 11*f. Let m(p) = -2*p**2 - 6*p + 2. Let x(w) = 3*b(w) + 5*m(w). Find o such that x(o) = 0.
1, 2
Let q(i) be the second derivative of -i**7/168 + i**6/30 - i**5/20 - i**4/24 + 5*i**3/24 - i**2/4 + 13*i. Find l, given that q(l) = 0.
-1, 1, 2
Let p(y) be the first derivative of -y**6/600 - y**5/100 - 10*y**3/3 + 4. Let i(n) be the third derivative of p(n). Factor i(w).
-3*w*(w + 2)/5
Suppose -i + 2*p + 10 = 0, -3*p - 25 = 5*i + 2*p. Solve 16/3*g**3 - 4/3*g**2 + i - 7*g**4 + 0*g + 3*g**5 = 0 for g.
0, 2/3, 1
Suppose -4/5*w**2 - 8/5 + 12/5*w = 0. Calculate w.
1, 2
Let h(z) be the first derivative of -z + 4*z**2 + 121/6*z**4 - 44/3*z**3 - 1. Let g(u) be the first derivative of h(u). Solve g(c) = 0.
2/11
Let l(y) be the third derivative of 1/60*y**5 + 0*y**4 + 0*y - y**2 + 0*y**3 + 0. Let l(j) = 0. What is j?
0
Let z(q) be the first derivative of q**5/25 - 3*q**4/10 + q**3/3 - 28. Solve z(i) = 0.
0, 1, 5
Let d be 6/(-16)*98/(-9) + -4. Let n(v) be the second derivative of 1/20*v**5 - d*v**4 - 2*v + 0 - 1/90*v**6 + 1/18*v**3 + 0*v**2. Solve n(s) = 0 for s.
0, 1
Let p(z) = z**2 + 9*z + 4. Let y(o) = -10*o - 5. Let c(u) = 5*p(u) + 4*y(u). Solve c(i) = 0 for i.
-1, 0
Let o(w) be the second derivative of w**4/12 - 12*w. Find i, given that o(i) = 0.
0
Let x(n) be the third derivative of -n**7/42 - 5*n**6/12 - 3*n**5 - 45*n**4/4 - 45*n**3/2 + 7*n**2. Factor x(v).
-5*(v + 1)*(v + 3)**3
Let z = -15 + 16. Let a be 3 - z/(-4)*0. Factor 1/5*n**2 + 1/5*n**a - 1/5*n - 1/5.
(n - 1)*(n + 1)**2/5
Let h(u) = -6*u**4 + 9*u**3 - 6*u**2 - 9*u + 6. Let d(j)