r**2/2 + 4*r - 2. Let s be l(-5). Solve -1/2*h**s + 0 - 1/2*h + 1/2*h**3 + 1/2*h**2 = 0 for h.
-1, 0, 1
Let n = 14 - 14. Let r be n*(-2)/2*1. Find j such that -4/3*j**2 + r - 2/3*j - 2/3*j**3 = 0.
-1, 0
Let a(p) be the second derivative of p**7/105 - p**6/25 + 3*p**5/50 - p**4/30 + 38*p. Factor a(k).
2*k**2*(k - 1)**3/5
Let v(u) be the first derivative of 7*u**3/6 + 19*u**2/4 - 3*u + 18. Factor v(y).
(y + 3)*(7*y - 2)/2
Let o(z) = -z**2 + 9*z + 7. Let a be o(7). Factor -a*s**4 + 6*s**3 + 0*s - 9*s**2 - 6*s + 23*s**3 + 7*s**3.
-3*s*(s - 1)**2*(7*s + 2)
Let m be 2 + -5 - 1 - -117. Let k = -449/4 + m. Factor 3/4*s + 0 - 3/2*s**2 + 3/2*s**4 - k*s**5 + 0*s**3.
-3*s*(s - 1)**3*(s + 1)/4
Let d(l) = 2*l + 57. Let p be d(-28). Factor 3/2*a**2 - p - 1/2*a.
(a - 1)*(3*a + 2)/2
Suppose 2*b = -3*o - o + 26, -o + 5 = 0. Let w(n) be the second derivative of 3/2*n**b + 3*n**2 + 0 + 4*n - 3/20*n**5 + 0*n**4. Suppose w(m) = 0. Calculate m.
-1, 2
Let s(d) = d**3 - 3*d**2 + 6*d - 2. Let w(y) = y**3 - y**2 + 2*y - 1. Let c(o) = -3*s(o) + 6*w(o). Factor c(h).
3*h*(h - 1)*(h + 2)
Let 0*d**4 + 2*d**2 - d**5 - 413*d + 414*d - 2*d**4 = 0. What is d?
-1, 0, 1
Suppose -7*c + 16 = -3*c. Factor c*f**2 - 4*f**2 - f - 2*f**2 + 3*f**3.
f*(f - 1)*(3*f + 1)
Let b(g) be the third derivative of -g**8/1176 - g**7/735 + g**6/420 + g**5/210 - 2*g**2 + 9. Find v such that b(v) = 0.
-1, 0, 1
Factor -1/4*y**5 - 3/4*y**3 - 1/4*y**2 + 0*y - 3/4*y**4 + 0.
-y**2*(y + 1)**3/4
Let v(j) be the second derivative of 1/2*j**3 - 1/2*j**4 + 0 + 0*j**2 + 3/20*j**5 + 6*j. Suppose v(y) = 0. What is y?
0, 1
Let x(c) be the first derivative of -6*c**5/5 + 4*c**4 - 4*c**3 + 2*c + 7. Factor x(h).
-2*(h - 1)**3*(3*h + 1)
Let f(o) = o**3 - 7*o**2 - 8*o + 11. Let v be f(8). Factor -21*g - v*g - 9*g**2 + 12 - 6*g**2 + 3*g**2.
-4*(g + 3)*(3*g - 1)
Let z(i) = -i + 6. Let k be z(6). Factor 0*r + r**3 - r + k*r**3 - r**2 + r**4.
r*(r - 1)*(r + 1)**2
Let t(m) = 6*m**5 + 6*m**4 - 6*m**2 - 3*m + 3. Let u(q) = 17*q**5 + 19*q**4 + q**3 - 19*q**2 - 10*q + 8. Let n(x) = 8*t(x) - 3*u(x). Find v such that n(v) = 0.
-2, -1, 0, 1
Let j(l) be the first derivative of l**3/7 + 6*l**2/7 + 9*l/7 - 18. Suppose j(h) = 0. Calculate h.
-3, -1
Let o(u) = -u**2 + 10*u - 9. Let r be o(9). Factor r*n - 1/4*n**2 + 0.
-n**2/4
Let j = 214 - 212. Factor -3/2*z**j + 0 + 1/2*z**4 - z + 0*z**3.
z*(z - 2)*(z + 1)**2/2
Let m(f) = -f**3 - 7*f**2 - 6*f. Let b be m(-6). Factor -9*y**2 + 2 + b + 10 + 3*y**3.
3*(y - 2)**2*(y + 1)
Let t(n) = n**4 + 2*n**3 - 4*n**2 + n - 3. Let d = 0 + -3. Let v = d - -6. Let u(m) = m**5 - m**4 - 1. Let f(k) = v*u(k) - t(k). Factor f(l).
l*(l - 1)**2*(l + 1)*(3*l - 1)
Let p(j) = -j**2 - 5*j + 38. Let m be p(-9). What is l in 4/5*l**3 - 1/5*l**4 - 6/5*l**m - 1/5 + 4/5*l = 0?
1
Let r(l) be the first derivative of l**8/6720 + l**7/3360 - l**6/1440 - l**5/480 + 2*l**3 - 7. Let j(f) be the third derivative of r(f). Factor j(s).
s*(s - 1)*(s + 1)**2/4
Suppose 19*t**3 - 23*t**3 + t**4 - 3*t + 5*t**2 + t = 0. Calculate t.
0, 1, 2
Suppose -7*s - 28 = -9*s. Suppose -4*b = -6 - s. Factor -9/2*k**4 + 3*k**3 + 2*k**b - 1/2*k**2 + 0*k + 0.
k**2*(k - 1)**2*(4*k - 1)/2
Let n(p) be the second derivative of p**5/60 - p**4/18 - p**3/18 + p**2/3 + 2*p. Factor n(z).
(z - 2)*(z - 1)*(z + 1)/3
Factor 2/3*b**4 - 2*b**3 - 4/3 + 2/3*b**2 + 2*b.
2*(b - 2)*(b - 1)**2*(b + 1)/3
Let z(n) be the first derivative of 0*n - 1/24*n**4 + 2 - 1/2*n**2 + 0*n**3 + 1/60*n**5. Let t(i) be the second derivative of z(i). Let t(l) = 0. What is l?
0, 1
Let w = -47/9 - -289/45. Solve 2/5*h**3 - 6/5*h**2 - 2/5 + w*h = 0 for h.
1
Suppose 5*j = 11*j. Let v be 0 - j - (-18)/45. Factor 6/5*u**2 + 0 + v*u.
2*u*(3*u + 1)/5
Let s(o) = -7*o**2 + 9*o + 3. Let p(c) = 3*c**2 - 4*c - 1. Let a(y) = 5*p(y) + 2*s(y). Solve a(i) = 0 for i.
1
Let m = -125 + 127. Factor 7/6*q**2 - 2/3 - m*q.
(q - 2)*(7*q + 2)/6
Factor -20*l**3 - 12*l**2 - 9*l**3 + 3*l**3 - 15*l**4 - 10*l**3.
-3*l**2*(l + 2)*(5*l + 2)
Let k(v) be the second derivative of -2*v**6/15 + 4*v**5/5 - 5*v**4/3 + 4*v**3/3 + 20*v. Factor k(r).
-4*r*(r - 2)*(r - 1)**2
Suppose 2*g + 6 = -3*n, -5*n - 15 = -2*n - g. Let t be 3/n*4/(-12). Find h, given that -1/4*h**2 + 1/2 + t*h = 0.
-1, 2
Let t(y) be the first derivative of y**4/60 - y**2/10 + 6*y + 6. Let x(n) be the first derivative of t(n). Factor x(g).
(g - 1)*(g + 1)/5
Let i(v) = -5*v - v**3 + 2*v - v - 4*v**2 + 1 + 0*v. Let t be i(-3). Factor 1/2*y**5 + 0 + y**t + 1/2*y**3 + 0*y**2 + 0*y.
y**3*(y + 1)**2/2
Let y(r) be the third derivative of r**6/60 + r**5/30 - r**4/12 - r**3/3 - 3*r**2. Solve y(u) = 0 for u.
-1, 1
Suppose -4 = -6*w + 2*w + 5*o, 5*w - 3*o = 5. Factor 1/2*b - w + 1/2*b**2.
(b - 1)*(b + 2)/2
Suppose -1/3*r**2 - 1/6*r**5 + 5/6*r**4 - r**3 - 1/2 + 7/6*r = 0. What is r?
-1, 1, 3
Let p = 30 - 88/3. Suppose 0 = 17*i - 1 - 33. Determine w so that 0*w + 0 - i*w**4 - p*w**2 + 8/3*w**3 = 0.
0, 1/3, 1
Let d be (-22)/(-77)*(-7)/(-36). Let z(o) be the third derivative of 0*o + 0 - d*o**3 - 3*o**2 + 7/360*o**5 - 5/144*o**4. Factor z(n).
(n - 1)*(7*n + 2)/6
Suppose 3*i + 3*y + 0*y + 99 = 0, -i - 2*y - 33 = 0. Let n(w) = w**2 - 6*w - 9. Let q(h) = 6*h**2 - 30*h - 45. Let s(p) = i*n(p) + 6*q(p). Factor s(u).
3*(u + 3)**2
Factor -7*k**3 - k**3 + 6*k**3.
-2*k**3
Let b(i) = -16*i. Let a be b(-1). Suppose h - 4*x = 0, 3*h + 6*x - 2*x = a. Find p, given that -p**2 - p**2 - 2*p**4 + h*p**2 = 0.
-1, 0, 1
Let s = -835 - -838. Suppose -2*y = m + 4*m + 15, -2*y + 3*m = -9. Determine n so that y*n - 2/3*n**2 + 0 + 2/3*n**s = 0.
0, 1
Let f(n) = n**4 + n**3 - n**2 + n - 1. Let q(h) = 2*h**5 - 10*h**4 + 8*h**3 - 2*h**2 - 2*h + 2. Let v(z) = 4*f(z) + 2*q(z). Suppose v(i) = 0. What is i?
0, 1, 2
Let o(t) be the third derivative of 4*t**7/105 + 3*t**6/20 + t**5/5 + t**4/12 + 3*t**2. Factor o(k).
2*k*(k + 1)**2*(4*k + 1)
Let y be (-3)/(4 - 1) + 3. Solve 6*v**4 + 8*v**2 - 3*v + 4*v**y + 0*v**3 - 6*v**3 - 9*v**3 = 0 for v.
0, 1/2, 1
Let u(z) be the second derivative of z**5/20 - 5*z**4/12 + z**3/2 + 9*z**2/2 + 24*z. Factor u(j).
(j - 3)**2*(j + 1)
Let p(j) be the first derivative of j**4/10 - j**2/5 + 4. Let p(c) = 0. What is c?
-1, 0, 1
Let s be 0 - (3/39*-4)/2. Solve 0 + 2/13*u**4 + 0*u + 0*u**3 - s*u**2 = 0 for u.
-1, 0, 1
Suppose 0 = -8*g + 7*g + 3. Let z(d) be the first derivative of 1 + 1/9*d**2 - 1/9*d**4 + 0*d + 0*d**g + 0*d**5 + 1/27*d**6. Factor z(w).
2*w*(w - 1)**2*(w + 1)**2/9
Let j be -1*(0 - -3 - -1). Let r(s) = s**3 + 5*s**2 + 5*s + 6. Let n be r(j). Factor 2*t**3 - 4*t**3 + n*t**5 + t**4 - 3*t**4 + 2*t**2.
2*t**2*(t - 1)**2*(t + 1)
Let r = 85/126 + -1/126. Let k be ((-4)/(-10))/((-3)/(-5)). Find i, given that -k*i + 0 + 0*i**2 + r*i**3 = 0.
-1, 0, 1
Let v(p) be the third derivative of p**5/12 - 5*p**4/6 + 5*p**3/2 - 7*p**2. Factor v(l).
5*(l - 3)*(l - 1)
Let u(o) be the third derivative of 4*o**2 + 0 + 0*o**3 + 1/360*o**6 + 1/180*o**5 + 0*o + 0*o**4. Suppose u(x) = 0. What is x?
-1, 0
Suppose -c**4 + 7*c**4 - c**3 - 4*c**4 - c**5 = 0. Calculate c.
0, 1
Suppose 0 = 2*j + j - 9. Suppose 2 = -j*u + 8. Factor -4*o**2 + 10*o**5 + 3*o - 3*o + 16*o**4 + u*o**3.
2*o**2*(o + 1)**2*(5*o - 2)
Suppose -18*l = -16*l - 8. Suppose -4/3*p**2 - 2/3*p**5 + 2*p**l + 2*p - 2/3 - 4/3*p**3 = 0. What is p?
-1, 1
Let q(b) be the third derivative of b**8/1008 - b**7/315 - b**6/360 + b**5/90 - 4*b**2. Let q(r) = 0. What is r?
-1, 0, 1, 2
Suppose -8 = 3*t - 4*o, 2*o = 2*t - 3*o + 10. Suppose -20*f = -8*f - 24. Factor -2/9*g - 2/9*g**3 + t - 4/9*g**f.
-2*g*(g + 1)**2/9
Let z(j) = -j**2 - 1. Let v(f) = -25*f**3 - 89*f**2 - 80*f - 24. Let k(h) = -v(h) + 4*z(h). Factor k(g).
5*(g + 1)*(g + 2)*(5*g + 2)
Let i(w) be the second derivative of -w**4/16 + w**3/12 - 11*w. Factor i(t).
-t*(3*t - 2)/4
Let j(s) = -6*s + 30. Let m be j(5). What is q in 0 + 1/4*q**3 - 1/4*q + m*q**2 = 0?
-1, 0, 1
Let h(m) = 3*m**3 - 5*m**2 + m + 3. Let c(u) = 6*u**3 - 10*u**2 + 2*u + 7. Let z(n) = -2*c(n) + 5*h(n). Factor z(r).
(r - 1)**2*(3*r + 1)
Let k(i) = -5*i**3 + 2*i**2 + 23*i - 17. Let j(u) = -5*u**3 + 3*u**2 + 22*u - 18. Let w(d) = -3*j(d) + 2*k(d). Solve w(c) = 0 for c.
-2, 1, 2
Let x(p) = p**2 + 4*p - 1. Let m be x(-5). Factor 0*i**2 + 4*i**2 + m + 6*i - 2*i**2.
2*(i + 1)*(i + 2)
Let f be (-2 - -3)/(-1) - -2. Let x be 0/(