 + 9*j**4 - 7*j**4 - j**2 + j**4 - j**3.
j**2*(j - 1)*(3*j + 2)
Suppose -32 = a + 4*s - 12, 2*a + 5*s + 25 = 0. Let q be (1 - (-1 - a)) + -2. Suppose 0 - 4/3*x**4 + 2/3*x**3 + 0*x**2 + q*x = 0. What is x?
0, 1/2
Suppose 0 = -4*r - 0 + 8. Solve -t**4 + 0 + 1/4*t + 1/4*t**5 + 3/2*t**3 - t**r = 0 for t.
0, 1
Let j = -87 - -611/7. Factor 2/7*q**5 + 0 - 2/7*q**3 + 2/7*q**4 - j*q**2 + 0*q.
2*q**2*(q - 1)*(q + 1)**2/7
Suppose -3 + 5 = s. Determine t so that 7*t**5 - t**5 + 0*t**5 - s*t**4 - 4*t**3 = 0.
-2/3, 0, 1
Let q be 6/18 - 20/6 - -5. Let r(d) be the first derivative of 1/5*d**5 + 0*d**q - 1/18*d**6 + 2 + 0*d + 1/9*d**3 - 1/4*d**4. Factor r(o).
-o**2*(o - 1)**3/3
Let c(k) be the second derivative of 1/21*k**3 + 0*k**2 - 2*k + 0 + 1/42*k**4. Factor c(x).
2*x*(x + 1)/7
Suppose -2/9 - 10/9*s**4 - 20/9*s**2 + 20/9*s**3 + 10/9*s + 2/9*s**5 = 0. What is s?
1
Let r(k) = -17*k**2 - 21*k + 6. Let a(t) = 16*t**2 - 29*t**2 - 20*t**2 - 42*t + 12. Let s(m) = -5*a(m) + 9*r(m). Solve s(p) = 0 for p.
-2, 1/4
Let b(q) = -q**4 + q. Let m(y) = -18*y**4 - 4*y**2 - 4*y - 5*y**5 - 44*y**5 + 24*y**3 + y. Let r(j) = -3*b(j) - m(j). What is u in r(u) = 0?
-1, 0, 2/7
Let m(q) be the first derivative of 2/21*q**3 - 1/14*q**4 - 3 + 1/7*q**2 - 2/7*q. Suppose m(c) = 0. What is c?
-1, 1
Let c(l) = l**2 - 24*l - 44. Let i(g) be the first derivative of 12*g**2 + 45*g + 4. Let f(v) = 3*c(v) + 4*i(v). Determine b so that f(b) = 0.
-4
Let r(a) be the first derivative of 27*a**4/20 - 6*a**3 + 42*a**2/5 - 24*a/5 + 17. Factor r(w).
3*(w - 2)*(3*w - 2)**2/5
Let d(m) = 10*m**2 - m - 1. Let y be d(-1). Suppose 3*i - 4 + y*i**2 + 3*i + 0*i = 0. What is i?
-1, 2/5
Let f(n) be the first derivative of n**2/2 - 4*n + 7. Let o be f(7). Factor 0 + 0*y - 1/4*y**o + 0*y**2.
-y**3/4
Let p(r) be the third derivative of -r**9/15120 + r**8/6720 + r**7/1260 + r**4/3 + 8*r**2. Let o(b) be the second derivative of p(b). Let o(n) = 0. Calculate n.
-1, 0, 2
What is p in 6*p**4 - 2*p**4 - 28*p**5 + 30*p**5 = 0?
-2, 0
What is v in -317*v + 308*v + 0*v**3 + 3*v**3 - 6 = 0?
-1, 2
Let b be 6*(-12)/(-16)*2. Suppose -4*x + b = -3. Find p such that -1 - 14*p**x - 17/2*p - 43/2*p**2 = 0.
-1, -2/7, -1/4
Let y(n) be the second derivative of n**5/20 + n**4/12 + 9*n. Factor y(a).
a**2*(a + 1)
Let b(r) = -23*r**4 + 12*r**3 + 6*r**2 + 5*r. Let j(k) = -8*k**4 + 4*k**3 + 2*k**2 + 2*k. Let f(z) = -6*b(z) + 17*j(z). Factor f(s).
2*s*(s - 2)*(s - 1)*(s + 1)
Suppose 3*r = 4*o + 134, -o = 2*o + 2*r + 109. Let s = o - -37. Factor -1/3 - 2/3*z - 1/3*z**s.
-(z + 1)**2/3
Let o = 1198/2655 + -2/295. Factor 14/9*l**2 - 4/9*l**3 - 14/9*l + o.
-2*(l - 2)*(l - 1)*(2*l - 1)/9
Let s(w) be the second derivative of 2/3*w**3 - 1/4*w**4 - 3*w + 2*w**2 + 0. Find x such that s(x) = 0.
-2/3, 2
Let b(i) be the first derivative of 4/15*i**3 + 3/10*i**4 + 5 + 0*i**5 + 0*i**2 - 1/15*i**6 + 0*i. Factor b(o).
-2*o**2*(o - 2)*(o + 1)**2/5
Let m(h) be the first derivative of -6/5*h**2 - 4 + 2/15*h**3 + 18/5*h. Solve m(i) = 0 for i.
3
Let b = -104 + 104. Factor b - 2/7*m**2 - 2/7*m.
-2*m*(m + 1)/7
Let h(x) = -x - 1. Let f(w) = 3*w**2 - 21*w + 6. Let o(a) = -f(a) + 6*h(a). Let o(j) = 0. Calculate j.
1, 4
Let p(d) be the first derivative of 0*d**2 + 1/6*d**6 + 1 - 3/4*d**5 - 5/6*d**3 + 5/4*d**4 + 1/4*d. Factor p(h).
(h - 1)**4*(4*h + 1)/4
Let v be (-3 - -2)/((-2)/6). Suppose 0*u**5 - v*u**3 + 3*u**5 + 2*u**4 - 2*u**4 = 0. What is u?
-1, 0, 1
Let z be 18/15 + (-12)/(-15). Factor -208/3*a**z - 96*a**3 - 4/3 - 50/3*a.
-2*(4*a + 1)**2*(9*a + 2)/3
Let w(v) be the third derivative of v**6/1020 - 7*v**5/510 + 11*v**4/204 - 5*v**3/51 - 2*v**2 - 3*v. Factor w(a).
2*(a - 5)*(a - 1)**2/17
Let w = -39 + 81/2. Suppose 2*u = -2*t + 6, 0 = -t + 4*u - 2*u. Factor 0*f**t - 3/2*f + w*f**3 + 0.
3*f*(f - 1)*(f + 1)/2
Factor 0*w + 10/13*w**3 + 6/13*w**2 - 2/13*w**5 + 0 + 2/13*w**4.
-2*w**2*(w - 3)*(w + 1)**2/13
Suppose -3*f + 1 = 5*v, f + 6 = -3*v + 5. Determine i so that 1/4*i**5 + 0*i - 1/4*i**4 + 1/4*i**f + 0 - 1/4*i**3 = 0.
-1, 0, 1
Suppose -4*p + 0*p = -12. What is r in 22*r**2 - 6*r**p - r - 3*r + 8 - 20*r = 0?
2/3, 1, 2
Factor -36/7*k**2 + 54/7 + 0*k - 2/7*k**4 + 16/7*k**3.
-2*(k - 3)**3*(k + 1)/7
Let s(c) be the third derivative of -c**5/120 - c**4/16 + c**3/3 + 7*c**2. Factor s(m).
-(m - 1)*(m + 4)/2
Let j = -268/5 - -54. Find d, given that 2/5*d - 4/5 + j*d**2 = 0.
-2, 1
Let i(s) be the third derivative of -s**5/25 - 3*s**4/40 + s**3/10 - 4*s**2 - 8. Factor i(u).
-3*(u + 1)*(4*u - 1)/5
Let t(a) = 4*a**3 - 5*a**2 + 2*a**2 - 15*a - 11*a**3 - 20 + 1. Let j(o) = -4*o**3 - 2*o**2 - 8*o - 10. Let k(y) = 11*j(y) - 6*t(y). Factor k(v).
-2*(v - 1)*(v + 1)*(v + 2)
Let f(o) = o**2 + 6*o - 2. Let w be f(-7). Suppose 0*b + w*k - 16 = -3*b, -k = 5*b - 12. Solve -3*i**b + 2*i**2 + 3*i**2 - 2*i = 0.
0, 1
Let b = -3 - -16. What is i in 30*i**2 + 0 + b*i + 9*i**3 + 2 - 10*i**2 = 0?
-1, -2/9
Let p(n) = -n**3 + n**2 + n - 1. Let s(j) = 3*j**4 + 6*j**2 - 9. Let b(l) = 6*p(l) - s(l). Suppose b(q) = 0. Calculate q.
-1, 1
Let b(r) = r**2 - r - 1. Let h(p) be the second derivative of -1/3*p**4 - 4*p + 0 + p**3 + 5/2*p**2. Let x(g) = 10*b(g) + 2*h(g). Factor x(c).
2*c*(c + 1)
Suppose 0 = 5*w - 6*w + 2. Factor 5*j + j + w*j**2 + 2*j + 7 + 1.
2*(j + 2)**2
Factor 2*x**2 + 4/13*x + 40/13*x**3 + 0.
2*x*(4*x + 1)*(5*x + 2)/13
Let g(v) be the third derivative of v**7/2205 + v**6/504 + v**5/420 + v**4/24 + 2*v**2. Let u(m) be the second derivative of g(m). Determine n so that u(n) = 0.
-1, -1/4
Let z(p) = -p + 13. Let g be z(10). Let o be (-2)/7 - 48/(-21). Factor -q**3 + q**o + 4*q**3 - g*q**5 - q**5.
-q**2*(q - 1)*(2*q + 1)**2
Suppose 3*z - 210 - 39 = 0. Let b be (-1)/6 + z/12. Factor -33/4*h**2 + 0 + b*h**3 + 3/2*h.
3*h*(h - 1)*(9*h - 2)/4
Let u(x) be the first derivative of -x**6/160 + x**5/80 + x**4/32 - x**3/8 - 3*x**2/2 - 3. Let z(r) be the second derivative of u(r). Factor z(l).
-3*(l - 1)**2*(l + 1)/4
Let y(p) = -2*p. Let z(c) = -2*c**2 + 40*c - 2. Let g(x) = 44*y(x) + 2*z(x). Factor g(f).
-4*(f + 1)**2
Let z(h) be the second derivative of -h + 0*h**4 + 0*h**2 - 1/27*h**3 + 1/90*h**5 + 0. Determine u, given that z(u) = 0.
-1, 0, 1
Let k(q) be the second derivative of 2/15*q**5 + 0 - 4/9*q**3 - 3*q - 1/3*q**2 + 1/18*q**4. Determine x, given that k(x) = 0.
-1, -1/4, 1
Let g(r) be the third derivative of -r**7/280 + r**6/40 - r**5/16 + r**4/16 - 5*r**2. Factor g(d).
-3*d*(d - 2)*(d - 1)**2/4
What is t in -1/2 - 1/4*t + 1/4*t**2 = 0?
-1, 2
Let t(g) be the first derivative of 2*g**3/7 - g**2/7 - 2. Factor t(b).
2*b*(3*b - 1)/7
Let y(m) = 22*m**3 + 22*m**2 + 8*m - 4. Let a(j) = -23*j**3 - 22*j**2 - 9*j + 5. Let c = 12 - 16. Let x(i) = c*a(i) - 5*y(i). Factor x(g).
-2*g*(g + 1)*(9*g + 2)
What is l in 0*l + 10*l**5 - 12*l**4 - 2 - 3*l**5 + 14*l**2 - 4*l**3 - 3*l = 0?
-1, -2/7, 1
Suppose -3*n + 25 - 7 = 0. Suppose n*q = 2*q. Factor q - 2/5*z - 2/5*z**2.
-2*z*(z + 1)/5
Let v(i) = 3 + 10*i**4 - i**2 - 11*i**4 - i**3 - i - 4. Let r(l) = 12*l**4 + 6*l**3 + 6*l**2 + 12*l + 15. Let w(t) = -r(t) - 15*v(t). Let w(y) = 0. What is y?
-1, 0
Let d be (-6)/(-3) + (0 - 0). Suppose 0*t = d*t - 6. Determine u, given that 76*u**t + 5*u + 98*u**4 + 78*u**3 + 3*u + 64*u**2 = 0.
-1, -2/7, 0
Let j be (-1)/9 + 46/9. Let m(h) be the first derivative of 10/3*h**3 - h**2 + 6/5*h**j - 7/2*h**4 + 1 + 0*h. Determine v, given that m(v) = 0.
0, 1/3, 1
Let z(v) = v**3 + 5*v**2 + 2*v - 3. Let r = -5 - -2. Let g be z(r). Solve 5*o**2 + 18*o**5 + 3*o + o**2 - g*o**3 - 12*o**4 - 6*o**5 = 0 for o.
-1/2, 0, 1
Let o(y) be the third derivative of -y**5/42 + 2*y**4/21 + 4*y**3/21 + 18*y**2. Factor o(r).
-2*(r - 2)*(5*r + 2)/7
Let p(x) be the third derivative of -1/60*x**4 + 0*x**3 + 3/100*x**6 + 0*x + 11/525*x**7 + 1/210*x**8 + 0 + 5*x**2 + 1/150*x**5. Factor p(y).
2*y*(y + 1)**3*(4*y - 1)/5
Let t(r) be the third derivative of 1/945*r**7 - 2/27*r**3 + 0*r + 0 - 1/36*r**4 + 1/270*r**5 + 2*r**2 + 1/180*r**6. Factor t(n).
2*(n - 1)*(n + 1)**2*(n + 2)/9
Let m(l) = -l + 6*l - 10 - 7*l + 2*l**2. Let u(y) = -4*y**2 + 4*y + 19. Let w(h) = -11*m(h) - 6*u(h). Solve w(j) = 0.
-1, 2
Factor -b**3 + 120*b**2 - 65*b**2 + 2*b - 56*b**2.
-b*(b - 1)*(b + 2)
Let u(a) be the first derivative of -1/3*a**2 + 0*a**3 + 3 + 1/18*a**4 + 4/9*a. Let u(b) = 0. 