*2
Let j(q) = q**2 - q. Let w be j(2). Let n(y) = -2*y**3 - 2*y**2 + y - 2. Let p be n(-2). What is o in -2*o**p + o**w + 6*o**3 - 4*o**3 - 2*o**5 + o**2 = 0?
-1, 0, 1
Let f be 2/(-31) - 448/(-217). Factor 2/3 + h**f + 1/3*h**3 - 5/3*h - 1/3*h**4.
-(h - 1)**3*(h + 2)/3
Let i(v) be the first derivative of 0*v + 3 - 1/3*v**3 + 5/4*v**4 - 4/5*v**5 + 0*v**2. Factor i(k).
-k**2*(k - 1)*(4*k - 1)
Let 1/2*i**3 - 1/2*i**5 - 7/2*i**2 + 0*i + 3/2*i**4 + 2 = 0. What is i?
-1, 1, 2
Suppose 0 = 3*n - n. Let s be (-1)/(-2)*(2 - 1). Determine k so that -1/2*k**3 + 0 + 1/2*k**5 - 1/2*k**4 + n*k + s*k**2 = 0.
-1, 0, 1
Suppose -3*y + 3 = 3*l, 3*l - 2*l = 5*y + 7. Let z be -14*(-2)/12 + y. Factor 0*h - 1/3*h**2 + z.
-(h - 2)*(h + 2)/3
Suppose -4*y = -8, 2*p - 2*y - 10 = 6. Determine t, given that -p + 10 + t**5 = 0.
0
Solve -15/7*f**2 + 36/7 + 6/7*f**3 - 12/7*f = 0.
-3/2, 2
Let s = 418 + -1252/3. Factor 2/3*m**2 + 0*m**3 - s*m**4 - 1/3*m**5 + 1/3*m + 0.
-m*(m - 1)*(m + 1)**3/3
Suppose -3*q + 3 - 6 = 3*o, 5*o = 3*q + 3. Solve -3/4*f**2 + o - 3/2*f = 0 for f.
-2, 0
Let q(t) be the first derivative of t**8/840 - t**7/420 - t**3/3 + 3. Let l(y) be the third derivative of q(y). Factor l(i).
2*i**3*(i - 1)
Factor 3/2 - 3/2*f**5 + 3/2*f**4 + 3*f**3 - 3/2*f - 3*f**2.
-3*(f - 1)**3*(f + 1)**2/2
Let l(c) be the second derivative of c**5/5 + 4*c**4/3 - 7*c. Find x such that l(x) = 0.
-4, 0
Let d(a) be the first derivative of -a**4/10 - 2*a**3/15 - 11. Factor d(q).
-2*q**2*(q + 1)/5
Let x(l) be the third derivative of -l**7/60 + 3*l**6/80 - l**5/60 + 3*l**2. Let x(v) = 0. What is v?
0, 2/7, 1
Let b = -7 + 6. Let m be (-3)/(-4 + 1) - b. Determine w so that 0*w + 5*w**3 - 3*w - m*w**2 - w - 3*w**3 = 0.
-1, 0, 2
Suppose -p + h = -2*p - 9, -2*p - 13 = h. Let o be (-18)/p + (1 - 5). Factor 0*m + 5/4*m**3 + o*m**2 + 3/4*m**4 + 0.
m**2*(m + 1)*(3*m + 2)/4
Suppose -8*s + 6 = -5*s. Let g(v) be the first derivative of -1/3*v**s + 2/3*v - 2/9*v**3 + 1/6*v**4 - 1. Suppose g(i) = 0. What is i?
-1, 1
Let 8*n**2 + 12*n**2 + 34*n**3 + 8*n**4 - 3*n**4 - 9*n**3 = 0. What is n?
-4, -1, 0
Let d = -5308/15 - -354. Factor 2/15*v**3 + d*v**2 + 0 + 0*v.
2*v**2*(v + 1)/15
Let f(g) = g**3 + g**2 - g - 3. Let l be f(-3). Let w be 4/l*5/(-5). Factor 0 - 8/9*j**2 - 8/9*j**3 - w*j.
-2*j*(2*j + 1)**2/9
Let g(q) be the third derivative of -q**5/90 + q**4/36 + 6*q**2. Factor g(d).
-2*d*(d - 1)/3
Let i(s) be the first derivative of -s**4/6 + s**3/3 + s**2/3 + 27. What is t in i(t) = 0?
-1/2, 0, 2
Let o = 82/35 - 15/7. Factor 0*a + o*a**2 + 0 - 1/5*a**3.
-a**2*(a - 1)/5
Let v(u) be the third derivative of -2*u**2 - 1/30*u**5 + 0 + 0*u - 3*u**3 + 1/2*u**4. Let v(k) = 0. Calculate k.
3
Let t(u) be the second derivative of 0 + 2*u - 1/5*u**2 - u**4 - 23/25*u**5 - 11/25*u**6 - 3/35*u**7 - 3/5*u**3. Factor t(n).
-2*(n + 1)**3*(3*n + 1)**2/5
Let k be 2/(-3) - (-14)/3. Suppose -k*w + 2*w = 2*y + 2, 4*w = y + 11. Solve 0*l**w + l**2 + 0*l + l = 0.
-1, 0
Let z(n) be the second derivative of n**6/6 - n**5/2 - 10*n**4/3 + 15*n**3 - 45*n**2/2 + 40*n. Let z(x) = 0. What is x?
-3, 1, 3
Let i = -357/5 + 73. Suppose 14/5*m**2 + 6/5*m**4 - 8/5 + 4*m**3 - i*m = 0. Calculate m.
-2, -1, 2/3
Let r(n) be the third derivative of -n**6/80 - n**5/40 + n**4/16 + n**3/4 - 5*n**2. Find t such that r(t) = 0.
-1, 1
Let k(r) be the second derivative of r**6/135 + r**5/15 + 2*r**4/9 + 10*r**3/27 + r**2/3 - 12*r. Determine s so that k(s) = 0.
-3, -1
Let u be 8/(-12) + 16/6. Factor -2/3*s**4 - 2/3*s**3 + 2/3*s + 0 + 2/3*s**u.
-2*s*(s - 1)*(s + 1)**2/3
Let m be -4 - (-5 + -7 + 6). Let q be (-34)/(-30) + 2/(-6). Find s, given that -m*s**4 + 0 + 2*s**2 + q*s + 14/5*s**5 - 18/5*s**3 = 0.
-1, -2/7, 0, 1
Suppose 3/5*g**4 + 0 + 0*g + 6/5*g**3 + 0*g**2 - 3/5*g**5 = 0. Calculate g.
-1, 0, 2
Suppose 0 = 8*m + 9*m. Let t(p) be the third derivative of 0*p**3 + 1/210*p**7 + 2/15*p**5 + 1/6*p**4 + 1/24*p**6 + 0*p + m + 3*p**2. Factor t(n).
n*(n + 1)*(n + 2)**2
Let s(z) = 4*z**2 - 1. Let f(t) = 0 - 1 - t + 5*t**2 - 4*t**2. Let q(r) = -3*f(r) + s(r). Find h, given that q(h) = 0.
-2, -1
Let s(y) be the third derivative of -y**11/831600 + y**9/50400 - y**8/25200 - y**5/60 - 3*y**2. Let p(x) be the third derivative of s(x). Solve p(n) = 0 for n.
-2, 0, 1
Let s be (-1473)/285 + 4/10. Let v = 3/95 - s. Suppose 16/5 + 12/5*w**2 - v*w - 2/5*w**3 = 0. What is w?
2
Suppose 0*t = -3*t + 9. Let n = 4 - 0. Solve -2*s**2 - 2*s**3 - 4*s**3 - 4*s**t - 8*s**n = 0.
-1, -1/4, 0
Let u be 1 + 0 - (-52)/(-308). Let z = 2/77 + u. Factor z*h**2 + 2/7 + 2/7*h**3 + 6/7*h.
2*(h + 1)**3/7
Let l be 2/6*(-2)/(-3). Let q be (-2 - -2)*(-2 + 1). Find p, given that q + l*p**2 - 2/9*p = 0.
0, 1
Suppose -28*p - 16*p = -14*p. Factor p*g - 3/4 + 9/4*g**2 - 3/2*g**3.
-3*(g - 1)**2*(2*g + 1)/4
Let k(i) = -i**3 + 3*i**2 - 19*i + 5. Let s(w) = w**2 + w + 1. Let l(t) = k(t) + 4*s(t). Determine a, given that l(a) = 0.
1, 3
Suppose g + 1 = 2*g. Factor 5 + 4*b + 0*b - g + 2*b**2 + 2*b.
2*(b + 1)*(b + 2)
Suppose -77 = 6*k + 85. Let y = k + 55/2. Suppose y*j - 1/2*j**3 + 0 + 0*j**2 = 0. What is j?
-1, 0, 1
Factor -1/3*n**5 + 1/3 + 2/3*n**2 - n**4 + n - 2/3*n**3.
-(n - 1)*(n + 1)**4/3
Let n(k) be the second derivative of 1/12*k**3 + 0 + 1/24*k**4 - 1/2*k**2 - 4*k. Solve n(z) = 0 for z.
-2, 1
Factor 6*n**3 - 48*n**3 + 24 - 16*n**2 + 22*n**3 + 28*n.
-4*(n + 1)**2*(5*n - 6)
Let o(x) be the second derivative of x**5/4 + 5*x**4/4 - 5*x**3/6 - 15*x**2/2 - 46*x. Suppose o(t) = 0. What is t?
-3, -1, 1
Let w = -5 + 7. Suppose 0*j**w + 17 - 8 + 6*j + j**2 = 0. Calculate j.
-3
Let -2/7*q**5 + 0*q**3 + 4/7*q**4 + 0 + 2/7*q - 4/7*q**2 = 0. What is q?
-1, 0, 1
Let v(k) = -70*k**4 + 85*k**3 - 15*k**2 + 55. Let x(s) = 5*s**4 - 6*s**3 + s**2 - 4. Let j(t) = 4*v(t) + 55*x(t). Factor j(w).
-5*w**2*(w - 1)**2
Let w(o) be the first derivative of o**5/55 + o**4/44 - o**3/11 - 5*o**2/22 - 2*o/11 - 7. Factor w(b).
(b - 2)*(b + 1)**3/11
Let t(x) = 6*x**5 - 24*x**3 - 3*x**2 + 27*x + 21. Let n(d) = -3*d**5 + 12*d**3 + 2*d**2 - 13*d - 10. Let u(s) = 9*n(s) + 4*t(s). Factor u(g).
-3*(g - 2)*(g - 1)*(g + 1)**3
Solve 3*r**3 + 152*r + 4 - 4*r**2 - 156*r + r**3 = 0 for r.
-1, 1
Factor 10/3*n + 2/3*n**3 + 4/3 + 8/3*n**2.
2*(n + 1)**2*(n + 2)/3
Let q(b) be the third derivative of 4*b**2 + 1/180*b**5 + 2/9*b**3 + 0*b + 0 + 1/18*b**4. What is j in q(j) = 0?
-2
Let c(x) be the first derivative of -x**4 + 32*x**3/3 - 14*x**2 - 28. Let c(d) = 0. Calculate d.
0, 1, 7
Let m(r) be the first derivative of -r**4/6 + 4*r**3/9 - r**2/3 + 12. Factor m(g).
-2*g*(g - 1)**2/3
Suppose c = 5*s + 39, s + 3*c + 3 = -8. Let f be ((-24)/(-4))/((-84)/s). Solve 0 - f*j**2 + 0*j - 2/7*j**3 = 0 for j.
-2, 0
Let w(l) be the third derivative of l**8/1512 - 4*l**7/945 + l**6/90 - 2*l**5/135 + l**4/108 - 20*l**2. Factor w(z).
2*z*(z - 1)**4/9
Suppose -111 - 6*j - 4*j**2 + 109 - 2*j**2 - 2*j**3 = 0. Calculate j.
-1
Let i(p) = -p**3 + 5*p**2 + 6*p + 3. Let f be i(6). Factor 2*z**2 - 3 + f - 2*z.
2*z*(z - 1)
Suppose -2*w = -g - 1, w + 4*g + 2 = 16. Factor 1/4 + 1/4*z**3 - 1/4*z**w - 1/4*z.
(z - 1)**2*(z + 1)/4
Let k(b) be the third derivative of -b**6/600 + b**5/75 - b**4/40 + 13*b**2. Suppose k(u) = 0. Calculate u.
0, 1, 3
Factor -5*r**5 + 24 - 11 + 5*r**3 - 13.
-5*r**3*(r - 1)*(r + 1)
Let t(w) be the third derivative of w**5/24 - 5*w**4/144 - 5*w**3/18 - 4*w**2. Suppose t(i) = 0. Calculate i.
-2/3, 1
Let i(c) be the first derivative of 1/2*c**3 + 21/16*c**4 + 0*c + 3/8*c**6 - 1 + 0*c**2 + 6/5*c**5. Factor i(g).
3*g**2*(g + 1)**2*(3*g + 2)/4
Let k = 0 - 0. Let q = 45 + -134/3. Let q*z + 1/3*z**2 + k = 0. Calculate z.
-1, 0
Let r(i) be the second derivative of -9*i**4/4 - 8*i**3 + 6*i**2 - 11*i. Factor r(s).
-3*(s + 2)*(9*s - 2)
Factor 2/3*o**3 + 0 + 2/3*o**2 + 0*o.
2*o**2*(o + 1)/3
Suppose -3 = -5*i + 2, -5*x - i = -11. Determine n so that -14*n + 8*n - 2*n**2 - n**x = 0.
-2, 0
Let p(d) be the second derivative of -d**6/210 - d**5/210 + d**4/42 + d**3/21 - 9*d**2/2 - 2*d. Let i(u) be the first derivative of p(u). Factor i(v).
-2*(v - 1)*(v + 1)*(2*v + 1)/7
Let l(g) be the first derivative of -2*g**3/15 - 3*g**2/5 + 8*g/5 - 23. Factor l(m).
-2*(m - 1)*(m + 4)/5
Let u be 1/(-2) - (-1 + 5/20). Factor u*y**2 - y + 1.
(y - 2)**2/4
Let m = 212 - 423/2. Factor 0 - c**2 + 