 2/9*o**3 + 5/12*o**4 - 2/3*o - 5/6*o**z. Find a, given that n(a) = 0.
-1, -2/5, 1
Suppose -6*u - 36 = -5*u. Let y be (2/5)/(u/(-30)). Determine v, given that y*v**5 - 2/3*v**2 + 1/3 + 1/3*v**4 + 1/3*v - 2/3*v**3 = 0.
-1, 1
Let g(c) = -c**2 + 9*c - 8. Let a be g(8). Let r(w) be the second derivative of -2*w + a*w**2 + 0 + 1/42*w**4 + 1/21*w**3. Let r(h) = 0. What is h?
-1, 0
Suppose 0 = y + y - 10. Let k = 88 - 86. Factor -l**3 + k*l**4 - 5*l**2 + l**4 + l + 7 - y.
(l - 1)**2*(l + 1)*(3*l + 2)
Let c(y) be the second derivative of 2*y**7/63 + 4*y**6/45 - 5*y. Find a such that c(a) = 0.
-2, 0
Suppose 3*m = 3*r + 9, 4*r = -m + 6*m - 15. Factor 0*i + r + 1/3*i**2 - 1/3*i**3.
-i**2*(i - 1)/3
Let n(y) be the first derivative of -1/84*y**4 + 0*y - y**2 + 1 + 1/210*y**5 + 0*y**3. Let k(t) be the second derivative of n(t). Factor k(r).
2*r*(r - 1)/7
Let d(z) be the third derivative of z**8/1680 - z**7/1050 - z**6/300 + z**5/150 + z**4/120 - z**3/30 - 13*z**2. Solve d(q) = 0.
-1, 1
Let z be (-40)/(-150) - 2/15. Factor 0 + z*v - 2/15*v**2.
-2*v*(v - 1)/15
Suppose -5*a - r = -3*a - 9, 4*a - 13 = -r. Let y(v) be the second derivative of 0*v**a + 0 + 2*v + 1/48*v**4 + 1/12*v**3. Factor y(h).
h*(h + 2)/4
Let a(q) = q**3 + 0*q**3 - q - 2*q**3 + 2 - 2*q**2 + 0*q**2. Let u be a(-2). Factor 0 + 2/9*z**2 - 2/9*z**u + 0*z - 2/9*z**3 + 2/9*z**5.
2*z**2*(z - 1)**2*(z + 1)/9
Suppose 0 = -4*u - 98 + 2. Let i be (-14)/u - (-3)/(-9). Factor 0*p - 1/4*p**2 + i*p**3 + 0.
p**2*(p - 1)/4
Let r be 1/(8/98) + 2. Let d = -14 + r. What is g in 0 - 1/4*g**2 + d*g = 0?
0, 1
Let r(u) be the second derivative of -u**5/50 + u**4/10 - 2*u**3/15 + 15*u. Determine f, given that r(f) = 0.
0, 1, 2
Let q(i) be the first derivative of 6/5*i**2 - 2 - 4/5*i + 7/15*i**3. Determine y so that q(y) = 0.
-2, 2/7
Suppose -2*k + 20 = 2*k. Suppose -m = -i, k*m - 2*i - 16 = -i. Suppose -m*a**2 + 6*a**2 - 2*a**3 + 2*a**2 = 0. Calculate a.
0, 2
Let r(f) be the second derivative of -1/21*f**7 + 0*f**2 + 1/10*f**5 + 0*f**3 - 1/15*f**6 + 0 + 1/6*f**4 - 5*f. Factor r(j).
-2*j**2*(j - 1)*(j + 1)**2
Let d(s) be the second derivative of -s + 1/15*s**6 - 4*s**3 + 0 + 4*s**2 - 3/5*s**5 + 13/6*s**4. Factor d(r).
2*(r - 2)**2*(r - 1)**2
Let d(y) be the first derivative of -y**4/3 - 17*y**3/9 - 2*y**2/3 - 11. Suppose d(u) = 0. What is u?
-4, -1/4, 0
Let q = -27 - -21. Let g be q/(-8)*(5 + -1). Factor 0*x**2 - 2/7*x**g + 2/7*x + 0.
-2*x*(x - 1)*(x + 1)/7
Let d(f) be the second derivative of -f**8/30240 - f**7/11340 - f**4/6 - 2*f. Let z(h) be the third derivative of d(h). Factor z(x).
-2*x**2*(x + 1)/9
Suppose 0 = m - 5, 6 = 2*q - 5*q + 3*m. Let j(t) = t**2 + 9*t + 17. Let c be j(-7). Factor -3*k**3 + 17*k + k + 6 - q*k - c*k**4 + 9*k**2 + 0.
-3*(k - 2)*(k + 1)**3
Let q(k) be the third derivative of -k**7/630 - k**6/360 + k**5/90 + 31*k**2. Let q(m) = 0. Calculate m.
-2, 0, 1
Factor 17*w**2 - 9*w**2 + 2*w**3 + 5*w**3 + 4*w - 3*w**3.
4*w*(w + 1)**2
Factor -1/2*b + 0 - 1/4*b**2.
-b*(b + 2)/4
Let w = 3 + -1. Factor 2*a**2 - 2*a**2 - a + w*a - a**3.
-a*(a - 1)*(a + 1)
Let s(b) be the second derivative of -b**6/10 + 3*b**5/20 + 2*b**4 - 6*b**3 - 16*b. Factor s(a).
-3*a*(a - 2)**2*(a + 3)
Suppose -4*i = 3*j - 61, 0 = i - 4 + 3. Factor 13*a - 4*a**2 - j*a + 2*a**3 + 8*a.
2*a*(a - 1)**2
Factor 0*y**2 + 0 + 0*y**4 + 1/7*y**3 - 1/7*y**5 + 0*y.
-y**3*(y - 1)*(y + 1)/7
Let n = 209/280 - -3/56. Factor 0*h + 0 - 6/5*h**3 - 2/5*h**4 - n*h**2.
-2*h**2*(h + 1)*(h + 2)/5
Let g(p) = 6*p + 4. Let v(i) = i**2 - 24*i - 16. Let o = -8 + 10. Let f(q) = o*v(q) + 9*g(q). Factor f(b).
2*(b + 1)*(b + 2)
Let c be (-19)/(-3) - 6/(-2 - -4). What is j in c*j**4 - 14/3*j**3 - 2*j**2 - 4/3 + 14/3*j = 0?
-1, 2/5, 1
Let a(y) = -4*y + 23. Let n be a(7). Let m be 10/4 + 10/n. Let -m - 1/4*p**3 - 5/4*p - p**2 = 0. What is p?
-2, -1
Let t(h) be the first derivative of 2*h**3/3 - 2*h**2 + 2*h - 3. Factor t(z).
2*(z - 1)**2
Let w(j) be the first derivative of 0*j**3 + 1 + 1/3*j**2 - 1/15*j**5 - 1/6*j**4 + 1/3*j. Factor w(f).
-(f - 1)*(f + 1)**3/3
Let s(y) = 5*y - 3. Let w be s(1). Let o(d) be the first derivative of 0*d + 0*d**w + 2 + 1/16*d**4 + 1/12*d**3. What is x in o(x) = 0?
-1, 0
Let n(j) = -j**5 + 2*j**4 - 7*j**3. Let l(z) = -6*z**3 + 205*z + 2*z**4 - 205*z. Let c(g) = 3*l(g) - 2*n(g). Let c(x) = 0. What is x?
-2, 0, 1
Let l(t) be the third derivative of 0*t + 0*t**3 + 3/10*t**5 + 0 - 1/6*t**4 + 3*t**2. Factor l(v).
2*v*(9*v - 2)
Find o, given that 1/3*o + 1/3 - 1/3*o**3 - 1/3*o**2 = 0.
-1, 1
Let a = 3 + 0. Suppose 0*t = -4*t + 12. Factor f + a*f**2 + 8*f + t - 3*f.
3*(f + 1)**2
Let q = 53 - 50. Solve 1/4*h**4 + 0 - 1/4*h**q - 1/4*h**2 + 1/4*h = 0 for h.
-1, 0, 1
Suppose -6 = p - 3*p. Let t = 3/8 + -1/24. Determine j, given that 1/3*j**p + t*j + 2/3*j**2 + 0 = 0.
-1, 0
Let k = 2715 + -38033/14. Let w = k + 22/7. Factor 0 + 3/4*t**3 + 3/4*t + w*t**2.
3*t*(t + 1)**2/4
Let v be (-1*(-1)/(-12))/(99/(-264)). Find q, given that v*q - 2/9*q**2 + 4/9 = 0.
-1, 2
Suppose 5*p - 45 = -35. Let n(x) be the first derivative of 4/3*x**3 + 2*x + 1/4*x**4 - 3 + 5/2*x**p. Determine d so that n(d) = 0.
-2, -1
Let n(f) = -f**3 - f**2 + f. Let o(w) = -w**3 - 6*w**2 + w. Let r(p) = 6*n(p) - o(p). Factor r(g).
-5*g*(g - 1)*(g + 1)
Let f be ((-2)/(-2))/(-1) - (-2 + 1). Factor 1/6*p**3 + 0 + 0*p**2 - 1/6*p**4 + f*p.
-p**3*(p - 1)/6
Let d(w) = w**4 + 6*w**3 + 4*w**2 + 6*w + 3. Let k(g) = 3*g**4 + 19*g**3 + 11*g**2 + 19*g + 10. Let o(y) = -21*d(y) + 6*k(y). Factor o(u).
-3*(u + 1)**4
Let i(k) be the second derivative of k**8/3360 - k**7/1680 - k**3/6 + 3*k. Let r(w) be the second derivative of i(w). Factor r(y).
y**3*(y - 1)/2
Find w such that -14*w - 7 - 5*w**2 + 9*w + 7 = 0.
-1, 0
Suppose 0 = 5*d - 2 - 3. Solve c - c**3 - 3*c + 3 - d + 3*c - 2*c**2 = 0.
-2, -1, 1
Let a(f) be the first derivative of f**6/105 - f**5/35 + f**4/42 + 3*f - 2. Let u(q) be the first derivative of a(q). Factor u(g).
2*g**2*(g - 1)**2/7
Let z(r) be the second derivative of -2197*r**6/10 + 507*r**5/25 + 312*r**4/5 - 136*r**3/5 + 24*r**2/5 + 7*r. Solve z(m) = 0.
-2/5, 2/13
Suppose 0 = -f - 5*p + 24, 0 = -3*f + 4*p - 2 - 2. Let v(h) be the first derivative of -2/3*h**3 + 3 - f*h - 3*h**2. Find b such that v(b) = 0.
-2, -1
Let m = 20 - 13. Let g(t) = -t**3 + 8*t**2 - 6*t - 7. Let b be g(m). Find r, given that b - 2/3*r**2 + 2/3*r = 0.
0, 1
Let j(c) be the first derivative of 1/20*c**4 - c + 3 + 0*c**2 + 1/10*c**3. Let b(a) be the first derivative of j(a). Factor b(i).
3*i*(i + 1)/5
Factor -1/2*z**2 - 2*z - 3/2.
-(z + 1)*(z + 3)/2
Let h(w) be the third derivative of w**9/504 - w**8/420 - w**7/420 + w**3/6 - 2*w**2. Let u(x) be the first derivative of h(x). Factor u(v).
2*v**3*(v - 1)*(3*v + 1)
Suppose 5*p = -3*c + 58, 3*c - 59 = 5*p + 9. Suppose -24 = -4*i + 4*h, -2*i + c = h - 6*h. Solve -5*s**i + 3*s**2 + 3*s**3 - s**2 = 0.
0, 1
Let o(m) be the first derivative of -2*m**3/3 + 3*m**2 - 4*m + 4. Solve o(f) = 0 for f.
1, 2
Let t(v) be the second derivative of 0*v**2 - 1/3*v**3 + v + 0 - 1/6*v**4. Let t(f) = 0. What is f?
-1, 0
Let f(o) = o**2 + 4*o. Let d be f(-4). Let 1/3*a + 0*a**2 - 1/3*a**3 + d = 0. What is a?
-1, 0, 1
Let i(j) be the third derivative of j**8/224 - 11*j**7/420 + j**6/16 - 3*j**5/40 + j**4/24 - 12*j**2. Suppose i(k) = 0. Calculate k.
0, 2/3, 1
Suppose 2*g + 2 - 3 = -5*x, -9 = -4*g - 3*x. Factor 3*t**2 - t**2 - 3*t**3 - 3*t + 6*t**g + 3 - 5*t**2.
3*(t - 1)**2*(t + 1)
Suppose 0 = u + 4*k - 30, -u = -4*k - k - 3. Let l be 27/u*(-4)/(-3). Find w, given that -1/4*w**l + 0 + 1/2*w = 0.
0, 2
Let a be (-3)/9 + 0 + (-26)/(-6). Let 0*i - 6/5*i**3 + 2/5*i**2 - 2/5*i**5 + 6/5*i**a + 0 = 0. What is i?
0, 1
Let k(t) be the second derivative of t**4/12 - t**3/2 + 3*t**2/2 - 2*t. Let b be k(2). Let -2*g**5 + g**4 + 1 - 5*g**4 + 4*g**2 + 2*g - b = 0. What is g?
-1, 0, 1
Suppose 2*t = -3*b + 28, 2*b - 4*t - 10 = -3*b. Let l(i) = -i**3 + 5*i**2 + 7*i - 4. Let f be l(b). Determine j, given that 6/5*j - 8/5*j**f + 2/5 = 0.
-1/4, 1
Let r(u) be the third derivative of 0*u**4 + u**2 + 0*u**5 + 0*u + 1/35*u**7 + 0 + 0*u**3 + 1/112*u**8 + 1/40*u**6. Factor r(o).
3*o**3*(o + 1)**2
Factor 0 - 5/6*h**2 - 1/3*h**3 + 5/6*h**4 + 1/3*h.
h*(h - 1)*(h + 1)*(5*h - 2)/6
Let j = -8 - -10. Let i be ((-5)/(-10))/(j/12). 