-(h - 1)**2*(h + 2)/2
Suppose -q = 4, 0 = 4*j - j - 4*q - 22. Let x(y) be the first derivative of y**2 - 2/5*y**5 - 1/2*y**4 + 0*y + 2/3*y**3 + j. Determine g so that x(g) = 0.
-1, 0, 1
Let n(z) be the second derivative of -7*z**6/120 + z**5/40 + z - 16. Solve n(p) = 0 for p.
0, 2/7
Suppose 0 = 12*o - 9*o. Let c(m) be the first derivative of m**3 + 3/2*m**2 - 3/5*m**5 + o*m - 3/4*m**4 + 2. Find z such that c(z) = 0.
-1, 0, 1
Let p(l) be the first derivative of -l**4/24 - 2*l**3/9 - 31. Suppose p(j) = 0. What is j?
-4, 0
Let w = -57 + 60. Factor 2/7*b**w + 2/7*b**4 - 2/7*b + 0 - 2/7*b**2.
2*b*(b - 1)*(b + 1)**2/7
Let u(y) = -y**2 + y. Let v(d) = 3*d**4 - 8*d**3 + 6*d**2 - d. Suppose 18 = 4*q + 6. Let f(w) = q*u(w) + v(w). What is i in f(i) = 0?
-1/3, 0, 1, 2
Let l(s) be the first derivative of -s**3/6 + 7*s**2/2 - 49*s/2 + 2. Suppose l(m) = 0. What is m?
7
Let p(o) be the first derivative of o**4/24 + o**3/18 - o**2/12 - o/6 - 4. Find j, given that p(j) = 0.
-1, 1
Let j = 4/23 - -15/46. Solve -1/2*x**4 + j*x**2 - 2*x**3 + 0 + 0*x + 2*x**5 = 0 for x.
-1, 0, 1/4, 1
Let w(f) be the third derivative of 1/15*f**5 + 0 + 7/60*f**6 + 8/105*f**7 - 3*f**2 + 0*f**3 + 0*f**4 + 1/56*f**8 + 0*f. Find t, given that w(t) = 0.
-1, -2/3, 0
Let m(o) be the first derivative of -o**8/1680 + o**7/420 - o**6/360 + 4*o**3/3 - 3. Let l(i) be the third derivative of m(i). Determine f, given that l(f) = 0.
0, 1
Let c = -6 + 8. Factor 3*x**5 - 6*x**4 - 6*x**c - 3*x + 10*x**4 + 2*x**4.
3*x*(x - 1)*(x + 1)**3
Let y(f) be the third derivative of f**7/210 + f**6/40 + f**5/30 - 3*f**2. Let y(z) = 0. Calculate z.
-2, -1, 0
Let i(l) be the first derivative of 2/3*l**3 + 0*l - 3 + 1/4*l**4 + 0*l**2. Find g, given that i(g) = 0.
-2, 0
Let l = -29 + -17. Let m = l - -140/3. Factor 2/3*q + m*q**3 + 4/3*q**2 + 0.
2*q*(q + 1)**2/3
Let x(j) be the second derivative of j**4/21 - 7*j. Determine s so that x(s) = 0.
0
Let l(g) = 11*g**3 - 24*g**2 + 60*g - 40. Let b(u) = -65*u**3 + 145*u**2 - 360*u + 240. Let w(p) = -6*b(p) - 35*l(p). Suppose w(s) = 0. Calculate s.
2
Let c(d) = d**3 + d**2 - d. Let y(r) = -r**4 + r**3 + 10*r**2 - 7*r. Let g(l) = 6*c(l) - 2*y(l). Factor g(b).
2*b*(b - 1)**2*(b + 4)
Suppose -4*m - 8 = n, -5*n + 2*m + 32 - 6 = 0. Factor -23*o**n - 8 - 46*o**4 - 60*o**3 + 11*o + 19*o**4 + 13*o + 22*o**2.
-2*(o + 1)**2*(5*o - 2)**2
Suppose 2*s + 42 = -38. Let r be ((s/6)/5)/(-2). Factor r*l**2 + 0 + 0*l + 2/3*l**3.
2*l**2*(l + 1)/3
Let b be ((-20)/12 - -1)/(5/(-9)). Determine t so that b*t - 4/5 - 2/5*t**2 = 0.
1, 2
Factor 0*n**5 - 2*n**5 + n**3 + n**5.
-n**3*(n - 1)*(n + 1)
Let a(s) be the third derivative of s**5/60 + s**4/2 + 6*s**3 + 4*s**2. Factor a(z).
(z + 6)**2
Let d(t) = t**2 + 3*t + 2. Let a be d(-2). Let g(m) = m**3 - m + 3. Let o be g(a). Suppose 2*x**4 + 2*x**4 + 2*x**3 - x**o - 3*x**4 = 0. What is x?
-1, 0
Let b(m) = m + 10. Let u be b(-5). Factor 61*x**5 + 6*x**4 - 57*x**u - 4*x + 2*x**4 - 8*x**2.
4*x*(x - 1)*(x + 1)**3
Suppose 4*r = -2*o + 2, r + 16 = 5*o - 0*o. Factor -6*s**2 + 0*s - 3*s**o + 5*s**3 + 4*s.
2*s*(s - 2)*(s - 1)
Let u(j) be the first derivative of -4 - 22/25*j**5 - 6/5*j**3 + 2/5*j**2 + 0*j + 1/5*j**6 + 3/2*j**4. Factor u(q).
2*q*(q - 1)**3*(3*q - 2)/5
Factor 4/5*s**2 - 24/5 - 4/5*s.
4*(s - 3)*(s + 2)/5
Let d be 6 + -4 + 8/(-4). Let t(g) be the second derivative of -1/10*g**5 - 1/18*g**3 + 2/45*g**6 - 1/126*g**7 + 0 + 1/9*g**4 + 2*g + d*g**2. Factor t(z).
-z*(z - 1)**4/3
Let y be (-8)/6*(-3)/2. Let a be (-2)/9 + ((-980)/225)/(-7). Solve -a*d + 0 + 4/5*d**3 + 2/5*d**y = 0.
-1, 0, 1/2
Let y(s) be the first derivative of s**5/30 + s**4/36 - 3*s**2/2 + 1. Let p(c) be the second derivative of y(c). Solve p(x) = 0 for x.
-1/3, 0
Let o(z) be the third derivative of -z**7/350 - z**6/100 + 3*z**5/100 + 9*z**2. Factor o(m).
-3*m**2*(m - 1)*(m + 3)/5
Let k be (-84)/(-9) - 5 - 3. Suppose -2*a**2 - 2/3*a**3 - k*a + 0 = 0. Calculate a.
-2, -1, 0
Let f(a) be the second derivative of -a**7/126 + a**6/90 - 6*a. Factor f(i).
-i**4*(i - 1)/3
Let f(u) = u + 1. Let h(m) = -8*m**2 + 5*m + 1. Let l(c) = -6*f(c) - h(c). Let o(q) = q**2 - q - 1. Let t(p) = l(p) - 3*o(p). Determine d, given that t(d) = 0.
-2/5, 2
Let -17 - 47 + 0*q**2 - 6*q**2 + 2*q**2 - 32*q = 0. What is q?
-4
Let u(c) = -5*c**3 - 7*c**2 + 4*c. Let q(o) = -o. Let h(a) = 30*q(a) + 5*u(a). Factor h(l).
-5*l*(l + 1)*(5*l + 2)
Let d(y) = 50*y**4 + 94*y**3 + 24*y**2 - 20*y. Let f(c) = 13*c**4 - 2*c**2 + 0*c**2 + 7*c**2 + 19*c**3 - 4*c - 3*c**4. Let k(r) = 3*d(r) - 14*f(r). Factor k(p).
2*p*(p + 1)**2*(5*p - 2)
Let k be (-5)/3*(-10)/200. Let o(n) be the first derivative of -4 + 1/8*n**4 - 1/6*n**3 + 0*n + 1/10*n**5 + 0*n**2 - k*n**6. Factor o(u).
-u**2*(u - 1)**2*(u + 1)/2
Let a(l) be the first derivative of -3*l**2 + 3/2*l**4 + 3*l - 7 - 3/5*l**5 + 0*l**3. Solve a(i) = 0 for i.
-1, 1
Suppose 9 = 2*s - 3. Factor 0*z - 2*z**4 - 2*z + 4*z**4 + 6*z**2 - s*z**3.
2*z*(z - 1)**3
Factor -297*x**3 + 283*x**3 - 5*x**2 - 20*x - 69*x**2.
-2*x*(x + 5)*(7*x + 2)
Let u be 90/(-27) + (-2)/(-6) - -3. Solve 0*f + u - 1/2*f**2 = 0 for f.
0
Let d(p) = 5*p**2 + 3. Let c(r) = 9*r**2 - 3*r + 4. Let j(q) = 10*q**2 - 4*q + 4. Let g(v) = 4*c(v) - 3*j(v). Let l(u) = 5*d(u) - 4*g(u). Factor l(s).
(s - 1)*(s + 1)
Let h = 239/3156 + 2/263. Let w(v) be the second derivative of 2*v - 1/42*v**7 + 0*v**2 + 0*v**3 + 0 - h*v**4 + 1/20*v**5 + 1/30*v**6. Factor w(i).
-i**2*(i - 1)**2*(i + 1)
Let b(w) be the third derivative of w**8/2520 + 2*w**7/1575 - w**6/450 - 4*w**5/225 - 7*w**4/180 - 2*w**3/45 - 10*w**2. Find z such that b(z) = 0.
-1, 2
Suppose -7*z + 2*z - 15 = 0. Let v = 5 + z. Factor 2*g - g**3 - 4*g**2 + 0*g**4 + v + 2*g**4 - 2*g**5 - 4*g + 5*g**3.
-2*(g - 1)**3*(g + 1)**2
Let q(n) = 6*n**5 + 22*n**4 + 30*n**3 + 18*n**2 + 4*n + 11. Let m(r) = 3*r**5 + 11*r**4 + 15*r**3 + 9*r**2 + 2*r + 6. Let x(l) = -11*m(l) + 6*q(l). Factor x(f).
f*(f + 1)**3*(3*f + 2)
Factor -469*p**2 + 466*p**2 + p - 9*p**4 + 2*p - 15*p**3.
-3*p*(p + 1)**2*(3*p - 1)
Let c = -589/675 - -22/25. Let k(s) be the third derivative of 0 + 0*s**3 + 3*s**2 + 0*s + c*s**5 + 0*s**4 - 1/540*s**6. Factor k(b).
-2*b**2*(b - 2)/9
Let z(r) be the first derivative of -5*r**9/1512 + r**8/105 - r**7/420 - r**6/90 - r**3 + 3. Let d(n) be the third derivative of z(n). Solve d(o) = 0 for o.
-2/5, 0, 1
Let v be (0 - 3) + 7 + -2. Let o = v + -2. Determine q, given that o + 8/9*q**3 + 2/9*q - 10/9*q**2 = 0.
0, 1/4, 1
Let p(j) be the first derivative of 1/3*j**6 - 2/3*j**3 - 1/2*j**4 + 0*j**2 + 0*j + 2/5*j**5 - 1. Determine l, given that p(l) = 0.
-1, 0, 1
Factor 4/3 + 8/3*z**3 - 14/3*z - 10/3*z**2.
2*(z - 2)*(z + 1)*(4*z - 1)/3
Let b be 12/(-8 + 222/12). Find c such that b*c + 0 + 0*c**2 - 6/7*c**3 - 2/7*c**4 = 0.
-2, 0, 1
Let y = -356063000/137007 - 330/15223. Let q = y - -2604. Solve -q*m**4 - 6*m**3 - 4/9*m - 14/9*m**5 - 26/9*m**2 + 0 = 0 for m.
-1, -2/7, 0
Let r(s) be the second derivative of 0 - 1/168*s**7 - 7*s - 1/48*s**4 + 0*s**3 + 0*s**2 - 3/80*s**5 - 1/40*s**6. Solve r(l) = 0 for l.
-1, 0
Let r(p) = -p**4 - p**2 + p. Let v = -7 + 11. Let m(o) = -1 + 2*o**3 + 0*o + o**2 + 3*o**4 - 4*o + o**2. Let h(z) = v*r(z) + 2*m(z). Factor h(k).
2*(k - 1)*(k + 1)**3
Let g = -4 + 6. Let x(b) be the first derivative of -2 + 7/4*b**4 + g*b + 3/2*b**2 - 4*b**3. Find s, given that x(s) = 0.
-2/7, 1
Suppose 3*m - m = -2*x, 5*m - 5*x = 20. Let u = 2 + m. What is j in -4*j**2 + 2*j**5 + 2*j**2 - 2*j**3 + 3*j**4 - j**u = 0?
-1, 0, 1
Let c(u) be the first derivative of -u**6/12 - u**5/20 + u**4/8 + u**3/12 + 33. Determine x so that c(x) = 0.
-1, -1/2, 0, 1
Let g(w) = -4*w**2 + 4*w + 6. Let j(m) = 3*m**2 - 4*m - 5. Let d(c) = -5*g(c) - 6*j(c). Factor d(b).
2*b*(b + 2)
Let z(b) be the second derivative of b**4/12 - 11*b**3/3 + 121*b**2/2 + 13*b - 1. Factor z(p).
(p - 11)**2
Let d(r) = -r**4 - r**3 + r**2 - 1. Suppose 0 = -0*w + 3*w + 66. Let h(c) = 10*c**4 + 12*c**3 - 8*c**2 - 5*c + 13. Let t(b) = w*d(b) - 2*h(b). Factor t(v).
2*(v - 1)**3*(v + 2)
Determine g so that 2/7*g**2 + 288/7 - 48/7*g = 0.
12
Suppose -21/2*j - 9/2 - 3/2*j**3 + 17/2*j**2 = 0. What is j?
-1/3, 3
Find s such that 0*s**3 - 2/13*s**4 + 0 + 6/13*s**2 + 4/13*s = 0.
-1, 0, 2
Let m(o) be the first derivative of o**4/2 + 6*o**3 + 24*o**2 + 