actor 0 + 2/3*b**2 - 2/3*b.
2*b*(b - 1)/3
Let r(c) be the first derivative of -2/35*c**5 + 1 - 2/7*c**2 - 10/21*c**3 + 0*c - 2/7*c**4. Factor r(a).
-2*a*(a + 1)**2*(a + 2)/7
Let n be (-78)/18 + (-2)/(-6). Let x be (-9)/(-6)*n/(-12). Solve -5*m**3 - 5/2*m + 1/2 + 5/2*m**4 + 5*m**2 - x*m**5 = 0 for m.
1
Suppose 2*x - 15 = -n, -1 + 6 = -n. Find h, given that -13*h**3 - h + x*h**3 + 4*h**3 = 0.
-1, 0, 1
Let j(t) be the first derivative of t**6/15 - 12*t**5/25 + 9*t**4/10 - 8*t**3/15 + 6. Find r, given that j(r) = 0.
0, 1, 4
Let l be ((-450)/108)/(((-2)/(-4))/(-1)). Find b, given that -20/3*b**2 + l*b - 5/3 = 0.
1/4, 1
Let l(g) be the third derivative of -g**8/336 + g**7/70 - g**6/60 - g**5/30 + g**4/8 - g**3/6 + g**2 + 1. Factor l(y).
-(y - 1)**4*(y + 1)
Let g(k) = -k**3 - 6*k**2 - k - 4. Let x be g(-6). Suppose -x*b + 3 - 4 = 3*f, -5*b + 3*f = -29. Solve 0 - 2/5*y**2 + 2/5*y**b - 2/5*y + 2/5*y**3 = 0.
-1, 0, 1
Let g be -1 - ((-28)/2)/2. Suppose -3*z - g = -5*z. What is i in -3*i + 0*i - 9*i**3 + 9*i**2 + z*i**4 + 0*i = 0?
0, 1
Let j(y) be the third derivative of -1/30*y**5 + 0*y**3 + y**2 + 0 + 1/12*y**4 + 0*y. Suppose j(q) = 0. Calculate q.
0, 1
Let l(s) = -6*s**2 + 31*s - 31. Let f = 18 + -22. Let g(d) = -2*d**2 + 10*d - 10. Let v(w) = f*l(w) + 14*g(w). Factor v(m).
-4*(m - 2)**2
Suppose 3*f + 2 = 2*b - 5, 0 = -2*f - 2. Suppose 17 = 5*h + b. Factor 0*t**2 - 2/9*t**h - 4/9 + 2/3*t.
-2*(t - 1)**2*(t + 2)/9
Suppose 3*p = 5*p + 46. Let u = 34 + p. Let g(c) = -c**2 - 6*c + 2. Let m(l) = -6*l**2 - 31*l + 9. Let w(j) = u*g(j) - 2*m(j). Factor w(q).
(q - 2)**2
Let u(g) be the second derivative of -g**7/63 + g**6/9 + g**5/5 - 16*g**4/9 - 32*g**3/9 + 39*g. What is x in u(x) = 0?
-2, -1, 0, 4
Let d = 6 - 4. Suppose -2*w + 7*w**d + 4 - 3*w**2 - 6*w**2 = 0. What is w?
-2, 1
Let c(y) be the first derivative of -y**6/33 + 2*y**5/55 + y**4/22 - 2*y**3/33 + 2. Find k, given that c(k) = 0.
-1, 0, 1
Factor 1/6*h**2 + 1/2 + 2/3*h.
(h + 1)*(h + 3)/6
Let w be (-568)/(-288) + 38/(-9) + 4. Solve 19/4*x**3 + 25/4*x**2 + 1 + w*x**4 + 1/4*x**5 + 4*x = 0 for x.
-2, -1
Let p = 338 - 338. Factor p*o**2 + 0 + 2/5*o**4 - 2/5*o**3 + 0*o.
2*o**3*(o - 1)/5
Let i(d) = -d**2 - 5*d + 2. Let n be i(-5). Let c(f) be the second derivative of 0*f**3 + 1/2*f**2 + 0 - 1/12*f**4 + n*f. Determine x, given that c(x) = 0.
-1, 1
Suppose 4*r = g + 1 + 2, 8 = 4*r + 4*g. Let z be r/(-7) + 1532/140. Suppose -z*f - 54/5 - 18/5*f**2 - 2/5*f**3 = 0. What is f?
-3
Let n(l) be the first derivative of -l**5/5 + 3*l**4/4 + 5*l**3/3 - 3*l**2/2 - 4*l + 2. Factor n(r).
-(r - 4)*(r - 1)*(r + 1)**2
Suppose 0 + 2/5*m**3 + 4/5*m - 6/5*m**2 = 0. What is m?
0, 1, 2
Let y(l) be the first derivative of l**4/4 + 2*l**3 + 2*l**2 - 5*l - 7. Let x be y(-5). Solve -2/7*i**3 + x + 2/7*i**2 + 0*i = 0.
0, 1
Solve 2/3*y**2 + 0 - 2/3*y**3 + 4/3*y = 0.
-1, 0, 2
Let i(j) = -j**2 + 7*j + 13. Let w(c) be the third derivative of c**4/6 + c**3 - c**2. Let q(p) = 2*i(p) - 5*w(p). Factor q(u).
-2*(u + 1)*(u + 2)
Suppose 4*m + 8 + 9 = 3*w, 3*w + 3*m - 3 = 0. Determine o, given that 0*o + 3/2*o**4 + 0*o**2 + 0 - 3*o**w = 0.
0, 2
Let i(n) be the first derivative of -2*n**3/3 + 8*n - 19. What is c in i(c) = 0?
-2, 2
Suppose 2*a = -3*a + 15. Solve n**5 + 3*n**a + 3*n**2 + 2*n**5 + 0*n**2 + 9*n**4 + 6*n**3 = 0.
-1, 0
Let o be (-2 + 1)/(2/(-10)). Factor 5*x**2 + 2*x - x**2 - 4*x**2 - o*x**2.
-x*(5*x - 2)
Let s(z) be the third derivative of z**8/320 + z**7/168 - z**6/120 - 5*z**4/24 - 3*z**2. Let k(n) be the second derivative of s(n). Factor k(p).
3*p*(p + 1)*(7*p - 2)
Let j(p) be the third derivative of -p**6/120 - p**5/30 - p**4/24 - 6*p**2. Find n, given that j(n) = 0.
-1, 0
Let g(b) be the first derivative of 1/4*b**4 + 0*b + 2/3*b**3 - 1 + 1/2*b**2. What is x in g(x) = 0?
-1, 0
Let n(g) = -11 - 3*g - 2*g**2 - g**2 + 4*g**2 - 10*g. Let r be n(14). What is o in -o**2 + 0 + 0*o - 1/2*o**r = 0?
-2, 0
Let l(m) be the second derivative of -m**4/30 + m**3/15 + 37*m. Suppose l(t) = 0. What is t?
0, 1
Find j, given that -2/5*j**2 + 3/5 + j = 0.
-1/2, 3
Let n(c) be the third derivative of -c**7/42 + c**6/12 + 5*c**5/4 + 5*c**4/6 - 50*c**3/3 + 11*c**2. Factor n(i).
-5*(i - 5)*(i - 1)*(i + 2)**2
Let q(l) = l**2 + 5*l + 1. Let f(c) = -c. Let b(y) = 2*y**2 - 1. Let n be b(-1). Let v = n + -2. Let h(j) = v*q(j) - 3*f(j). Let h(w) = 0. What is w?
-1
Let c(k) be the third derivative of -k**7/70 - 7*k**6/40 - 7*k**5/10 - k**4 + 35*k**2 + 1. Find t, given that c(t) = 0.
-4, -2, -1, 0
Let r(n) be the third derivative of n**7/1680 - n**6/144 + 7*n**5/240 - n**4/16 - 4*n**3/3 + n**2. Let d(l) be the first derivative of r(l). Factor d(z).
(z - 3)*(z - 1)**2/2
Let d = -4/3 + -33/2. Let l = d + 18. Factor l*f**3 - 1/6*f - 1/6 + 1/6*f**2.
(f - 1)*(f + 1)**2/6
Let w = -9 + 15. Let m be (3/(w/8))/10. Find z such that -2/5*z**2 + m*z + 4/5 = 0.
-1, 2
Let u(g) be the second derivative of -3/20*g**5 + g**4 + 3*g**2 - 5/2*g**3 - 5*g + 0. Factor u(n).
-3*(n - 2)*(n - 1)**2
Let w(c) be the second derivative of 1/84*c**7 + 4*c + 0 + 1/6*c**3 - 3/40*c**5 + 0*c**2 - 1/24*c**4 + 1/60*c**6. Factor w(x).
x*(x - 1)**2*(x + 1)*(x + 2)/2
Let d(r) be the second derivative of -5*r**7/126 - 2*r**6/9 - r**5/6 + 5*r**4/9 + 5*r**3/6 - 47*r. Solve d(a) = 0 for a.
-3, -1, 0, 1
Suppose 5*b + i + 45 = -0*i, i = 3*b + 19. Let c = 12 + b. Determine w so that -8/3*w**2 + 3*w**c - 2*w + 2*w**3 - 1/3 = 0.
-1, -1/3, 1
Let g(o) be the second derivative of o + 1/120*o**5 - 1/6*o**3 + 0*o**4 + 0*o**2 + 0 + 1/720*o**6. Let y(c) be the second derivative of g(c). Factor y(k).
k*(k + 2)/2
Suppose 18 = 5*k + z, 2*z - 1 - 8 = -k. Factor 5/3*t**2 + 4/3 + 8/3*t + 1/3*t**k.
(t + 1)*(t + 2)**2/3
Solve -2/7*x - 2/7*x**2 + 2/7*x**3 + 2/7 = 0.
-1, 1
Let y(u) = u**3 + 6*u**2 + 4*u - 5. Let l be y(-5). Let b be (-9)/(-12)*(-32)/(-60). Factor l + b*x**2 + 2/5*x.
2*x*(x + 1)/5
Let i(c) be the third derivative of -c**2 + 1/48*c**4 + 1/240*c**5 + 0*c**3 + 0 + 0*c. Suppose i(k) = 0. What is k?
-2, 0
Let z(n) = -n**3 - 3*n**2 + 2*n - 5. Let u be z(-4). Factor b + u*b**3 + 6*b**2 - b**4 + b - 9*b**2 - b.
-b*(b - 1)**3
Let q = 810 - 810. Determine v so that 0*v**4 + 2/7*v + 2/7*v**5 + q + 0*v**2 - 4/7*v**3 = 0.
-1, 0, 1
Let f = -6 - -12. Let x = 10 - f. Factor -1/4*b**5 + 1/4 + 5/2*b**2 - 5/4*b - 5/2*b**3 + 5/4*b**x.
-(b - 1)**5/4
Let w(r) = -r**3 - 5*r**2 + 5*r + 3. Let n be w(-6). Let -12*o**3 - 7*o + n*o**2 + 22*o + 10*o + 2*o + 6 = 0. Calculate o.
-1, -1/4, 2
Let u(r) = r**3 - 5*r**2 - 2*r - 8. Let m be u(6). Suppose m = 5*j - 4. Find f, given that -5*f**2 + 5*f**2 + 2*f**j - 2*f**3 = 0.
0, 1
Let z(q) be the first derivative of -3*q**7/70 - 3*q**6/40 - q**5/30 - 3*q**2 - 6. Let b(m) be the second derivative of z(m). Factor b(p).
-p**2*(3*p + 1)*(3*p + 2)
Suppose -k + 85 = 4*k. Let u = k + -15. Factor -2/7*s**3 + 0 + 0*s - 4/7*s**u.
-2*s**2*(s + 2)/7
Let m = -23 + 19. Let q be 2 + 5 + 16/m. Factor 4/3*d**4 - 1/3 - 1/3*d + q*d**2 - 11/3*d**3.
(d - 1)**3*(4*d + 1)/3
Factor 0 + 0*s + 2/5*s**3 + 0*s**2 - 2/5*s**5 + 0*s**4.
-2*s**3*(s - 1)*(s + 1)/5
Let s(y) be the third derivative of -1/120*y**4 + 0 + 0*y + 1/75*y**5 + 5*y**2 + 1/200*y**6 - 1/15*y**3. Factor s(o).
(o + 1)**2*(3*o - 2)/5
Let r(w) = -6*w - 1. Let l(s) = -2*s. Let c(v) = -7*l(v) + 2*r(v). Let d be c(1). Factor d*g - 1/3*g**2 - 1/3*g**3 + 0.
-g**2*(g + 1)/3
Let s(l) be the second derivative of 0*l**3 + 2*l - 1/20*l**6 + 0*l**2 + 0*l**4 + 0 + 3/40*l**5. Factor s(u).
-3*u**3*(u - 1)/2
Suppose 3/2*m**3 - 8 + 8*m**2 + 6*m = 0. Calculate m.
-4, -2, 2/3
Let z(j) be the third derivative of 0 + 1/24*j**4 + 0*j**5 - 3*j**2 - 1/120*j**6 - 1/420*j**7 + 0*j + 1/12*j**3. Factor z(y).
-(y - 1)*(y + 1)**3/2
Let 22/15*m**2 - 2/15*m**4 - 12/5*m + 16/15 + 0*m**3 = 0. What is m?
-4, 1, 2
Suppose -10/7 - 8/7*d**2 - 18/7*d = 0. Calculate d.
-5/4, -1
Let l be (11 - 9)*1/1. Let i(z) be the second derivative of -1/105*z**6 + 1/21*z**3 + 0 + 0*z**l + 1/42*z**4 + 2*z - 1/70*z**5. Let i(q) = 0. Calculate q.
-1, 0, 1
Let s(x) = 12*x**3 + 3*x**2 + 5. Let z(d) = 13*d**3 + 4*d**2 + 6. Let j(a) = 6*s(a) - 5*z(a). Find i, given that j(i) = 0.
0, 2/7
Let y(v) be the third derivative of v**6/30 + 11*v**5/5 + 121*v**4/2 + 2662*v**3/3 - 35*v**2. Factor y(q).
4*(q + 11)**3
Let p = 5 - 5. 