/7*r**4 + 3/7*r**2.
3*r**2*(r + 1)**2/7
Suppose x - 4*g = 29, -2*x = -2*g - g - 43. Suppose -12*l**3 + 4*l**2 - 4*l + 1 - 5*l**4 + 31*l**3 - x*l**3 + 2*l**5 = 0. Calculate l.
-1, 1/2, 1
Let h be (-6)/8*(0 - 4). Let b be 51/(-9) + h + 3. What is f in -f**3 + 1/3*f**2 + f**5 + 0*f + 0 - b*f**4 = 0?
-1, 0, 1/3, 1
Let o(d) be the second derivative of 0 - 1/12*d**4 - 1/3*d**3 + 3*d - 1/2*d**2. Determine a so that o(a) = 0.
-1
Let w = -29 + 35. Let k(a) be the second derivative of -1/120*a**w + 0*a**5 - 1/8*a**2 + 0 + 0*a**3 + 1/24*a**4 - 2*a. Let k(v) = 0. Calculate v.
-1, 1
Find q such that 52/3*q - 4 - 5*q**2 - 50*q**3 + 125/3*q**4 = 0.
-3/5, 2/5, 1
Suppose 2*d = 3*q, q - 5*d = -3*d. Factor 2/5*p**2 + 2/5*p + q.
2*p*(p + 1)/5
Let b be (2 - 69/36)/(5/49). Let y(t) be the third derivative of 0*t - b*t**6 - 7/10*t**5 + 0 + 2*t**4 + t**2 - 4/3*t**3. Factor y(u).
-2*(u + 1)*(7*u - 2)**2
Let l(v) = 4 + 17*v**2 - 4 - 6*v + 2*v. Let o(f) = 9*f**2 - 2*f. Let u(i) = 6*l(i) - 11*o(i). Factor u(x).
x*(3*x - 2)
Factor 2*j - 10 - 8*j**3 + 9*j**2 + j**2 + 3*j + 3*j**3.
-5*(j - 2)*(j - 1)*(j + 1)
Factor -332*y**4 - y**3 + 331*y**4 - y**3.
-y**3*(y + 2)
Let y(t) be the second derivative of -t**7/315 - t**6/45 - 3*t**5/50 - 7*t**4/90 - 2*t**3/45 + 53*t. Let y(f) = 0. Calculate f.
-2, -1, 0
What is s in -1/4*s**5 + 1/4*s + 0*s**3 + 0 + 1/2*s**4 - 1/2*s**2 = 0?
-1, 0, 1
Find q, given that 5*q**2 - 32*q - 77 - q**2 + 141 = 0.
4
Factor -12*d + 0*d**3 - d**3 + 2*d + 11*d.
-d*(d - 1)*(d + 1)
Let 48*z**2 - 72 + 3*z**5 + 118 - 4*z + 8*z**3 - 70 - 24*z**4 - 7*z**5 = 0. What is z?
-6, -1, 1
Let u(o) = -o**2 + 8*o - 7. Let d be u(6). Factor -6*m**2 - 2*m + 2*m**4 + 17*m**2 - d*m**2 - 6*m**3.
2*m*(m - 1)**3
Let f(r) be the third derivative of r**5/120 + r**4/48 + 14*r**2. What is a in f(a) = 0?
-1, 0
Let k(o) be the second derivative of -o**5/20 - o**4/2 - o**3/6 - 3*o**2/2 - 2*o. Let i be k(-6). Factor 0*y**2 + 2/7*y**4 + 0*y**i + 0*y + 0.
2*y**4/7
Let z(f) = f**3 + 6*f**2 + 6*f - 4. Let c be z(-5). Let k be (-1)/3 - 3/c. Factor -2 + k + 0*b**2 + 4*b - 2*b**2.
-2*(b - 1)**2
Let n be 4*(-4)/(16/(-5)). What is s in s**2 + 0*s + s - n*s + 3*s = 0?
0, 1
Let j(b) be the second derivative of 7*b**6/150 - 3*b**5/25 + b**4/20 + b**3/15 - 26*b. Factor j(v).
v*(v - 1)**2*(7*v + 2)/5
Let r(p) be the first derivative of -2*p**5/45 - p**4/9 + 2*p**3/9 + 4*p**2/9 - 8*p/9 + 7. Solve r(m) = 0 for m.
-2, 1
Let p(u) be the second derivative of 0 + 16/3*u**3 + 2*u + 32*u**2 + 1/3*u**4. Suppose p(g) = 0. Calculate g.
-4
Let a = -1/353 - -357/1412. Factor 0*w - 1/2*w**3 + 0 + 1/4*w**2 + a*w**4.
w**2*(w - 1)**2/4
Suppose 4/9*m - 2/9*m**3 - 2/9*m**2 + 0 = 0. What is m?
-2, 0, 1
Suppose 2*h = 3*b + 6 - 14, -3*b - 3*h + 3 = 0. Let z(y) be the first derivative of 2*y**b + 4*y + 3 + 1/3*y**3. Factor z(o).
(o + 2)**2
Let g(z) = -9*z**2 - 6*z + 9. Let k(m) = -8*m**2 - 5*m + 8. Suppose 18*t + 5 = 19*t. Let d(h) = t*g(h) - 6*k(h). Solve d(n) = 0 for n.
-1, 1
Let i(p) be the first derivative of -p**7/168 - p**6/60 - p**5/80 - 4*p + 1. Let n(q) be the first derivative of i(q). Let n(w) = 0. What is w?
-1, 0
Let m = 157/240 - -7/48. Find k such that -2/5*k**2 + m*k + 2/5*k**4 + 0 - 4/5*k**3 = 0.
-1, 0, 1, 2
Suppose 3*p - 14 = -x, -2*p = 3 - 11. Suppose o**3 + 16*o**3 + 8*o**x + 3*o**3 = 0. What is o?
-2/5, 0
Let c(k) be the first derivative of k**5/40 + k**4/6 + k**3/3 - 3*k + 5. Let y(s) be the first derivative of c(s). Suppose y(r) = 0. Calculate r.
-2, 0
Let s = 219 - 217. Factor -2/7*p**4 + 2/7*p**s + 2/7*p - 2/7*p**3 + 0.
-2*p*(p - 1)*(p + 1)**2/7
Let q(d) be the second derivative of d**6/360 - d**5/120 + d**3/6 - 3*d. Let o(u) be the second derivative of q(u). Determine b, given that o(b) = 0.
0, 1
Let p be 1 + -5 + 3 - -3. Solve 2 + 3*s - s**2 - p + 1 - 3 = 0.
1, 2
Let l(r) = 9*r**2 + 5*r. Suppose 2*d = -3*s - 3*d - 16, -s - 3*d - 4 = 0. Let g(h) = 4*h**2 + 2*h. Let b(f) = s*g(f) + 3*l(f). Factor b(k).
-k*(k - 1)
Suppose 0 = 8*h - 6*h. Let s(r) be the second derivative of 1/189*r**7 + h + 1/45*r**5 - 1/9*r**3 + 1/45*r**6 - 1/9*r**2 - 5*r - 1/27*r**4. Factor s(w).
2*(w - 1)*(w + 1)**4/9
Let t(n) be the first derivative of 0*n + 0*n**3 + 0*n**2 + 1/12*n**4 + 1. Find j such that t(j) = 0.
0
Let n be (1 - 13)/(6 - 7). Find t, given that -21*t**3 - 42*t**3 + 34*t**2 - n*t + 26*t**2 = 0.
0, 2/7, 2/3
Let u = 68/411 - -50693/2466. Let x = u - 41/2. Factor -2/9 - x*g**3 + 2/9*g + 2/9*g**2.
-2*(g - 1)**2*(g + 1)/9
Let k be (-2)/(-4)*0/(-40). Factor 1/5*i**2 + k + 1/5*i**3 + 0*i.
i**2*(i + 1)/5
Let u(p) be the third derivative of -p**6/540 + p**4/108 + 3*p**2. Find l, given that u(l) = 0.
-1, 0, 1
Let b(f) be the second derivative of 0 - 1/9*f**3 + 0*f**2 - 5/36*f**4 - 1/20*f**5 - 4*f. Factor b(c).
-c*(c + 1)*(3*c + 2)/3
Let m(k) be the second derivative of -k**6/1260 - k**5/420 - 5*k**3/6 - 6*k. Let g(s) be the second derivative of m(s). Factor g(c).
-2*c*(c + 1)/7
Factor -4*m - 5 - 8*m**2 + 13 + 3*m**3 + m**3 + 0*m**3.
4*(m - 2)*(m - 1)*(m + 1)
Let a = 125/4 - 31. Factor a*g**3 + 1/4 + 3/4*g + 3/4*g**2.
(g + 1)**3/4
Let k be (2 - 3)/(2/(-6)). Find r such that -3*r**3 + 2*r**3 + 4*r - 3*r + 0*r**k = 0.
-1, 0, 1
Let q(n) = -n + 10. Let s be q(8). What is j in -2*j - 3 - 3*j**s + 2*j**4 - 6*j**3 + 3 + 9*j**2 = 0?
0, 1
Factor 6*b**4 + 4*b**5 - 4*b**4 - 9*b**5 + 3*b**5.
-2*b**4*(b - 1)
Let t(x) be the second derivative of x**6/195 - 2*x**5/65 + x**4/26 - 3*x. Let t(u) = 0. Calculate u.
0, 1, 3
Let g = 9 - 51. Let u be (g/(-24))/((-2)/(-6)). Factor p + 0 - 6*p**2 + u*p**3 + 49/4*p**4.
p*(p + 1)*(7*p - 2)**2/4
Suppose 9*k - 5*k - 24 = 0. Let w(y) be the third derivative of 0 - 1/240*y**5 + y**2 + 0*y + 1/96*y**4 + 1/24*y**3 - 1/480*y**k. Solve w(l) = 0.
-1, 1
Suppose -18*a**3 - 36*a**2 - 12*a + 34*a**3 + 5*a**3 = 0. What is a?
-2/7, 0, 2
Factor -25*a**3 + 3*a + 14*a + 9*a**3 - 10*a**2 - 8 + 17*a**3.
(a - 8)*(a - 1)**2
Let a(c) be the third derivative of c**5/450 - c**4/90 + c**3/45 - c**2. Factor a(d).
2*(d - 1)**2/15
Let z(l) be the first derivative of -l**5/10 + l**4/8 - l**3/24 - 4*l + 5. Let j(c) be the first derivative of z(c). Factor j(n).
-n*(2*n - 1)*(4*n - 1)/4
Let r(t) be the third derivative of -t**7/840 + t**6/160 - t**5/240 - t**4/32 + t**3/12 - t**2. Factor r(s).
-(s - 2)*(s - 1)**2*(s + 1)/4
Let t(j) be the third derivative of 0*j**3 - 1/30*j**6 + 0 + 1/126*j**7 + 2*j**2 + 1/20*j**5 + 0*j - 1/36*j**4. Suppose t(m) = 0. Calculate m.
0, 2/5, 1
Factor -2/13*g**3 + 0 + 4/13*g**2 + 0*g.
-2*g**2*(g - 2)/13
Let k(o) be the third derivative of -o**6/30 + o**4/6 + 10*o**2. Factor k(g).
-4*g*(g - 1)*(g + 1)
Let m be 0 - 0 - (-7)/1. Suppose -3*j - 1 = -m. Determine n, given that -2*n + n - n**2 + j*n = 0.
0, 1
Let k(j) be the first derivative of -j**4/6 + 2*j**3/3 - j**2 + 2*j/3 + 2. Determine i so that k(i) = 0.
1
Factor -2/13*b**5 + 0*b**2 - 2/13*b + 0*b**4 + 0 + 4/13*b**3.
-2*b*(b - 1)**2*(b + 1)**2/13
Let h(b) be the third derivative of b**6/120 + 2*b**5/15 + 5*b**4/24 + b**3/6 + 3*b**2. Let t(s) = s**3 + s**2 - 1. Let o(p) = 2*h(p) + 6*t(p). Factor o(l).
2*(l + 1)*(l + 2)*(4*l - 1)
Let f(g) be the first derivative of -g**6/360 - g**5/480 + 4*g**3/3 - 3. Let j(d) be the third derivative of f(d). Factor j(l).
-l*(4*l + 1)/4
Let l(g) be the first derivative of -1/5*g**5 + 5 + 0*g - 1/8*g**2 - 1/3*g**3 - 1/24*g**6 - 3/8*g**4. Factor l(y).
-y*(y + 1)**4/4
Let m = -1 - -4. Suppose 4*w = -5*v + 25, 0 = m*w - 3*v - 0*v + 15. Suppose 3*r**3 + w*r**2 + 2*r**2 - r**4 + 2*r**4 = 0. What is r?
-2, -1, 0
Let k = -4 + 7. Suppose -i - 10 = -k*i. Factor 1/2*j**i - 1/2*j**4 - j**3 + j**2 - 1/2 + 1/2*j.
(j - 1)**3*(j + 1)**2/2
Let y(f) be the first derivative of -1/6*f**3 - 3/10*f**5 + 0*f - 1/12*f**6 + 0*f**2 - 3/8*f**4 + 1. Factor y(q).
-q**2*(q + 1)**3/2
Let m be -3 + (2 - -1) + 0. Determine p, given that -3/4*p**4 + m*p + 0 - 3/4*p**2 + 3/2*p**3 = 0.
0, 1
Let c(v) be the third derivative of -2*v**2 + 0*v + 1/210*v**7 - 1/60*v**5 + 0 + 0*v**3 + 1/112*v**8 - 1/40*v**6 + 0*v**4. Factor c(i).
i**2*(i - 1)*(i + 1)*(3*i + 1)
Suppose -3*f**2 - 7*f + 3*f**3 + f + 1 - 1 = 0. Calculate f.
-1, 0, 2
Let q be ((-118)/(-30) - 4)/(-1). Let t(n) be the second derivative of 0 - n - 1/30*n**4 + 0*n**2 - q*n**3. Suppose t(r) = 0. Calcul