(d + 1)*(2*d + 1)**4/2
Let f(s) = -12*s**4 - 48*s**3 - 33*s**2 + 48*s + 45. Let l(r) = 3*r**4 + 12*r**3 + 8*r**2 - 12*r - 11. Let t(b) = -2*f(b) - 9*l(b). Find x, given that t(x) = 0.
-3, -1, 1
Let p(o) be the second derivative of -o**6/6 - o**5/4 + 5*o**4/6 - 7*o. Factor p(d).
-5*d**2*(d - 1)*(d + 2)
Let z(c) be the first derivative of c**4/2 - 4*c**3/3 + c**2 - 21. Factor z(r).
2*r*(r - 1)**2
Solve 7*h**4 + 5*h - h**4 - 6*h**4 - 5*h**2 + 5*h**4 - 5*h**3 = 0 for h.
-1, 0, 1
Let w be -3 - (-32)/(-36) - (-1 + -3). Let k(i) be the first derivative of 0*i**2 + 1/24*i**4 + 1 + w*i**3 + 0*i. Suppose k(s) = 0. Calculate s.
-2, 0
Let h(y) be the third derivative of y**6/60 + y**5/5 + 3*y**4/4 + 4*y**3/3 + 14*y**2. Find b such that h(b) = 0.
-4, -1
Let w(s) be the second derivative of s**7/6 + 23*s**6/30 + s**5 + s**4/3 + s. Factor w(z).
z**2*(z + 1)*(z + 2)*(7*z + 2)
Let s(z) be the second derivative of -z**6/45 + 17*z**5/90 - 17*z**4/27 + 28*z**3/27 - 8*z**2/9 + 24*z. Solve s(t) = 0.
2/3, 1, 2
Suppose -3*j + 3*c + 15 = 0, 5*j - 14*c = -18*c + 7. Factor -4/7*u**2 + 4/7 - 2/7*u**j + 2/7*u.
-2*(u - 1)*(u + 1)*(u + 2)/7
Let a = -2 - -4. Let r(h) = 7*h**4 - 13*h**3 + 12*h**2 - 8*h + 7. Let k(p) = -3*p**4 + 6*p**3 - 6*p**2 + 4*p - 3. Let i(n) = a*r(n) + 5*k(n). Factor i(j).
-(j - 1)**4
Factor -6*o + o**3 + 4*o - 3*o - 10 + 4*o**3 + 10*o**2.
5*(o - 1)*(o + 1)*(o + 2)
Let m(i) be the second derivative of i**9/22680 - i**8/3360 + i**7/1260 - i**6/1080 + i**4/6 - 3*i. Let d(h) be the third derivative of m(h). Factor d(q).
2*q*(q - 1)**3/3
Find o, given that -71*o**3 + 0*o**4 + 22*o**2 + 20*o**4 + 12*o - 2*o**2 + o**4 = 0.
-2/7, 0, 2/3, 3
Let -3/8*s**2 - 3/8 + 3/4*s = 0. What is s?
1
Let x = 24 - 45/2. Find o, given that -1/2*o**4 + 0 + 1/2*o**2 + 3/2*o**3 + 0*o - x*o**5 = 0.
-1, -1/3, 0, 1
Suppose 0 = 4*m - m - 12. Suppose -5*c + 2*c - m*c**3 - c**3 + 2*c**3 - 6*c**2 = 0. What is c?
-1, 0
Solve 6/5*q**3 + 0*q + 4/5*q**2 + 0 + 2/5*q**4 = 0.
-2, -1, 0
Let b(j) be the second derivative of -j**6/1080 + j**5/360 + j**3/3 - j. Let s(z) be the second derivative of b(z). Determine v, given that s(v) = 0.
0, 1
Suppose 3*s = -2*s + 10. Suppose -s + 0*m + m**2 - 2*m + 3 = 0. What is m?
1
Let q(h) = 6*h. Let v be q(3). Factor -5*c**2 + v - 2*c**3 - 4*c**2 - c**2 - 6*c.
-2*(c - 1)*(c + 3)**2
Let 0*o**2 + 14*o + 18*o**2 - 3*o**3 - 41*o = 0. What is o?
0, 3
Let h = -31 - -28. Let v be (((-28)/h)/7)/2. Factor -v*w**2 - 2/3 - 4/3*w.
-2*(w + 1)**2/3
Let r(x) = -3*x**3 - x**2 - x - 1. Let b be r(-1). Let t be -3*(-1 + 1/3). Find q, given that 9*q - 2 - 8*q**2 + 2*q**b - q**t = 0.
2/7, 1
Let a be (-30)/24 + -3 - -7. Let u = -23/2 - -12. Determine z, given that u - 9/4*z - a*z**2 = 0.
-1, 2/11
Let h(i) be the second derivative of -5*i**4/22 + 14*i**3/33 - 3*i**2/11 - 2*i. Factor h(j).
-2*(3*j - 1)*(5*j - 3)/11
Let d = 4 - -1. Suppose 3*t - 3*p - 25 = t, t = p + 10. What is g in g**4 + g**5 - 3*g**d + g**3 - g**2 + g**t = 0?
-1, 0, 1
Let q(z) be the third derivative of 5*z**8/336 - z**7/42 + 3*z**2. Factor q(y).
5*y**4*(y - 1)
Let c = -8 + 10. Let o(a) = -4*a**5 + 15*a**4 - 31*a**3 + 21*a**2 + 11*a + 10. Let h(i) = -i**3 + i**2 + i + 1. Let w(f) = c*o(f) - 22*h(f). Factor w(m).
-2*(m - 1)**4*(4*m + 1)
Factor -3*q - 7*q**2 + 2*q**2 + 4 + 4*q**2.
-(q - 1)*(q + 4)
Let q = 1 + -1. What is x in x**3 - x**4 - 2*x + x + q*x - 2 + 3*x**2 + 0*x**2 = 0?
-1, 1, 2
Let q(l) be the third derivative of l**7/945 - l**6/540 - l**5/270 + l**4/108 + 12*l**2. Factor q(w).
2*w*(w - 1)**2*(w + 1)/9
Let v = -182/3 - -731/12. Factor 1/4*a**4 - v*a**2 + 0 - 1/4*a + 1/4*a**3.
a*(a - 1)*(a + 1)**2/4
Let m(q) be the third derivative of -2*q**7/315 - q**6/90 + q**5/45 + q**4/18 - 9*q**2. Factor m(l).
-4*l*(l - 1)*(l + 1)**2/3
Find h such that 2/17 - 2/17*h**3 + 6/17*h**2 - 6/17*h = 0.
1
Let g(f) be the second derivative of f**7/1680 + f**6/720 - f**3/6 - 2*f. Let t(h) be the second derivative of g(h). Suppose t(p) = 0. Calculate p.
-1, 0
Find c, given that 10/9*c**2 - 4/9*c + 0 + 14/9*c**3 = 0.
-1, 0, 2/7
Factor 12/7 + 15/7*q + 3/7*q**2.
3*(q + 1)*(q + 4)/7
Let h = 5/34 + -103/816. Let b(t) be the second derivative of 0*t**2 + h*t**4 + 0 + 1/24*t**3 - t. Determine q so that b(q) = 0.
-1, 0
Let b be 0/2 - ((-8 - 2) + 6). Let o(t) be the third derivative of 1/480*t**6 + 1/32*t**b + 1/80*t**5 - 4*t**2 + 0 + 0*t + 1/24*t**3. Factor o(a).
(a + 1)**3/4
Let a be ((-27)/(-21) - 2) + 1. Let j be (-6)/9 + 6/9. Factor a*b**2 + j + 2/7*b.
2*b*(b + 1)/7
Let x(v) be the third derivative of v**6/30 - 2*v**5/15 - v**4/6 + 4*v**3/3 + 10*v**2. Find l, given that x(l) = 0.
-1, 1, 2
Suppose 0*x**2 - 8/9*x + 0 + 2/9*x**3 = 0. Calculate x.
-2, 0, 2
Suppose 3*m = -3*s + 9, -4*m - 5*s + 21 = -4*s. Suppose -m = -a - a. Factor -o**a + 0*o**2 + o + 1/2*o**4 - 1/2.
(o - 1)**3*(o + 1)/2
Let s(v) be the first derivative of -v**8/672 - v**7/420 + v**2/2 + 4. Let t(h) be the second derivative of s(h). Factor t(q).
-q**4*(q + 1)/2
Let h(z) be the third derivative of -1/12*z**3 + 5*z**2 + 0 + 0*z - 27/320*z**6 + 1/6*z**4 - 3/32*z**5. Factor h(d).
-(d + 1)*(9*d - 2)**2/8
Let j(x) be the second derivative of 0 + 0*x**3 - 3*x + 1/36*x**4 - 1/6*x**2. Solve j(c) = 0 for c.
-1, 1
Let x(z) = z**2 - z - 4. Suppose 2*i = 1 + 5. Let y be x(i). Solve -7*w**3 - 3*w**2 - y*w - 1 - w + 6*w**3 = 0.
-1
Factor -1/2*z**5 - 73/2*z**3 - 88*z - 86*z**2 - 32 - 7*z**4.
-(z + 1)**2*(z + 4)**3/2
Let t = -68/13 + 1645/312. Let z(l) be the second derivative of 0 + 1/4*l**2 + 1/120*l**6 - t*l**3 + 2*l - 1/16*l**4 + 1/80*l**5. Factor z(d).
(d - 1)**2*(d + 1)*(d + 2)/4
Let r = 0 + -5. Let v = r - -5. What is h in 1/3 - 2/3*h**3 - 1/3*h**4 + v*h**2 + 2/3*h = 0?
-1, 1
Let c(l) be the third derivative of 0*l + 0*l**3 + 0 + 3/10*l**5 + 1/10*l**6 + 0*l**4 + 1/105*l**7 + 5*l**2. Factor c(d).
2*d**2*(d + 3)**2
Let q(c) be the third derivative of -1/210*c**5 + 0*c**4 + 0*c**3 + 0 - 4/735*c**7 + 0*c + 2*c**2 + 1/84*c**6. Suppose q(i) = 0. What is i?
0, 1/4, 1
Suppose 2*n - 2*t - 6 = 0, -2*t - 8 = -4*n + n. Factor 4*g**3 + 0 + g + 3*g**4 + 2 - 5*g**3 - 5*g**n.
(g - 1)**2*(g + 1)*(3*g + 2)
Suppose -4*r = -0*r - 6*r. Let k(z) be the first derivative of 0*z**4 - 3 + 0*z**2 + 3/20*z**5 + r*z**3 + 0*z. Determine a, given that k(a) = 0.
0
Let x(v) be the third derivative of v**5/60 - v**4/3 + 8*v**3/3 + v**2. Find c, given that x(c) = 0.
4
Solve -1/4*q**2 - 1/2*q - 1/4 = 0.
-1
Let v(d) be the third derivative of d**7/315 + d**6/90 - d**4/18 - d**3/9 - 20*d**2. Suppose v(f) = 0. What is f?
-1, 1
Solve 0 + 5/3*f**4 + 5*f**2 + 0*f + 20/3*f**3 = 0 for f.
-3, -1, 0
Suppose 6*h - 8 = 2*h. Let t be (2*3/(-12))/(-1). Find s, given that s**h + 0 - t*s**5 + 0*s**4 + 0*s + 3/2*s**3 = 0.
-1, 0, 2
Let x(j) = -j**3 + 6*j**2 - 4*j - 1. Suppose -4*h + 5 = -3*h. Let c be x(h). Factor 0 + 1/5*r**2 - 1/5*r**3 + 1/5*r**5 - 1/5*r**c + 0*r.
r**2*(r - 1)**2*(r + 1)/5
Let o(z) be the second derivative of z**6/6 + z**5/2 - 5*z**4/12 - 5*z**3/3 - 3*z. Factor o(a).
5*a*(a - 1)*(a + 1)*(a + 2)
Let k(n) be the first derivative of -n**4/2 - 10*n**3/3 - 8*n**2 - 8*n - 5. Suppose k(f) = 0. What is f?
-2, -1
Let a be 33/12 - 3 - 9/(-12). Let x(h) be the first derivative of -1/3*h**3 + 1/4*h**2 + 1 + a*h. Suppose x(r) = 0. Calculate r.
-1/2, 1
Let r = -397 - -400. Find b such that 0*b**r - 4*b - 3/2 - 3*b**2 + 1/2*b**4 = 0.
-1, 3
Let a(j) = 3*j**2 + 12*j - 4. Let t(v) = -9*v**2 - 36*v + 11. Let x(w) = -11*a(w) - 4*t(w). Factor x(k).
3*k*(k + 4)
Let s(p) be the third derivative of -p**7/420 + p**5/120 - 5*p**2. Factor s(h).
-h**2*(h - 1)*(h + 1)/2
Let b(p) be the third derivative of 0*p + 0 + 1/180*p**5 + 1/36*p**4 + 1/18*p**3 - p**2. Solve b(d) = 0 for d.
-1
Suppose 0*k = 3*k + 219. Let n = -655/9 - k. Factor 2/9 + n*i**2 + 4/9*i.
2*(i + 1)**2/9
Let t(v) be the third derivative of -v**7/630 + v**6/120 - v**5/90 - 11*v**2. Factor t(x).
-x**2*(x - 2)*(x - 1)/3
Let j(h) = -h**3 - h**2 + 1. Let s(f) = -2*f**3 + f**2 - 21*f + 17. Let w(z) = 5*j(z) - s(z). What is m in w(m) = 0?
-4, 1
Suppose 4*n + 18 = 5*n. Suppose n*r**4 - 3*r**5 + 6 - 27*r - 42*r**3 + 48*r**2 + 4 - 3 - 1 = 0. What is r?
1, 2
Suppose 0 = -3*h - 2*h - u + 9, -4*h + 6 = 2*u. Factor 3*r - 6*r**2 - 6*r**4 + r + r**5 + 13*r**3 - 2*r**h - 4*r**2.
r*(r - 2)**2