9/6720 - x**8/6720 - x**7/840 + x**5/60 - x**2. Let r(u) be the third derivative of k(u). Solve r(t) = 0 for t.
-2/3, 0, 1
Let i be 6/(-18)*3/(-3). What is d in -1/3*d**5 - 1/3*d**4 + 0*d + i*d**3 + 1/3*d**2 + 0 = 0?
-1, 0, 1
Let o(s) be the first derivative of 1/5*s**2 - 2/15*s**3 + 4 + 0*s. Solve o(d) = 0.
0, 1
Find c, given that -2*c + 2/5*c**2 + 8/5 = 0.
1, 4
Let v(j) = -j**3 - 89*j**2 - 175*j - 73. Let a(b) = b**3 + 45*b**2 + 87*b + 37. Let r(z) = -7*a(z) - 3*v(z). Solve r(g) = 0 for g.
-10, -1
Let w(s) be the third derivative of -1/15*s**6 + 1/3*s**3 + s**2 + 0*s + 1/105*s**7 + 0 - 1/3*s**4 + 1/5*s**5. Determine t, given that w(t) = 0.
1
Let c = 68/415 - -3/83. Factor -c*s**4 + 0*s + 0 + 1/5*s**2 + 1/5*s**3 - 1/5*s**5.
-s**2*(s - 1)*(s + 1)**2/5
Let d(r) be the third derivative of r**5/150 + r**4/20 - 4*r**3/15 - 9*r**2. Suppose d(m) = 0. What is m?
-4, 1
Let q(i) be the third derivative of i**6/720 - i**4/48 + i**3/6 - 2*i**2. Let a(b) be the first derivative of q(b). Factor a(u).
(u - 1)*(u + 1)/2
Determine c, given that 3/8*c**4 + 3/8*c**3 + 0*c + 1/8*c**2 + 0 + 1/8*c**5 = 0.
-1, 0
Let q(l) be the first derivative of 6*l**5/5 - 9*l**4/2 + l**3/2 + 9*l**2 + 6*l - 6. Factor q(h).
3*(h - 2)**2*(2*h + 1)**2/2
Let k(q) be the first derivative of q**4/18 - q**3/9 - 2*q**2/3 + 2*q + 3. Let s(l) be the first derivative of k(l). Suppose s(d) = 0. What is d?
-1, 2
Let c(u) be the third derivative of -u**7/5040 - u**6/1440 + u**5/120 - u**4/24 + 2*u**2. Let x(b) be the second derivative of c(b). Factor x(w).
-(w - 1)*(w + 2)/2
Let c(x) be the first derivative of 2/7*x**4 + 10/21*x**3 + 2/7*x**2 - 5 + 0*x + 2/35*x**5. Suppose c(n) = 0. Calculate n.
-2, -1, 0
Let k(w) be the first derivative of -2*w**3/21 - 6*w**2/7 - 18*w/7 - 17. Let k(x) = 0. Calculate x.
-3
Let l(y) be the second derivative of -y**8/13440 - y**7/2520 - y**6/1440 - y**4/6 + 2*y. Let z(d) be the third derivative of l(d). Let z(x) = 0. Calculate x.
-1, 0
Let f(v) be the first derivative of v**4/2 + 5*v**3/3 - 3*v**2/2 - 3*v - 1. Let m(c) = c**3 + c**2 - c - 1. Let d(w) = f(w) - 3*m(w). Factor d(z).
-z**2*(z - 2)
Suppose 4*j - 4*l = l + 18, 0 = -3*j + 2*l + 10. Let b(a) be the second derivative of 2*a - 1/50*a**5 + 0*a**4 + 0*a**j + 1/75*a**6 + 0 + 0*a**3. Factor b(s).
2*s**3*(s - 1)/5
Let r(v) = v - 4. Let h be r(6). Suppose 0*m = h*m - 4. Factor 8 - 2*y**3 - 4*y**m + 0*y**2 - 16*y + 14*y**2 + 0*y**3.
-2*(y - 2)**2*(y - 1)
Let w(c) be the second derivative of c**7/56 + 17*c**6/120 + 37*c**5/80 + 13*c**4/16 + 5*c**3/6 + c**2/2 + 9*c. Factor w(a).
(a + 1)**3*(a + 2)*(3*a + 2)/4
Let c(j) = 2*j**2 - 18*j. Let m(s) = -s**2 + 19*s. Let u(r) = -4*c(r) - 3*m(r). Factor u(a).
-5*a*(a - 3)
Let q be ((-2)/30)/(30/(-75)). Let t(j) be the first derivative of -q*j**2 + 0*j - 1/12*j**4 - 2/9*j**3 + 1. Factor t(o).
-o*(o + 1)**2/3
Let s(u) = -4*u**2 - 3*u + 27. Let k(o) = 6*o**2 + 4*o - 40. Let i(x) = -5*k(x) - 8*s(x). Suppose i(q) = 0. Calculate q.
-4, 2
Let i(h) = 4*h**2 - 18*h + 14. Let d(o) = o**3 - o**2 - o + 1. Let y be 8/2 - 6/1. Let z(f) = y*i(f) + 28*d(f). Suppose z(p) = 0. What is p?
0, 2/7, 1
Let d(p) be the third derivative of p**7/420 + p**6/40 + 3*p**5/40 + 14*p**2. Factor d(x).
x**2*(x + 3)**2/2
Let w(f) be the first derivative of 0*f + 1/2*f**4 + 2 - 10/3*f**3 + 2*f**2 + 2*f**5 - f**6. Find r, given that w(r) = 0.
-1, 0, 2/3, 1
Suppose 10*h - 2 = -2. Let 4/3*j**3 + h*j**2 + 0 + 0*j + 14/3*j**4 + 10/3*j**5 = 0. Calculate j.
-1, -2/5, 0
Let z(v) = 5*v**5 - 3*v**4 + 8*v**3 + 18*v**2 + 8*v. Let u(d) = d**5 + d**3 + d**2. Let q(h) = 6*u(h) - z(h). Find r, given that q(r) = 0.
-2, -1, 0, 2
Let f(r) be the second derivative of -1/10*r**6 + 3/28*r**7 + 0*r**2 + 1/6*r**4 - 11/40*r**5 - 3*r + 1/3*r**3 + 0. Determine i, given that f(i) = 0.
-2/3, 0, 1
Let l(m) be the second derivative of -3*m**7/14 - 7*m**6/5 - 33*m**5/10 - 3*m**4 + m**3/2 + 3*m**2 - 4*m. Suppose l(c) = 0. What is c?
-2, -1, 1/3
Let a(l) = -19*l**3 - 19*l**2 - 7*l + 19. Let x(u) = -u - 6*u**2 + 9 - u**2 - 2*u - 9*u**3 - 2*u**2. Let m(c) = -6*a(c) + 13*x(c). Factor m(w).
-3*(w - 1)*(w + 1)**2
Let d(x) be the first derivative of 3*x**6 - 42*x**5/5 + 7*x**4/2 + 34*x**3/3 - 16*x**2 + 8*x + 16. Suppose d(a) = 0. What is a?
-1, 2/3, 1
Let p(l) = l**3 + 2*l**2 - l + 2. Let u be p(0). Let f(j) be the first derivative of 0*j + 1/4*j**4 + 1/2*j**2 - 2/3*j**3 - u. Factor f(t).
t*(t - 1)**2
Let r = 325/4 + -81. Let x(t) be the second derivative of 1/60*t**6 - r*t**3 - 1/2*t**2 + 2*t + 0 + 1/24*t**4 + 3/40*t**5. Factor x(q).
(q - 1)*(q + 1)**2*(q + 2)/2
Let b = 79/15 - 21/4. Let r(f) be the third derivative of 4*f**2 + 0 + b*f**6 - 1/12*f**4 - 1/30*f**5 + 1/105*f**7 + 0*f**3 + 0*f. Find o such that r(o) = 0.
-1, 0, 1
Let r(f) be the third derivative of f**8/168 + f**7/105 + 23*f**2. Factor r(j).
2*j**4*(j + 1)
Suppose -4*o + 5*b + 20 = 0, 3*o + 5*b = 3*b - 8. Solve o*h + 0 - 1/3*h**3 + 0*h**2 = 0.
0
Let j(o) be the first derivative of -o**4/2 + 16*o**3/3 - 16*o**2 + 9. Find m such that j(m) = 0.
0, 4
Let h be -7*(2 + -1) + 0. Let j be 4/h*(-14)/20. Factor -2/5*b**2 + j + 0*b.
-2*(b - 1)*(b + 1)/5
Suppose 0*m**3 + 4/5*m**2 + 2/5*m**5 - 4/5*m**4 - 2/5*m + 0 = 0. Calculate m.
-1, 0, 1
Let b = 764/5 - 152. Factor -b*k**2 - 4/5*k**4 + 1/5*k**5 + 1/5*k + 6/5*k**3 + 0.
k*(k - 1)**4/5
Let v be (9 - 15)*2/(-6). Suppose -5*m + 5*i = v*i + 4, 12 = 4*i. Factor 3/2*w + 1/2*w**2 + m.
(w + 1)*(w + 2)/2
Let q(p) = p**2. Let a be q(-1). Let n(r) be the first derivative of a + 1/12*r**3 + 1/8*r**2 + 0*r. Determine g so that n(g) = 0.
-1, 0
Let d(l) be the second derivative of -l**6/30 + l**5/15 + l**4/6 - 2*l**3/3 + 11*l**2/2 + 3*l. Let q(p) be the first derivative of d(p). Factor q(v).
-4*(v - 1)**2*(v + 1)
Let w(q) be the first derivative of 0*q + 8/3*q**3 + 5 + 4*q**2 + 1/2*q**4. Determine t, given that w(t) = 0.
-2, 0
Let o(a) = -a**3 - 18*a**2 + 20*a + 24. Let h be o(-19). Let j be -5 + 20/h - -1. Determine w, given that j - 3/2*w**3 + 0*w**2 + 0*w = 0.
0
Suppose -2*c = -5*c + 9. Factor -f + 4 - 4 + f**c.
f*(f - 1)*(f + 1)
Suppose 6*o + 0 - 12 = 0. Let i(s) be the second derivative of 2*s - 1/2*s**o + 0 + 1/3*s**3 - 1/12*s**4. Factor i(h).
-(h - 1)**2
Solve 4/7*j**5 + 0*j**4 - 20/7*j**3 + 0*j**2 + 0 + 16/7*j = 0.
-2, -1, 0, 1, 2
Solve 15/2*z + 15*z**3 - 15*z**2 + 3/2*z**5 - 15/2*z**4 - 3/2 = 0.
1
Let 0*q + 0 + 0*q**2 - 9/5*q**4 + 3/5*q**5 + 6/5*q**3 = 0. What is q?
0, 1, 2
Let o(b) be the first derivative of -4*b**6/21 - 26*b**5/35 - 15*b**4/14 - 2*b**3/3 - b**2/7 + 1. Factor o(t).
-2*t*(t + 1)**3*(4*t + 1)/7
Let f(l) be the third derivative of -l**8/672 + l**7/105 - l**6/60 - 3*l**2. Factor f(g).
-g**3*(g - 2)**2/2
Let j = -70 + 212/3. Suppose -7*z + 2*z + 10 = 0. Factor -1/3 - 1/3*d**z - j*d.
-(d + 1)**2/3
Let a be 5/(-2)*(-8)/10. Let d(k) be the first derivative of -3 + 0*k - 1/18*k**4 + 0*k**3 + 1/9*k**a. Suppose d(t) = 0. Calculate t.
-1, 0, 1
Let c = -1 + 1. Let s be -1 - (-7 + c + 2). Determine l, given that -l - 3*l + 2 - 2*l**2 - s = 0.
-1
Let g(d) be the first derivative of d**5/120 - d**4/24 + d**3/12 + 3*d**2/2 - 2. Let y(v) be the second derivative of g(v). Factor y(z).
(z - 1)**2/2
Let q(z) be the third derivative of -z**5/12 - 25*z**4/24 - 2*z**2. Let q(i) = 0. Calculate i.
-5, 0
Let n(w) = -12*w + 9. Let x(t) = -t**2 - 23*t + 17. Let l(y) = 7*n(y) - 3*x(y). Factor l(i).
3*(i - 4)*(i - 1)
Let o = 11 - 11. Let v(r) be the second derivative of 1/24*r**4 + 1/30*r**6 + 7/80*r**5 - r - 1/24*r**3 + 0 + o*r**2. Factor v(d).
d*(d + 1)**2*(4*d - 1)/4
Let b be (10 + -4)*8/12. Suppose 3*m**2 - 8 - b*m - 2*m + 11 = 0. What is m?
1
What is i in -51/4*i**2 + 55/4*i**4 + 21/4*i**5 - 7*i + 7/4*i**3 - 1 = 0?
-2, -1, -1/3, -2/7, 1
Suppose -33 = -2*j - l, 0 = j - l + 4*l - 24. Let c be 10/3*18/j. Factor 2*s**3 - c*s**2 + 8*s + 0*s**3 - 8*s.
2*s**2*(s - 2)
Factor 0 + 0*h + 0*h**2 - 2/17*h**3.
-2*h**3/17
Let b(x) be the second derivative of x**7/12 + 37*x**6/60 + 73*x**5/40 + 67*x**4/24 + 7*x**3/3 + x**2 - 7*x. Determine d, given that b(d) = 0.
-2, -1, -2/7
Let q be (8/(-3))/2*(-33)/154. Find b such that 4/7*b**2 - 4/7*b**4 + q*b - 2/7*b**5 + 0*b**3 + 0 = 0.
-1, 0, 1
Let k = 4194/2615 + -2/523. Let s(b) be the first derivative of -1 - 3/5*b**4 - 2/25*