*k**3 + k**2 = 0. Calculate k.
-2, -1, 0
Let g(u) be the third derivative of -u**8/48 - u**7/42 + u**6/60 - 13*u**2. Solve g(j) = 0.
-1, 0, 2/7
Let w(q) be the second derivative of 3*q**6/10 + 3*q**5/10 - 9*q**4/4 + 6*q**2 + 6*q. Factor w(t).
3*(t - 1)**2*(t + 2)*(3*t + 2)
Factor -2/3*t**3 + 4/9 - 8/9*t**2 + 2/9*t.
-2*(t + 1)**2*(3*t - 2)/9
Let o be -203*12/(-308) - (-5)/(-1). Let 2/11*d**2 + o - 16/11*d = 0. What is d?
4
Suppose 2*s + 1 = -1. Let o be s/5*15/(-9). Find p, given that -o*p - 2/3*p**2 + 2/3 + 1/3*p**3 = 0.
-1, 1, 2
Let n = -300757 + 5412271/18. Let a = n - -151/2. Suppose -2/9*t**2 + 0 + a*t = 0. Calculate t.
0, 1
Factor 12/7*c - 12/7 + 3/7*c**2 - 3/7*c**3.
-3*(c - 2)*(c - 1)*(c + 2)/7
Let a(i) = 2*i + 12. Let j be a(-5). Let m(o) be the second derivative of 1/36*o**4 + 1/18*o**3 + 0 - 2*o + 0*o**j. Find q such that m(q) = 0.
-1, 0
Let l(a) be the first derivative of 1/6*a**6 + 0*a**2 - 1/4*a**4 - 1/3*a**3 + 0*a + 1 + 1/5*a**5. Suppose l(b) = 0. What is b?
-1, 0, 1
Let k(b) be the first derivative of -3*b**5/5 + 3*b**3 - 3*b**2 - 8. Factor k(d).
-3*d*(d - 1)**2*(d + 2)
Let l(d) be the third derivative of d**5/180 - 23*d**4/72 + 11*d**3/9 - d**2 - 2. Factor l(m).
(m - 22)*(m - 1)/3
Suppose -2/3*f**2 + 0 + 10/3*f**3 - 2*f**4 - 2/3*f = 0. Calculate f.
-1/3, 0, 1
Factor -24*o**2 - 16*o**3 + 4*o**4 - 21*o**3 + 41*o**3.
4*o**2*(o - 2)*(o + 3)
Let s(i) be the second derivative of -2*i**7/21 + 2*i**6/45 + i**5/3 - i**4/9 - 4*i**3/9 + 3*i. Find a, given that s(a) = 0.
-1, -2/3, 0, 1
Let r(g) be the third derivative of 0 + 3*g**2 + 1/4*g**4 + 1/15*g**5 - 1/35*g**7 - 1/168*g**8 + 1/3*g**3 + 0*g - 1/30*g**6. Find m such that r(m) = 0.
-1, 1
Let w(r) be the second derivative of 1/25*r**5 - 2/15*r**3 + 2/5*r**2 - 9*r - 1/150*r**6 + 0 - 1/20*r**4. Find x such that w(x) = 0.
-1, 1, 2
Let p(j) be the second derivative of -3*j - j**3 + 0 - 3/4*j**4 - 1/2*j**2. Factor p(y).
-(3*y + 1)**2
Let d = 0 - -5. Factor 5*s**2 + 6*s**3 - 3*s**4 - 3*s**2 - d*s**2.
-3*s**2*(s - 1)**2
Let t(b) = -3*b**4 + 3*b**3 + 5*b**2 - 5*b - 2. Let h(i) = -2*i**4 + 2*i**3 + 5*i**2 - 5*i - 3. Let r(f) = 2*h(f) - 3*t(f). Determine a so that r(a) = 0.
-1, 0, 1
Factor 0 + 1/6*j - j**2 + 5/6*j**3.
j*(j - 1)*(5*j - 1)/6
Let i be (0 + -7)*(-5 + 12)/(-35). Determine y so that i*y**4 - 1/5 + 2/5*y**3 - 6/5*y**2 + 3/5*y**5 - y = 0.
-1, -1/3, 1
Let v(r) be the first derivative of -r**4/6 + 4*r**3/3 - 4*r**2 + 16*r/3 - 23. Determine x so that v(x) = 0.
2
Solve -32 - 25*p**4 + 212*p**3 - 32*p**3 - 296*p**2 + 176*p - 11*p**4 = 0.
1/3, 2/3, 2
Let c = 5 - 0. Suppose -c*t = -t. Factor -1/2*q + 3/2*q**2 - 3/2*q**3 + t + 1/2*q**4.
q*(q - 1)**3/2
Let y(l) be the second derivative of 49*l**6/10 + 483*l**5/10 + 141*l**4 + 124*l**3 + 48*l**2 - 27*l. Factor y(i).
3*(i + 2)*(i + 4)*(7*i + 2)**2
Let x be (-6)/(-10) - (-14)/10. What is k in 0 - k + 1/2*k**x = 0?
0, 2
Let f(r) be the second derivative of -r**5/4 - 65*r**4/12 - 40*r**3 - 90*r**2 - 11*r. Suppose f(a) = 0. What is a?
-6, -1
Suppose -21*y + 23*y = l - 3, -2*y + 9 = 3*l. Solve 2/9*m**2 + 0*m + y - 4/3*m**3 - 8/9*m**5 + 2*m**4 = 0 for m.
0, 1/4, 1
Let y = -325/2 - -163. Factor y*d**2 - 2/3 - 2/3*d.
(d - 2)*(3*d + 2)/6
Let w(t) = 7 + 5*t - 1 - 8 - t**2 + 0*t**2. Let h be w(4). Factor 2/3*u**h + 8/3*u - 8/3*u**3 - 2/3.
-2*(u - 1)*(u + 1)*(4*u - 1)/3
Let j(z) be the second derivative of 0*z**3 + 1/56*z**7 + 0*z**2 - 9*z + 0*z**6 + 0 + 0*z**4 - 3/80*z**5. What is d in j(d) = 0?
-1, 0, 1
Let d(y) = -4*y**5 - 4*y**4 + 36*y**3 + 4*y**2 - 60*y + 4. Let v(a) = -8*a**5 - 7*a**4 + 71*a**3 + 7*a**2 - 121*a + 7. Let f(q) = -7*d(q) + 4*v(q). Factor f(t).
-4*t*(t - 2)**2*(t + 2)**2
Suppose 0 = -g + 4 - 1. Let p(r) be the second derivative of 0*r**g + 1/40*r**5 + 2*r - 1/24*r**4 + 0*r**2 + 0. Factor p(x).
x**2*(x - 1)/2
Let i(v) = -2*v - 4. Let b be i(-4). Suppose -b = -3*r + 11. Find j, given that 2*j**3 + 0*j**4 - 2*j**4 - j**3 + j**r = 0.
0, 1
Factor -2/3*o + 0 - 2/3*o**2.
-2*o*(o + 1)/3
Let j = -2/3 + 5/6. Let p(y) be the second derivative of -j*y**3 + 0*y**4 - 3*y + 0 + 0*y**2 + 1/20*y**5. Factor p(l).
l*(l - 1)*(l + 1)
Factor 4/9*y + 4/9 - 4/9*y**2 - 4/9*y**3.
-4*(y - 1)*(y + 1)**2/9
Let t be (0/3)/(0 - -1). What is o in t*o + o**5 + 4*o**3 - 4*o**2 + 3*o**3 - 4*o**4 - o**3 + o = 0?
0, 1
Let w be (-56)/(-90) + 10/(-25). Let z(v) be the first derivative of w*v**3 + 0*v + 1 - 1/12*v**4 - 1/6*v**2. Factor z(l).
-l*(l - 1)**2/3
Let n(o) be the first derivative of 0*o**2 - 3 - 1/15*o**3 - 4*o - 1/12*o**4. Let d(h) be the first derivative of n(h). Suppose d(x) = 0. What is x?
-2/5, 0
Let f(b) be the first derivative of 2/3*b**3 + 1/6*b**4 + 2 + 3*b + b**2. Let a(c) be the first derivative of f(c). Let a(z) = 0. Calculate z.
-1
Let q(l) be the first derivative of -l**6/63 + 2*l**5/105 + 3*l**4/14 + 22*l**3/63 + 4*l**2/21 + 32. Factor q(p).
-2*p*(p - 4)*(p + 1)**3/21
Let s(j) be the first derivative of -4*j**5/5 + j**4 + 8*j**3/3 + 3. Factor s(t).
-4*t**2*(t - 2)*(t + 1)
Let b(v) be the third derivative of 17/480*v**6 + 0 - 1/6*v**3 + 1/80*v**5 - 1/12*v**4 + 1/448*v**8 - 3*v**2 + 13/840*v**7 + 0*v. Factor b(q).
(q + 1)**3*(q + 2)*(3*q - 2)/4
Let l(v) be the third derivative of -1/270*v**5 + 4*v**2 + 0*v**3 + 1/108*v**4 + 0 + 0*v. Factor l(k).
-2*k*(k - 1)/9
Find r such that 1/6*r + 1/6*r**3 + 0 - 1/3*r**2 = 0.
0, 1
Let a(v) = v**3 + 5*v**2 + v + 7. Let d be a(-5). Suppose -1/3*f + 1/3*f**d + 1/3*f**3 - 1/3*f**4 + 0 = 0. What is f?
-1, 0, 1
Suppose -5*r - 12 = -7*r. Factor 41*w + 7*w - 2*w**4 - 44*w**2 + 22*w**3 - 18 - r*w**3.
-2*(w - 3)**2*(w - 1)**2
Factor 3/5*g**2 + 11/5*g + 6/5.
(g + 3)*(3*g + 2)/5
Let i(c) be the first derivative of 1/6*c**3 - 1/2*c + 1/4*c**2 - 3 - 1/8*c**4. Find a, given that i(a) = 0.
-1, 1
Factor -6/5*m - 2*m**3 + 2/5*m**4 + 0 + 14/5*m**2.
2*m*(m - 3)*(m - 1)**2/5
Let f(k) = -k - 1. Let r be f(-2). Let 2*j**5 - 2*j**4 + 2*j**2 + r - 2 - 2*j**3 + 1 = 0. Calculate j.
-1, 0, 1
Let 1/8*w**2 + 3/8*w**3 - 3/8*w + 1/8*w**4 - 1/4 = 0. What is w?
-2, -1, 1
Let r(o) be the second derivative of -o**6/165 - o**5/22 - 4*o**4/33 - 4*o**3/33 - 7*o. Factor r(f).
-2*f*(f + 1)*(f + 2)**2/11
Suppose 3*a = 10 - 4. Let r(z) be the second derivative of -2*z - 7/6*z**4 - 5/3*z**3 + 0 + 2*z**a. Factor r(j).
-2*(j + 1)*(7*j - 2)
Let p(q) be the first derivative of q**8/168 - 2*q**2 - 3. Let a(f) be the second derivative of p(f). Find c, given that a(c) = 0.
0
Solve y**4 - 1/2*y**3 + 1/2*y**5 + 0*y - y**2 + 0 = 0.
-2, -1, 0, 1
Let o(v) = -1. Let y(g) = -405*g**3 + 360*g**2 - 80*g - 4. Let z(u) = -4*o(u) + y(u). What is x in z(x) = 0?
0, 4/9
Let j(u) be the second derivative of u**7/14 - u**6/10 - 9*u**5/20 + 5*u**4/4 - u**3 + 3*u. Factor j(d).
3*d*(d - 1)**3*(d + 2)
Suppose -6*d + 3*d = 0. Suppose d = k - 5*z + 16, -z + 0*z = k - 8. Determine o, given that 3 - 21/2*o**k + 27/2*o**3 + 15/2*o**2 - 27/2*o = 0.
-1, 2/7, 1
Let n(z) be the second derivative of z**7/189 - 2*z**6/135 + z**4/27 - z**3/27 + 7*z. Find w, given that n(w) = 0.
-1, 0, 1
Let p(m) = m**2. Let q = -7 + 9. Let u(c) = -4*c**2 - 6*c - 4. Let n(b) = q*p(b) + u(b). Let n(a) = 0. What is a?
-2, -1
Let p(n) be the second derivative of 5*n**4/12 + 10*n**3/3 - 8*n. Factor p(i).
5*i*(i + 4)
Let r be ((-216)/210)/9 + (-2)/(-5). Find z, given that 0 - 10/7*z**2 - 2*z**4 - 4/7*z**5 - r*z - 18/7*z**3 = 0.
-1, -1/2, 0
Let m(l) be the second derivative of -2*l**7/35 - 7*l**6/50 + 3*l**5/50 + 2*l**4/5 + l**3/5 - 3*l**2/10 - l. Let m(o) = 0. What is o?
-1, 1/4, 1
Let d(s) be the second derivative of -s**6/60 - 3*s**5/40 - s**4/8 - s**3/12 + 3*s. Factor d(b).
-b*(b + 1)**3/2
Let o(a) = -a**3 - a**2 + a - 1. Let p(h) = 7*h**3 + 3*h**2 - 5*h + 5. Let f(m) = 5*o(m) + p(m). What is j in f(j) = 0?
0, 1
Let i(c) = 4*c**2 - c - 1. Let x be i(-1). Determine b so that 3*b - 5*b**3 + b**x + 2*b**3 + 5*b**4 - 3*b**2 - 3*b**4 = 0.
-1, 0, 1
Let l(x) = x**4 + 6*x**3 + 5*x**2 + 8. Let h(b) = b**3 + b**2 + 1. Let r(m) = 40*h(m) - 5*l(m). Factor r(k).
-5*k**2*(k - 3)*(k + 1)
Suppose 4*u - 10 = -2*a, 3*u + 7*a = 3*a + 10. Let z be 2 + (0/u)/1. Factor z - 6*b + 0*b + 3*b + b**2.
(b - 2)*(b - 1)
Determine q, given that -2*q**3 - 36 + 17 + 21 - 2*q**2 + 2*q = 0.
-1, 1
Let o be 4/18*30/40. Let c(q) be the third derivative of -