*g**3/3 + 3. Let v(k) be the third derivative of a(k). Let v(b) = 0. Calculate b.
-1, 0
Let r(t) = t**2 - 2*t + 1. Let p be r(1). Let c be (-2 + 2)*(1 + p). Let c + 245/4*s**4 - s - 189/4*s**3 + 12*s**2 = 0. Calculate s.
0, 1/5, 2/7
Let x(g) = g**3 + g. Let t(d) = 12*d**3 - 4*d**2 + 4*d. Let q(b) = t(b) - 10*x(b). What is v in q(v) = 0?
-1, 0, 3
Let j(m) be the second derivative of -1/27*m**3 + 1/90*m**5 + 0*m**2 + 0*m**4 + 0 + 2*m. Factor j(z).
2*z*(z - 1)*(z + 1)/9
Let v(r) = r**3 - 5*r**2 + r - 3. Let l be v(5). Let o be (-2)/3 + 238/168. Factor -3/4 + o*h**l + 0*h.
3*(h - 1)*(h + 1)/4
Let f(p) be the third derivative of p**8/504 + p**7/315 - p**6/90 - p**5/45 + p**4/36 + p**3/9 - 16*p**2. Factor f(g).
2*(g - 1)**2*(g + 1)**3/3
Let l(w) = 11*w - 64. Let p be l(6). Solve p - 4/3*u + 2/9*u**2 = 0 for u.
3
Let i(d) be the second derivative of -3*d - 1/5*d**2 + 1/6*d**3 - 1/15*d**4 + 1/100*d**5 + 0. Let i(o) = 0. What is o?
1, 2
Let s(h) be the second derivative of 3*h**6/10 - 33*h**5/20 - 17*h**4/12 + 7*h**3/2 - 2*h**2 - h. Factor s(b).
(b - 4)*(b + 1)*(3*b - 1)**2
Factor -2*r + 12*r**4 + 2*r + 639*r**5 + 8*r**3 - 635*r**5.
4*r**3*(r + 1)*(r + 2)
Solve -4*c**4 + c**2 - 3*c**3 + 2*c**2 + 0*c - c + 5*c**4 = 0 for c.
0, 1
Let g(r) = -37*r**3 + r**2 + 37*r - 1. Let n(b) = -19*b**3 + b**2 + 19*b - 1. Let v(a) = -3*g(a) + 5*n(a). Factor v(d).
2*(d - 1)*(d + 1)*(8*d + 1)
Let y(f) = 13*f**3 + f**2 + f + 2. Let q be y(-2). Let j = -496/5 - q. Factor j + 2/5*b**2 + 6/5*b.
2*(b + 1)*(b + 2)/5
Factor 11*v**4 + v**3 - 27*v**4 + 17*v**4.
v**3*(v + 1)
Let p(b) be the second derivative of -b**4/42 + 4*b**3/21 - 4*b**2/7 + 36*b. Suppose p(s) = 0. What is s?
2
Let y(f) be the first derivative of -15*f**6/2 - 12*f**5 + 5*f**4/2 + 20*f**3/3 - 5*f**2/2 - 9. Solve y(s) = 0 for s.
-1, 0, 1/3
Suppose 13 = 2*d + 9. Let z = -4/21 + 6/7. Determine s, given that 0 - z*s - 1/3*s**d = 0.
-2, 0
Let s be 16/(-28) - (-20)/35. Let g = -1/6 - -3/2. Solve -g*f**2 - 2/3*f + s = 0.
-1/2, 0
Let r = 18 - 54. Let m = r - -109/3. Factor 0 - m*f**3 + 0*f**2 + 0*f.
-f**3/3
Let q(h) be the first derivative of 9*h**5/25 + 3*h**4/5 + h**3/5 + 26. Factor q(v).
3*v**2*(v + 1)*(3*v + 1)/5
Find o such that 80/3*o + 148/3*o**3 + 68/3*o**4 + 16/3 + 52*o**2 + 4*o**5 = 0.
-2, -1, -2/3
Determine s so that 0 + 1/3*s + 3/2*s**2 = 0.
-2/9, 0
Let t(y) be the first derivative of -6*y**3 - 3*y + 3*y**4 + 8 - 3/5*y**5 + 6*y**2. Find v, given that t(v) = 0.
1
Factor 4/3*v**2 + 1/2*v**3 - 1/3 + 1/2*v.
(v + 1)*(v + 2)*(3*v - 1)/6
Let y(o) = -o - 2*o**2 + o**2 - 4*o**2. Let i(v) = 16*v**2 + 0*v - 7*v**2 + 2*v. Let w(h) = 6*i(h) + 11*y(h). Let w(k) = 0. What is k?
0, 1
Let k = 4 - 5. Let q be -2 - (6 - 0)*k. Determine t so that 0*t**3 - q*t - 2*t**3 + 6*t = 0.
-1, 0, 1
Let y = 9 + -4. Let q(b) be the third derivative of -1/20*b**6 + 0*b**3 + 0 - 1/12*b**4 + 1/10*b**y + 1/105*b**7 + b**2 + 0*b. What is u in q(u) = 0?
0, 1
Suppose 2*a = -0*a + 40. Let m = -98/5 + a. Factor 0 - 2/5*d**3 + m*d**2 + 0*d.
-2*d**2*(d - 1)/5
Let s = 2 + 6. Suppose -7*h + s = -3*h. Factor 1/3*a**h + 0*a + 0.
a**2/3
Let y(t) = t**3 - 9*t**2 + 2. Let k be y(9). Suppose -k*i = i. Suppose 0*u + 2/7*u**2 + i = 0. Calculate u.
0
Let h(y) be the second derivative of 7*y**4/24 - 3*y**3/4 + y**2/2 + 8*y. Factor h(c).
(c - 1)*(7*c - 2)/2
Suppose -1/7*u**2 + 0 + 1/7*u**3 + 0*u = 0. What is u?
0, 1
Let f(r) = 3*r**5 - 3*r**4 + 3*r**3 + 3*r**2 - 18*r - 12. Let d(i) = i**4 - i**2 + i + 1. Let u(s) = -12*d(s) - f(s). What is k in u(k) = 0?
-2, -1, 0, 1
Let p(h) be the second derivative of h**4/4 + 4*h**3 + 24*h**2 - 6*h. Find u such that p(u) = 0.
-4
Let d(w) be the first derivative of w**6/240 - 7*w**2/2 - 3. Let y(c) be the second derivative of d(c). Solve y(j) = 0.
0
Let s(p) = -p**3 - 15*p**2 + 33*p - 17. Let b be s(-17). Factor b + 4/11*x + 2/11*x**2.
2*x*(x + 2)/11
Let r(k) be the second derivative of 4*k**6/135 - 2*k**5/45 - k**4/18 + 4*k**3/27 - k**2/9 + 18*k. Solve r(c) = 0 for c.
-1, 1/2, 1
Factor 7 + 2*t**3 - 7 - 4 - 6*t.
2*(t - 2)*(t + 1)**2
Suppose -2*g - 287 + 60 = -c, 5*c = -4*g - 447. Let b = 795/7 + g. Suppose 2/7*t**4 + 0*t + 0 + b*t**3 + 2/7*t**2 = 0. Calculate t.
-1, 0
Let l(a) be the first derivative of -2 - 2/3*a**3 + 0*a + 1/1080*a**6 + 0*a**2 + 1/36*a**4 + 1/120*a**5. Let d(r) be the third derivative of l(r). Factor d(x).
(x + 1)*(x + 2)/3
Let u(d) be the third derivative of -d**6/480 - d**5/160 - d**3/2 - 8*d**2. Let n(k) be the first derivative of u(k). Factor n(s).
-3*s*(s + 1)/4
Let y(f) = 8*f**2 - 6*f - 9. Let i(w) = 7*w**2 - 5*w - 8. Let n(b) = -7*i(b) + 6*y(b). Suppose n(x) = 0. What is x?
-2, 1
Let d = 21 - 17. Factor 2*l**5 - 4*l + l**5 + 16*l**2 + 16*l**d - 3*l**5 - 4*l**5 - 24*l**3.
-4*l*(l - 1)**4
Let o be 56/(-12)*((-8)/(-7) + -2). Determine i so that 0*i**3 + 1/4*i**o - 1/4*i**2 + 0*i + 0 = 0.
-1, 0, 1
Let t(y) = -y**3 + 19*y**2 - 84*y + 3. Let l be t(12). Factor 0 + 14/11*v**2 + 4/11*v - 8/11*v**l.
-2*v*(v - 2)*(4*v + 1)/11
Suppose 0 = -4*q + 3*q + 6. Solve 0*i + 3*i - 3*i**3 + q*i**2 - 7*i + i = 0.
0, 1
Factor 0*d**4 - 15*d - 85*d**2 + 49*d**2 - 18 - 3*d**4 + 57*d**2 + 15*d**3.
-3*(d - 6)*(d - 1)*(d + 1)**2
Let p(h) be the third derivative of -h**7/105 - h**6/60 + h**5/15 + 6*h**2. Let p(n) = 0. What is n?
-2, 0, 1
Let x(g) be the second derivative of g**7/63 - g**6/45 - g**5/15 - 14*g. Find q, given that x(q) = 0.
-1, 0, 2
Let o(c) = -c**2 - 6. Let f be o(0). Let u(k) = k**2 + 7*k + 10. Let n be u(f). Factor 2/3*m + 2*m**3 + 2*m**2 + 2/3*m**n + 0.
2*m*(m + 1)**3/3
Factor -47*y - 35 + 5*y**2 + 43*y + 34*y.
5*(y - 1)*(y + 7)
Let j(z) = -3*z**2 - 17*z - 14. Let n(m) = -21*m**2 - 120*m - 99. Let u(t) = 15*j(t) - 2*n(t). Let u(h) = 0. Calculate h.
-4, -1
Suppose 2*n = 5*n - 6. Find l, given that -12/5 + 12/5*l - 3/5*l**n = 0.
2
Factor 4*u**4 - 16*u**3 - 26 - 72 + 34 + 64*u.
4*(u - 2)**3*(u + 2)
Let o(x) = -x**2 - 3*x - 2. Suppose -14 = 5*l + 4*j, -l - 3 = 3*j + 2. Let f be o(l). Solve f*p**2 + p**2 - 3*p**2 + p**2 + p = 0 for p.
0, 1
Suppose 2*x - 8 = -0*x. Suppose -9 = -x*j + j. Solve 3*c**2 + j*c**2 + c**3 + 4 - 2*c**4 - 10*c + c**3 = 0.
-2, 1
Let g(q) be the first derivative of -3*q**4/4 - 4*q**3 - 6*q**2 + 2. Factor g(l).
-3*l*(l + 2)**2
Let q(v) be the third derivative of v**6/360 - v**5/60 + 2*v**3/9 - 11*v**2. Factor q(r).
(r - 2)**2*(r + 1)/3
Let d(f) be the third derivative of -5*f**8/2352 + f**7/735 + f**6/168 - f**5/210 - f**2. What is o in d(o) = 0?
-1, 0, 2/5, 1
Let l be (8/(-12))/((-5)/15). Factor 8/3 - 2/3*z**3 - 2*z**l + 0*z.
-2*(z - 1)*(z + 2)**2/3
Let m(s) be the third derivative of -5*s**2 + 1/10*s**5 - 3/70*s**7 - 3/8*s**4 + 0 + 0*s + 1/112*s**8 + 1/2*s**3 + 1/20*s**6. Factor m(b).
3*(b - 1)**4*(b + 1)
Let r(f) be the second derivative of f**4/6 + 2*f**3/3 - 10*f. Factor r(t).
2*t*(t + 2)
Suppose o + 3*r + 9 = 0, o = 2*r + 3 + 3. Factor 1/4*x**4 + o - 1/4*x**2 + 0*x - 1/4*x**3 + 1/4*x**5.
x**2*(x - 1)*(x + 1)**2/4
Let o(z) = -z**3 - 11*z**2 - 11*z - 5. Let f be o(-10). Let u(s) = -2*s**2 + 3*s - 1. Let r(t) = 4*t**2 - 7*t + 3. Let w(x) = f*u(x) + 3*r(x). Factor w(a).
2*(a - 2)*(a - 1)
Let y(q) be the third derivative of 0*q**3 - 1/240*q**5 + 0*q**4 + 0 + 0*q + 3*q**2 + 1/480*q**6. Factor y(x).
x**2*(x - 1)/4
Let r(w) = w**2 - 5*w + 2. Let y be r(5). Let 0*o**4 + o + 0*o**5 - o**5 + 2*o**4 - 2*o**y = 0. What is o?
-1, 0, 1
Suppose 3*p - 6 = 0, 10 = 2*t - p - 4. Solve 20*w**4 + 0 + 50/3*w**5 + 8/3*w - 22/3*w**3 - t*w**2 = 0 for w.
-1, 0, 2/5
Let p(i) be the second derivative of -1/120*i**6 + 0 - 1/24*i**3 + 0*i**2 - 3/80*i**5 - 2*i - 1/16*i**4. Factor p(r).
-r*(r + 1)**3/4
Let i be (0/(11 - (2 - -3)))/(-1). Factor 1/2*k - 1/2*k**3 + 1/2*k**4 - 1/2*k**2 + i.
k*(k - 1)**2*(k + 1)/2
Factor 8/7*q - 4/7*q**2 + 0 + 4/7*q**4 - 8/7*q**3.
4*q*(q - 2)*(q - 1)*(q + 1)/7
Let t be -1 - (-6)/(-4)*-2. Let c(x) be the third derivative of 0 - t*x**2 + 1/120*x**5 + 0*x + 0*x**3 - 1/24*x**4. Factor c(w).
w*(w - 2)/2
Let a = -4 + 4. Let -4*x - 3*x**3 - 9*x**2 + a*x**3 - 2*x = 0. What is x?
-2, -1, 0
Let q(m) = -2*m**4 + 11*m**3 + m**2 - 16*m - 7. Let f(o) = -o**4 + 6*o**3 - 8*o - 4. Let r(l) = -7*f(l) + 4*q(l). Find j such that r(j) = 0.
-2, 0, 2
What is f in -44/7*f**5 - 76/7*f - 8/7 - 296/7*f**3 - 32*f**2 - 18