 - 3/4*k**2.
-k*(k - 1)**3/4
Factor 2*r**2 + 3 + 1 - 3 - 3.
2*(r - 1)*(r + 1)
Let i(s) = -7*s**3 - 14*s**2 + 4*s - 2. Let v(t) = 35*t**3 + 71*t**2 - 20*t + 11. Let b(l) = 11*i(l) + 2*v(l). Determine d, given that b(d) = 0.
-2, 0, 2/7
Find i such that 3*i**4 - 40*i - i**5 + 3 + 39*i + 4*i**3 - 2*i**3 - 6*i**2 = 0.
-1, 1, 3
Let a(z) = z**2 + 9*z + 8. Let y be a(-8). Factor 2*m**2 + m**5 - m**3 + 0*m**5 - 2*m**4 + y*m**3.
m**2*(m - 2)*(m - 1)*(m + 1)
Let j(r) = 4*r**3 - 5*r**3 - r + 10 - 3 + 5*r**2. Let l be j(5). Factor k - 1 + 4*k**l - k**3 - 1 - 2*k**2.
-(k - 2)*(k - 1)*(k + 1)
Let w be (-12)/(5/(-4) - -2). Let u = w + 20. What is n in 9/5*n - 6/5*n**3 - 3/5*n**5 + 9/5*n**u - 3/5 - 6/5*n**2 = 0?
-1, 1
Suppose -2*w - 186 = 4*f, -f + 215 = -6*f + w. Let c = 265/6 + f. Suppose 0 + 1/6*n**5 + 1/2*n**4 + c*n**2 + 1/2*n**3 + 0*n = 0. What is n?
-1, 0
Let k(l) be the third derivative of -2/21*l**5 + 11/140*l**6 + 1/294*l**8 + 1/21*l**4 + 0*l + 0 - 4*l**2 + 0*l**3 - 4/147*l**7. Let k(c) = 0. What is c?
0, 1/2, 2
Let i be (-2)/(-2)*(-30)/(-3). Suppose -8*h = -4*h + 3*a - 23, 3*h - i = 5*a. Let -g**5 + 8*g**4 - 7*g**3 - g**5 - g**h + 2*g**2 = 0. Calculate g.
0, 2/3, 1
Let u(c) be the first derivative of -16*c**5/35 - 19*c**4/42 - 4*c**3/63 - 24. Factor u(r).
-2*r**2*(3*r + 2)*(8*r + 1)/21
Let m be (-294)/(-70) + (-4 - 0). Suppose -3/5*y + m*y**2 + 2/5 = 0. What is y?
1, 2
Factor 3/7*w**3 + 0*w**2 - 6/7 - 9/7*w.
3*(w - 2)*(w + 1)**2/7
Suppose -g + 1 = -4. Let t(n) be the third derivative of 5/24*n**4 + 1/3*n**3 + 0*n + 1/120*n**6 + 2*n**2 + 1/15*n**g + 0. Factor t(v).
(v + 1)**2*(v + 2)
Solve 7 + b**2 - b**4 + 5 + 321*b - 4*b**3 - 305*b = 0.
-3, -2, -1, 2
Let r(u) = -5*u**4 - 6*u**3 + 16*u**2 - 16*u + 11. Let b(o) = -o**4 - o**3 + 3*o**2 - 3*o + 2. Let l(s) = -11*b(s) + 2*r(s). Find v, given that l(v) = 0.
-1, 0, 1
Let s be 6/27 + (-64)/(-198). Let v = -1/33 + 19/33. What is f in 0 + 2/11*f**4 + 2/11*f + s*f**3 + v*f**2 = 0?
-1, 0
Let z(y) = y**3. Let r(l) = 4*l + 6*l**3 + 0*l**3 - 2*l**2 + 0*l**3. Let b(x) = -r(x) + 8*z(x). Find i, given that b(i) = 0.
-2, 0, 1
Let c(t) be the second derivative of -t**6/900 + t**3/6 + 2*t. Let y(u) be the second derivative of c(u). Suppose y(p) = 0. What is p?
0
Factor 1/2*h**4 + 0*h**2 + 1/2*h**3 + 0*h + 0.
h**3*(h + 1)/2
Let z(j) = -j. Suppose 12 = 3*t, -2*t = 2*i + 2*t - 18. Let q(p) = -28*p**3 + 160*p**2 - 208*p - 72. Let u(f) = i*q(f) - 4*z(f). Solve u(g) = 0 for g.
-2/7, 3
Let u(r) be the third derivative of 1/1050*r**7 + 0*r + 0*r**4 + 0 + 0*r**6 + 0*r**3 - r**2 - 1/300*r**5. Factor u(s).
s**2*(s - 1)*(s + 1)/5
Let z(m) = 3*m**2 + 13*m + 10. Let i(d) = -14*d**2 - 64*d - 50. Let b(c) = 2*i(c) + 11*z(c). Solve b(o) = 0.
-2, -1
Let q(z) be the first derivative of z**7/1260 + z**6/540 - z**5/90 + z**3 + 3. Let v(g) be the third derivative of q(g). What is j in v(j) = 0?
-2, 0, 1
Let v = 9/59 - -2215/177. Let x(a) be the first derivative of 4*a + 2 - 38/5*a**5 - v*a**3 + a**2 + 31/2*a**4 + 4/3*a**6. Factor x(t).
2*(t - 2)*(t - 1)**3*(4*t + 1)
Suppose -6 = -2*d - 2. Let -7*g - g**d + 4*g**2 + 4*g = 0. Calculate g.
0, 1
Let y(g) = -g**3 + 25*g**2 - 3*g + 77. Let m be y(25). Factor 10/9*u**m + 4/9*u + 0.
2*u*(5*u + 2)/9
Let d(c) be the first derivative of 0*c**2 + 0*c**3 + 0*c - 1/2*c**4 + 2 + 2/5*c**5. Factor d(r).
2*r**3*(r - 1)
Factor 1/4*a**4 + 1/4 + 3/2*a**2 - a**3 - a.
(a - 1)**4/4
Let w(l) = 3*l - 4. Let a(u) = 2*u - 3. Let o(n) = 7*a(n) - 5*w(n). Let j be o(-3). Factor 0*z - 9/2*z**5 - 8*z**3 + 0 + 21/2*z**4 + j*z**2.
-z**2*(z - 1)*(3*z - 2)**2/2
Factor -2/3*n - 1/3*n**2 - 1/3.
-(n + 1)**2/3
Let u(n) be the second derivative of n**7/6300 - n**6/900 - n**5/100 - 5*n**4/12 - 4*n. Let w(m) be the third derivative of u(m). Factor w(a).
2*(a - 3)*(a + 1)/5
Let w(q) = -q - 1. Let x(i) = -1 + 20 + 24*i - 3 - 8*i**2. Let r(m) = 4*w(m) + x(m). Factor r(f).
-4*(f - 3)*(2*f + 1)
Let v(t) be the third derivative of -4*t**7/105 - t**6/3 - 3*t**5/10 + 13*t**4/6 - 8*t**3/3 + 22*t**2. Find g such that v(g) = 0.
-4, -2, 1/2
Let j(p) be the first derivative of 3*p**4/16 - p**3/4 - 3*p**2/8 + 3*p/4 - 9. Factor j(m).
3*(m - 1)**2*(m + 1)/4
Suppose 5*p - n + 31 = -4, 4*p - 5*n = -49. Let t(a) = a + 8. Let w be t(p). Let -1/4 + 0*b + 1/4*b**w = 0. Calculate b.
-1, 1
Factor 7*j**2 + 12 + 8*j**2 + 16*j - 11*j**2.
4*(j + 1)*(j + 3)
Let t(f) be the third derivative of -f**5/50 + f**4/12 - 2*f**3/15 + 11*f**2. Factor t(c).
-2*(c - 1)*(3*c - 2)/5
Let u(h) = -h**3 - 25*h**2 - 23*h + 26. Let o be u(-24). Let s(d) be the first derivative of 1/10*d**2 + o - 1/15*d**3 + 2/5*d. Find j, given that s(j) = 0.
-1, 2
Suppose 3*o - 8 = -o. Factor 4*g**4 + 2*g**2 + 0*g**o - 5*g**3 - 7*g**4.
-g**2*(g + 2)*(3*g - 1)
Let q(g) = 6*g**4 + 7*g**3 + 15*g**2 + 3*g + 1. Let c(w) = 11*w**4 + 15*w**3 + 29*w**2 + 7*w + 2. Let m(f) = -3*c(f) + 5*q(f). Factor m(a).
-(a + 1)**3*(3*a + 1)
Let j = 87 + -85. Factor 0 + 3*h - 3/2*h**j.
-3*h*(h - 2)/2
Let c(x) = -x. Let a be c(-7). Suppose 3*m = -1 + a. Factor 1/4*n - 1/4*n**m + 0.
-n*(n - 1)/4
Suppose -2*i + 11 - 5 = 0. Factor 2*a**4 - 7*a**3 - 2*a**3 + 5*a**i.
2*a**3*(a - 2)
Let c(b) = 8*b**4 + 4*b**3 - 10*b - 2. Let m = 20 + -14. Let n(j) be the third derivative of j**7/210 - j**4/24 - 2*j**2. Let p(i) = m*n(i) - c(i). Factor p(o).
-2*(o - 1)*(o + 1)**3
Let q(z) = z**2 - 5*z + 4. Let c be q(4). Factor 0 + 2*b**3 + c*b - 12/7*b**4 - 2/7*b**2.
-2*b**2*(b - 1)*(6*b - 1)/7
Let m = 13/506 - -3/46. Let v(r) be the second derivative of -2*r - 1/22*r**4 + 1/110*r**5 - 1/11*r**2 + m*r**3 + 0. What is b in v(b) = 0?
1
Factor -4*y**4 - 32*y**2 - 64/5 + 32*y + 2/5*y**5 + 16*y**3.
2*(y - 2)**5/5
Find h such that -12*h**3 + 5*h**4 + 6*h**3 - 5*h**2 - 9*h**3 + h + 14*h = 0.
-1, 0, 1, 3
Let a be 3 + (2 - 1) + -3. Suppose a - 9 = -4*u. Solve 8/9 - 2/3*j**u + 0*j - 2/9*j**3 = 0.
-2, 1
Suppose q = 5*q - 8. Factor q*z**2 - 4*z + z + z.
2*z*(z - 1)
Suppose 0 = 3*r - 19 + 1. Let l be (2/r)/(3/18). Solve 0 - l*q**3 + 4/7*q**4 + 2*q**5 - 4/7*q**2 + 0*q = 0 for q.
-1, -2/7, 0, 1
Let n(h) = -h**2 + 3*h. Let w be n(3). Let m = w + 2. Factor -2*f + f + 2*f**2 + m - 3*f.
2*(f - 1)**2
Let q(r) be the second derivative of 1/9*r**3 + 0*r**2 + 0 + 2*r - 1/10*r**5 + 2/45*r**6 + 0*r**4. Solve q(f) = 0 for f.
-1/2, 0, 1
Let o(t) be the second derivative of t**6/60 - t**5/30 - t**4/6 + t**2/2 + 3*t. Let b(r) be the first derivative of o(r). Find c, given that b(c) = 0.
-1, 0, 2
Let a = 0 - -4. Let f be ((-12)/(-3))/(-2 + 4). Solve 4 - x - 4 - 3*x + x**f + a = 0 for x.
2
Let c(g) = -g - 11. Let q be c(-13). Solve -3*o**3 - 211*o**2 + 3 - 7 - 15*o - 2 + 199*o**q = 0.
-2, -1
Factor -3*w + 3/4*w**2 + 0.
3*w*(w - 4)/4
Solve -y**4 + 12*y**2 - 8 - 2*y - y**4 - 6*y + 10*y**3 - 2*y**5 - 2*y**2 = 0 for y.
-2, -1, 1, 2
Let r(p) be the second derivative of p**7/2 + p**6/2 - 27*p**5/20 - 5*p**4/4 + p**3 - 3*p. What is d in r(d) = 0?
-1, 0, 2/7, 1
Suppose -2*w - 22 - 1 = -5*p, -16 = 4*w. Factor 0 + y - y**p + 1/2*y**4 - 1/2*y**2.
y*(y - 2)*(y - 1)*(y + 1)/2
Let g(z) = -4*z**2 + 4. Let m(y) = -3*y**2 + 3. Suppose 3*t - 31 = 4*u, 0*u - 2*u - 5*t = -17. Let n(h) = u*g(h) + 5*m(h). Determine a so that n(a) = 0.
-1, 1
Let f be ((-12)/9)/(70/(-15)). Let h = 61/287 + 3/41. Factor f*g**2 + 10/7*g + 6/7 - h*g**3.
-2*(g - 3)*(g + 1)**2/7
Let t(s) be the first derivative of s**6/24 + 7*s**5/20 + 9*s**4/8 + 11*s**3/6 + 13*s**2/8 + 3*s/4 - 30. Factor t(w).
(w + 1)**4*(w + 3)/4
Suppose 4*k + 6 = 22. Let d(u) be the second derivative of -1/15*u**6 + 0 + 0*u**2 - 1/10*u**5 + 1/3*u**3 - 2*u + 1/6*u**k. Determine m, given that d(m) = 0.
-1, 0, 1
Let i(z) be the first derivative of 5*z**3/12 + 10*z**2 + 80*z + 18. Determine c, given that i(c) = 0.
-8
Let k(o) be the second derivative of -o**7/140 + o**6/40 - o**5/40 - o**3/2 - 3*o. Let r(i) be the second derivative of k(i). Factor r(x).
-3*x*(x - 1)*(2*x - 1)
Let f(n) be the first derivative of 0*n + 1/30*n**4 + 4/3*n**3 + 3 - 1/300*n**5 - 1/900*n**6 + 0*n**2. Let s(t) be the third derivative of f(t). Factor s(x).
-2*(x - 1)*(x + 2)/5
Let p(m) = 34*m**4 - 204*m**3 + 230*m**2 - 44*m. Let j(c) = -7*c**4 + 41*c**3 - 46*c**2 + 9*c. Let x(y) = -16*j(y) - 3*p(y). Factor x(f).
2*f*(f - 3)*(f - 1)*(5*f - 2)
Factor 1/2*o**2 - o + 1/2.
(o - 1)