5/40 - 5*s**4/16 + s**3 + 7*s**2. Let b(k) = 0. Calculate k.
1, 4
Let v be 5 - ((2 - 0) + 0). Let t = 44 - 42. What is u in u**v + 3*u**t + u**2 + u**2 + 4 + 8*u + 0 = 0?
-2, -1
Let j(m) = 11*m**4 + 18*m**3 + 3*m**2 - 4*m - 2. Let i(f) = 45*f**4 + 73*f**3 + 11*f**2 - 17*f - 9. Let o(c) = -4*i(c) + 18*j(c). Factor o(k).
2*k*(k + 1)**2*(9*k - 2)
Factor 0*l - 4/3*l**2 + 0 - 2/3*l**4 - 2*l**3.
-2*l**2*(l + 1)*(l + 2)/3
Let h(l) be the first derivative of -1/15*l**5 - 1/3*l**2 + 1/6*l**4 - 2 + 1/3*l + 0*l**3. Determine u, given that h(u) = 0.
-1, 1
What is j in 3*j**2 + 3*j - 3*j**3 - 7*j**2 + 3 + j**2 = 0?
-1, 1
Let l(k) = k**2 - 12*k + 11. Let s be l(11). Let s - 1/4*y**2 + 1/4*y = 0. Calculate y.
0, 1
Suppose w - 3*w = 0. Suppose -u + w*u = -2. Factor 2*x**u - 3*x**3 + 0*x - 2*x**4 + 2*x + x**3.
-2*x*(x - 1)*(x + 1)**2
Let a(r) be the second derivative of r**5/30 + 5*r**4/18 + 7*r**3/9 + r**2 + 11*r. Factor a(v).
2*(v + 1)**2*(v + 3)/3
Let y(x) = x**2 - 8*x - 12. Let t(k) = 5*k**2 - 4*k + 9. Let c(n) = -n**2 + n - 2. Let f(z) = 9*c(z) + 2*t(z). Let d(q) = 4*f(q) - y(q). Factor d(b).
3*(b + 2)**2
Let d(h) be the third derivative of h**5/140 + 5*h**4/56 - 8*h**2 + h. What is r in d(r) = 0?
-5, 0
Let o(t) be the first derivative of -t**4/24 + t**3/18 + 5. Factor o(i).
-i**2*(i - 1)/6
Solve 0*m + 12*m + 1 + 15 - 4*m**2 + 0*m = 0.
-1, 4
Factor 6*m**3 - 429 + m**2 - 3*m**3 - 3*m + m**4 + 427.
(m - 1)*(m + 1)**2*(m + 2)
Let q(c) be the first derivative of 0*c**3 + 2/15*c**5 - 2/3*c**2 - 2/3*c - 6 + 1/3*c**4. Determine o so that q(o) = 0.
-1, 1
Factor 6*b**2 - 38*b**3 + 73*b**3 - 38*b**3 + 9*b.
-3*b*(b - 3)*(b + 1)
Factor 2/3*w**4 - 14/3*w - 10/3*w**3 + 6*w**2 + 4/3.
2*(w - 2)*(w - 1)**3/3
Factor 4/5*f**2 + 2/5*f + 1/2*f**3 + 1/10*f**4 + 0.
f*(f + 1)*(f + 2)**2/10
Let v(r) = 8*r**2 - r**3 + 1 + 0*r**4 - r**4 + 6 + r. Let x(z) = -z**2 - 1. Let q(g) = 2*v(g) + 14*x(g). Factor q(i).
-2*i*(i - 1)*(i + 1)**2
Let f(i) be the first derivative of -2*i**3/3 + 5*i**2/7 + 4*i/7 + 4. Factor f(t).
-2*(t - 1)*(7*t + 2)/7
Let y = 635 + -632. Factor -1/2*c**2 - c + 1/2*c**4 + c**y + 0.
c*(c - 1)*(c + 1)*(c + 2)/2
Let p(o) = -o**3 + 2*o**2 + 4*o - 5. Let l be p(2). Let a(w) be the second derivative of 0 - 1/42*w**4 + 1/7*w**2 - l*w + 0*w**3. Factor a(v).
-2*(v - 1)*(v + 1)/7
Factor 37*f + 15 + 5*f**2 + 5 - 12*f.
5*(f + 1)*(f + 4)
Let t be -3 - ((-8)/28 + 116/(-35)). Factor t*a**5 + 27/5*a + 18/5*a**4 + 42/5*a**3 + 6/5 + 48/5*a**2.
3*(a + 1)**4*(a + 2)/5
Let f be (-24)/7 - 4/7. Let o be (2/3)/(f/(-2)). Factor 4/3*t**2 + o*t**4 - 4/3*t**3 + 0 + 0*t.
t**2*(t - 2)**2/3
Suppose 2*n = -5 + 11. Let f(m) be the second derivative of 0*m**n + 0 - 1/30*m**6 + 0*m**5 + 1/42*m**7 + 0*m**2 + 0*m**4 + 2*m. Find h such that f(h) = 0.
0, 1
Factor 6*a**3 - 8*a**3 - 5*a**2 - 18*a**3.
-5*a**2*(4*a + 1)
Factor 0 + 2*r**2 + 4/3*r + 2/3*r**3.
2*r*(r + 1)*(r + 2)/3
Let m be (-128)/(-12)*-3*(-4)/24. Factor -m*c**2 + 0 + 4/3*c.
-4*c*(4*c - 1)/3
Let p(s) = 3*s**2 - 7. Let k(l) = -6*l**2 + 13. Let y(z) = -4*k(z) - 7*p(z). Factor y(v).
3*(v - 1)*(v + 1)
Let g be -4 + 2/1 + 4. Factor -u**g + 3 + 2*u**2 + 12*u**3 + 15*u + 23*u**2.
3*(u + 1)*(2*u + 1)**2
Let f(b) be the first derivative of -b**3/3 + b**2 + 3*b - 16. Factor f(w).
-(w - 3)*(w + 1)
Let b be (-254)/30 + 4/(-12). Let s = b + 504/55. Determine q so that -4/11 - 6/11*q**3 + s*q**2 + 6/11*q = 0.
-1, 2/3, 1
Determine f so that -61*f + 61*f + 4*f**3 - 8*f**4 + 4*f**2 = 0.
-1/2, 0, 1
Suppose 2*i + 4*x - 16 = 6*x, -x + 22 = 5*i. Find z, given that 3*z**5 - z**4 - z**5 - z**i + z**2 - z**3 = 0.
-1, 0, 1
Suppose l + 2*l - 18 = -3*c, -3*c + 4*l + 4 = 0. Let g = -2 + c. Factor u**2 - 2*u - u + g*u + 2*u.
u*(u + 1)
Let f(q) be the third derivative of 3*q**7/280 + 7*q**6/480 - 11*q**5/240 - 7*q**4/96 + q**3/12 + 19*q**2. Factor f(z).
(z - 1)*(z + 1)**2*(9*z - 2)/4
Let c be 1 + -10*(-2)/(-4). Let i(v) = v**2 - 1. Let n(f) = 11*f**2 - 9*f - 2. Let p(r) = c*i(r) + n(r). Solve p(j) = 0.
2/7, 1
Let u(i) be the first derivative of -1/2*i**5 - 1/4*i**6 + i**3 - 1/2*i + 1/4*i**2 - 8 + 1/4*i**4. Solve u(r) = 0 for r.
-1, 1/3, 1
Let z(d) be the third derivative of -d**5/180 - d**4/36 - d**3/18 - 8*d**2. Factor z(u).
-(u + 1)**2/3
Let l(i) be the first derivative of -i**5/70 - i**4/21 - i**3/21 + 8*i - 9. Let u(f) be the first derivative of l(f). Factor u(m).
-2*m*(m + 1)**2/7
Let a(k) be the first derivative of 4*k**3/3 - 16*k + 8. Factor a(v).
4*(v - 2)*(v + 2)
Suppose 78*t + 681*t**3 + 215*t**3 + 1248*t**2 + 196*t**4 + 434*t + 64 = 0. What is t?
-2, -2/7
Let f(l) = l**3 - l**2. Let t(a) = -2*a**4 + 6*a**3 - 4*a**2. Let p(c) = -4*f(c) + 2*t(c). Suppose p(s) = 0. Calculate s.
0, 1
Suppose 0 = 3*n - l - 7, -n + 2 - 3 = -2*l. Let t(h) be the second derivative of 2/9*h**n - 4*h + 1/3*h**2 + 1/18*h**4 + 0. Let t(b) = 0. What is b?
-1
Factor 3/4*y**2 + 3/4 - 3/2*y.
3*(y - 1)**2/4
Let d(x) = x**3 - 3*x**2 + 3*x + 4. Let q be d(0). Suppose 36/11*p**3 + 0*p + 16/11*p**q - 2/11 + 2*p**2 = 0. What is p?
-1, -1/2, 1/4
Let k(b) be the first derivative of 7/18*b**6 - 2*b**5 - 2 + 25/6*b**4 + 5/2*b**2 - 2/3*b - 40/9*b**3. Factor k(o).
(o - 1)**4*(7*o - 2)/3
Suppose -2*c = -5*c - 3. Let y = 3 - c. Determine q so that y*q + q**3 - 2 - 5*q**3 + 3*q**4 - q**4 = 0.
-1, 1
Factor -18*m**3 + 4*m**4 - 16*m**4 + 7*m**5 - 4*m**5 - 2*m + 17*m + 12*m**2.
3*m*(m - 5)*(m - 1)*(m + 1)**2
Suppose 0*p - 50 = -10*p. Suppose 4*u + p*u = 0. Solve u + 2/3*a + 2/3*a**2 = 0 for a.
-1, 0
Let w(z) be the third derivative of 1/72*z**6 + 0*z**4 + 4*z**2 + 0*z + 1/180*z**5 + 0 + 2/315*z**7 + 0*z**3. Factor w(b).
b**2*(b + 1)*(4*b + 1)/3
Let k(b) be the first derivative of b**4/12 - 4*b**3/9 + 5*b**2/6 - 2*b/3 + 6. Factor k(l).
(l - 2)*(l - 1)**2/3
Let n(d) be the first derivative of -2/3*d**3 - 2 + 0*d**2 + 2*d. Factor n(t).
-2*(t - 1)*(t + 1)
Let v(i) = 2*i - 10. Let h be v(9). Let k = h + -5. Factor -1/3*x + 4/3*x**2 + x**k - 2/3.
(x + 1)**2*(3*x - 2)/3
Let z(y) be the first derivative of -y**5/6 - y**4/3 - y**3/18 + y**2/6 + 7. Factor z(i).
-i*(i + 1)**2*(5*i - 2)/6
Let c be (-7)/(-6) + (-4)/6. Suppose 0 = -5*d + 22 + 13. Determine i so that 29/4*i**3 + 0 - d*i**4 - c*i + 1/4*i**2 = 0.
-1/4, 0, 2/7, 1
Determine k, given that 16/3*k**3 - 2*k**2 - 2*k**4 + 0 - 4/3*k = 0.
-1/3, 0, 1, 2
Let o be ((-3)/6)/((-3)/18). Factor 5*k + 3*k**5 + 2*k**5 - 4*k**o - 4*k**4 + 2*k**2 - 6*k**5 + 2.
-(k - 1)*(k + 1)**3*(k + 2)
Let r(v) be the second derivative of 1/90*v**5 + 0 + 0*v**2 + 1/18*v**4 + 2/27*v**3 + v. Factor r(z).
2*z*(z + 1)*(z + 2)/9
Let l be -4 + 1 - (-11)/3. Let n(u) be the first derivative of l*u**3 + 0*u**4 + 0*u - 1/6*u**6 + 1/2*u**2 - 2/5*u**5 + 1. Factor n(w).
-w*(w - 1)*(w + 1)**3
Solve 0 + 9/4*g**4 + 15/4*g**3 + 3/4*g**2 - 3/4*g = 0.
-1, 0, 1/3
Suppose -5*c + 0*i + 3*i = -3, 3*c = 4*i + 4. What is b in -1/3*b**2 + 0*b - 1/3*b**3 + c = 0?
-1, 0
Let r(m) be the third derivative of m**5/480 + m**4/192 - m**3/24 - 5*m**2. Factor r(c).
(c - 1)*(c + 2)/8
Let d(x) be the first derivative of -4 + 1/3*x**2 - 4/3*x + 2/9*x**3. Factor d(v).
2*(v - 1)*(v + 2)/3
Let w(k) be the third derivative of 1/20*k**5 - 1/8*k**4 + 0 - 1/120*k**6 - 2*k**2 + 0*k + 1/6*k**3. Factor w(p).
-(p - 1)**3
Let i(c) be the third derivative of -c**2 + 3/20*c**5 + 1/70*c**7 + 0 + 0*c**3 + 0*c - 3/40*c**6 - 1/8*c**4. Factor i(x).
3*x*(x - 1)**3
Let o(t) be the second derivative of -t**4/48 + t**3/12 + 3*t**2/8 - 31*t. Find l, given that o(l) = 0.
-1, 3
Suppose 0 = -5*i - 3*c - 15, 8*i + 5 = 3*i - c. Let o(h) be the second derivative of 2*h + 0 + 1/6*h**4 + i*h**2 - 1/20*h**5 - 1/6*h**3. What is j in o(j) = 0?
0, 1
Let u(b) be the third derivative of b**8/3360 + b**7/420 + b**6/180 - b**4/8 - 4*b**2. Let i(g) be the second derivative of u(g). Let i(c) = 0. Calculate c.
-2, -1, 0
Determine k so that k**2 + k**2 + k - 3*k**2 + 0*k = 0.
0, 1
Let a be 1/(-2)*70/(-5). Let 12*j**2 + 2*j**3 - 19*j**2 - a*j**3 + 10*j**2 + 2*j = 0. What is j?
-2/5, 0, 1
Let j(l) be the first derivative of -3*l**4/4 + l**3 - 6. Factor j(n).
-3*n**2*(n - 1)
Let d = -257 + 259. What is o in -45/7*o**5 - 6/7*o + 3/7*o**4 + 51/7*o**3 + 0 - 3/7*o**d = 0?
-1, -1/3, 0, 2/5, 1
Let o be 6/(-4)*2/(-150). Let m(f) be the second derivative of f + o*f**5 + 1/10*f**4 + 1