78/5 - u. Let 4/5 - 6/5*v + a*v**2 = 0. Calculate v.
1, 2
Let x(f) be the third derivative of f**8/168 + f**7/420 - f**6/30 - f**5/60 + f**4/12 + f**3/12 + 28*f**2. Let x(b) = 0. Calculate b.
-1, -1/4, 1
Determine t, given that 2/15*t**2 + 2/15*t**4 - 2/5*t + 2/5*t**3 - 4/15 = 0.
-2, -1, 1
Find d such that 35*d**3 + 7*d**2 - 18*d**5 + 3*d**4 - 2*d**5 - 17*d**2 + 22*d**4 = 0.
-1, 0, 1/4, 2
Let m(c) = 9*c**3 + 69*c**2 + 90*c + 51. Let d(g) = -6*g - 3 - 7*g**2 - 4*g - g**3 + g - 2. Let q(f) = 21*d(f) + 2*m(f). Find k, given that q(k) = 0.
-1
Let d(l) be the third derivative of l**7/735 - l**6/420 - l**5/42 - l**4/28 + l**2 - 8*l. What is r in d(r) = 0?
-1, 0, 3
Let g be 8/2 + (-2)/1. Let h be 11/9 + 6/(-27). Factor -h + 0*i**g + 3 - i**2 - i.
-(i - 1)*(i + 2)
Determine l, given that -48/5*l**3 + 0 + 21/5*l**4 + 33/5*l**2 - 6/5*l = 0.
0, 2/7, 1
Let s(q) be the first derivative of 9*q**5 + 15*q**4/2 - 40*q**3/3 - 15*q**2 - 5*q + 2. Factor s(h).
5*(h - 1)*(h + 1)*(3*h + 1)**2
Factor -2/9 + 10/9*x - 8/9*x**2.
-2*(x - 1)*(4*x - 1)/9
Factor 0 + 2/11*j + 0*j**2 - 2/11*j**3.
-2*j*(j - 1)*(j + 1)/11
Let i(x) = x**2 + 11*x + 2. Let u be i(-11). Suppose -4 = -u*a - 4*f, 5*f = -0*a + a - 23. Determine b so that a + 0 + 2*b**2 + 8*b + 0*b**2 = 0.
-2
Suppose -3*t - 583 + 583 = 0. Factor t*u + 1/6*u**2 - 1/6*u**5 + 1/6*u**3 - 1/6*u**4 + 0.
-u**2*(u - 1)*(u + 1)**2/6
Let i(a) be the first derivative of -a**6/1440 - a**5/80 - 3*a**4/32 + 2*a**3 + 4. Let f(t) be the third derivative of i(t). Factor f(d).
-(d + 3)**2/4
Let c(w) be the first derivative of -2 + 3*w + 0*w**2 - 1/6*w**4 - 2/3*w**3. Let q(f) be the first derivative of c(f). Suppose q(u) = 0. Calculate u.
-2, 0
Let x = 1 + 1. Factor -2*m**3 - 2*m**x - 8 + 8.
-2*m**2*(m + 1)
Let k = -20 - -51. Factor 1 - 24*w - 1 - 25*w**3 + 14*w**2 + 4 + k*w**2.
-(w - 1)*(5*w - 2)**2
Let c(d) = -1 - d - 2 + 0 + d**3 + 5*d**2. Let q be c(-5). Suppose 4 - 7*x**2 + 3*x**q + 2*x**3 - 4*x**3 + 2*x = 0. What is x?
-2, -1, 1
Suppose -u - u = 0. Let g = -2/27 + 31/54. Find z, given that u + 0*z**2 + 0*z**4 + z**3 - g*z**5 - 1/2*z = 0.
-1, 0, 1
Let k(z) be the first derivative of 0*z**3 + 1/6*z**4 + 3 + 0*z + 1/2*z**2 + 3/10*z**5. Let a(j) be the second derivative of k(j). Factor a(q).
2*q*(9*q + 2)
Factor 4/3*q**3 + 4/3*q**2 + 1/3*q**4 + 0 + 0*q.
q**2*(q + 2)**2/3
Let h(p) be the first derivative of -4*p**5/5 - 4*p**4 + 8*p**3/3 + 24*p**2 - 36*p + 8. Determine u, given that h(u) = 0.
-3, 1
Let 54*o - 12*o**2 + 2*o**2 - 4 - 16 = 0. What is o?
2/5, 5
Let q(o) = -2*o**2 - 7*o + 3. Let h(a) = -9*a**2 - 29*a + 13. Let g(p) = 6*h(p) - 26*q(p). Determine w so that g(w) = 0.
0, 4
Factor 0 + 0*y + 2/3*y**2 + 1/12*y**3.
y**2*(y + 8)/12
Let y(k) = -k**3 - 6*k**2 - 7*k - 6. Let w be y(-5). Let h(b) = b. Let p(g) = g**2 + 4*g. Let q(i) = w*h(i) - p(i). Factor q(a).
-a**2
Let o(p) be the first derivative of 0*p**2 + 1/3*p**3 - 2 + 0*p + 1/8*p**4. Factor o(c).
c**2*(c + 2)/2
Let n = 5 - -1. Let q(h) be the third derivative of 2*h**2 - 1/30*h**5 + 1/12*h**4 - 1/9*h**3 + 0 + 1/180*h**n + 0*h. Factor q(p).
2*(p - 1)**3/3
Suppose 3*d - 17 - 7 = 0. Let f(i) = i**2 - 7*i + 1. Let y(a) = 2*a**2 - 20*a + 2. Let k(j) = d*f(j) - 3*y(j). Solve k(n) = 0 for n.
-1
Let m(b) be the second derivative of -b**5/40 + b**4/12 - b**3/12 - 7*b. What is c in m(c) = 0?
0, 1
Let r(n) = n**4 + n**3 + n**2 + 1. Let y(h) = 12*h**4 - 8*h**3 + 28*h**2 - 8*h + 8. Let f(c) = 8*r(c) - y(c). Suppose f(d) = 0. What is d?
0, 1, 2
Solve 0 + 3/7*b**3 - 12/7*b**2 + 9/7*b = 0 for b.
0, 1, 3
Factor -2/7*b**3 - 4/7*b - 6/7*b**2 + 0.
-2*b*(b + 1)*(b + 2)/7
Suppose -14 + 22 = 4*i. Suppose 12*b**2 + 12*b**i + 12*b**4 - 3*b - 33*b**2 = 0. What is b?
-1/2, 0, 1
Factor 512/5 + 24/5*m**2 - 1/5*m**3 - 192/5*m.
-(m - 8)**3/5
Let f(s) = s**3 + 6*s**2 - s - 6. Suppose -2*m - 3 = -3*o, 0*m - o - 9 = m. Let b be f(m). Factor 2/3*u**2 + b*u - 2/3.
2*(u - 1)*(u + 1)/3
Factor 4/3*y**3 + 1/3*y**4 + y**2 - 4/3 - 4/3*y.
(y - 1)*(y + 1)*(y + 2)**2/3
Suppose -2*m - 1 = o - 3, 3*m = -2*o + 4. Let c(k) be the second derivative of 0 + 0*k**o + 1/6*k**3 + 1/20*k**5 + 2*k - 1/6*k**4. Factor c(h).
h*(h - 1)**2
Let m be 1*3 - (7 + -17). Suppose -2*c - 5*x - m = -38, -4*c - 5*x = -25. Let -2/5*k + c + 4/5*k**2 - 2/5*k**3 = 0. What is k?
0, 1
Let c be 105/(-56) - (-2)/1. Let z(k) be the first derivative of 0*k**3 - k + 3 + c*k**4 - 3/4*k**2. Factor z(h).
(h - 2)*(h + 1)**2/2
Factor -q**3 - 1/4*q**5 + 1/2 + 5/4*q + 1/2*q**2 - q**4.
-(q - 1)*(q + 1)**3*(q + 2)/4
Factor 27/4*k**2 - 3/4*k**3 + 12 - 18*k.
-3*(k - 4)**2*(k - 1)/4
Let o(i) = -2*i**4 - 8*i**3 + 7*i**2 + 13*i - 5. Let p(x) = -3*x**4 - 12*x**3 + 10*x**2 + 19*x - 7. Let f(a) = -7*o(a) + 5*p(a). Factor f(w).
-w*(w - 1)*(w + 1)*(w + 4)
Let r = -3 - -6. Factor -t**3 - t**r - t - 4*t**2 - t.
-2*t*(t + 1)**2
Let k = 5 + -1. Let g(b) = -2*b**5 + 4*b**4 - 6*b**3 - 4*b**2 - 4. Let i(x) = -x**5 + x**4 - x**3 - x**2 - 1. Let m(c) = k*i(c) - g(c). Factor m(a).
-2*a**3*(a - 1)*(a + 1)
Let o(n) be the second derivative of 3/50*n**5 + 0*n**2 + 0 + 0*n**4 + 0*n**3 - 1/50*n**6 + 4*n. Factor o(g).
-3*g**3*(g - 2)/5
Let f be (1*(-1 - 0))/((-20)/8). Find g such that 0 - f*g - 2/5*g**2 = 0.
-1, 0
Suppose -5*a + 31 = -9. Let j be (1/(-2))/((-10)/a). Solve j*s - 2/5*s**2 + 4/5 = 0 for s.
-1, 2
Let z = 10 - 7. Suppose z*n - 12 = -3. Factor -4 - 16*l**n - 6*l**4 + 4 - 14*l**2 - 4*l.
-2*l*(l + 1)**2*(3*l + 2)
Let x(p) be the first derivative of -p**4/18 - p**3/9 - p**2/18 + 13. Factor x(b).
-b*(b + 1)*(2*b + 1)/9
Suppose -2*r - 5*r + 70 = 0. Suppose -2*q + r = -0*q. Suppose 4/9*b**2 - 2/9*b + 2/9*b**q - 4/9*b**4 + 0*b**3 + 0 = 0. Calculate b.
-1, 0, 1
Factor -2*s**3 - 14/5*s**2 + 12/5 + 2*s + 2/5*s**4.
2*(s - 6)*(s - 1)*(s + 1)**2/5
Let v(r) be the third derivative of -r**5/9 + 2*r**4/3 - 8*r**3/9 + 8*r**2. Factor v(k).
-4*(k - 2)*(5*k - 2)/3
Suppose -2*v + 393 = -6*v - 3*l, -3*l + 471 = -5*v. Let g be (v/81)/((-4)/6). Determine r so that -8/3*r - 2/9*r**3 + g + 4/3*r**2 = 0.
2
Suppose 4*h - 9*h + 5*v + 100 = 0, 5*h - 115 = 2*v. Let o = -20 + h. Factor 6/5*t**3 + 1/5*t**o + 0 + 4/5*t**2 + 1/5*t + 4/5*t**4.
t*(t + 1)**4/5
What is l in 10/21 + 22/21*l + 2/3*l**2 + 2/21*l**3 = 0?
-5, -1
Factor -4*w - 3*w + w**2 + 3*w**2 + 3*w - 8.
4*(w - 2)*(w + 1)
Solve 0*y**2 - 48 + 3*y**2 + 51 - 6*y = 0 for y.
1
Factor 2*s**4 + s**3 - 4*s**2 + 7*s**3 + 3*s**3 - 13*s**3.
2*s**2*(s - 2)*(s + 1)
Suppose 5*i - 21 - 4 = 0. Suppose -5 = v + 4*v + 4*k, 3*v + i*k + 16 = 0. Determine x so that 1/2*x**5 - 1/2 - 5/2*x**4 + 5*x**v - 5*x**2 + 5/2*x = 0.
1
Let l(j) be the third derivative of -1/672*j**8 + 0*j**3 + 0*j - 1/40*j**5 + 0 + 1/72*j**4 + 1/80*j**6 - 6*j**2 + 1/1260*j**7. Find y, given that l(y) = 0.
-2, 0, 1/3, 1
Let m(r) = 28*r**4 - 56*r**3 + 52*r**2 - 20*r. Let h(u) = -u**5 + 55*u**4 - 111*u**3 + 103*u**2 - 39*u. Let a(i) = 4*h(i) - 7*m(i). Suppose a(d) = 0. What is d?
0, 1, 2
Let i(p) be the third derivative of 0*p + 1/180*p**5 + 0*p**4 + 0 + 0*p**3 + 2*p**2. Factor i(n).
n**2/3
Factor -1/5*c**4 - 12/5*c - 4/5 - 13/5*c**2 - 6/5*c**3.
-(c + 1)**2*(c + 2)**2/5
Suppose -5*m**4 - 2937 - 100*m**2 + 80*m + 40*m**3 + 2937 = 0. What is m?
0, 2, 4
Let k(y) be the first derivative of y**6/780 + 3*y**5/130 + 9*y**4/52 + 9*y**3/13 + 2*y**2 - 3. Let l(n) be the second derivative of k(n). Factor l(u).
2*(u + 3)**3/13
Let r = 41 + -81/2. Factor r*h + 1/4*h**4 - 1/2*h**3 + 0*h**2 - 1/4.
(h - 1)**3*(h + 1)/4
Factor 0*n + 0 + 2/11*n**3 - 2/11*n**2.
2*n**2*(n - 1)/11
Let b be ((-2)/4)/(-1)*0. Let k(g) be the first derivative of 0*g + 1/4*g**4 - 1/6*g**3 - 2 + b*g**2 + 1/3*g**6 + 7/10*g**5. Determine o so that k(o) = 0.
-1, 0, 1/4
Let w(p) be the third derivative of -p**8/112 + p**6/8 - p**4/2 + 22*p**2. Let w(t) = 0. What is t?
-2, -1, 0, 1, 2
Suppose -4*p - l + 21 = 0, 0*p - 5*p - 5 = -5*l. Suppose -3*y**2 + 2*y + y**3 - 3*y**2 + 6*y**p - y**3 - 4*y**5 + 2*y**3 = 0. Calculate y.
-1, 0, 1/2, 1
Let p = -1132 + 1132. Let 2/9*v**2 - 2/9*v + p = 0. Calculate v.
0, 1
Let z = 5 - 0. Suppose -b**2 - 6*b**2 - 2*b + z*b**2 = 0. What is b?
-1, 0
Let b(k) = k**2 - 2*k - 4. Let v be b(4). Suppose 0 = v*f - 3*u + 1, 5*f + u - 16 = -3. Find a such that 4/9*a + 2/9*a**f + 2/9 = 0.
-1
Let c be (-2 + (-15)/(-12))*(-20)/25. Factor 