Calculate y.
0, 1
Factor -1/6*t**5 + 2/3*t**2 + 0 - 3/2*t**3 + 0*t + t**4.
-t**2*(t - 4)*(t - 1)**2/6
Suppose 0 = 10*s - 28 - 2. Solve -4 + 4*j**5 + 51*j**2 - 10*j - 4*j**4 - 8*j**s + 14*j - 43*j**2 = 0.
-1, 1
Let q(i) be the first derivative of 0*i + 12 + 1/5*i**5 + 1/8*i**4 + 0*i**3 + 0*i**2 + 1/12*i**6. Factor q(n).
n**3*(n + 1)**2/2
Let x(n) be the third derivative of n**5/690 - 71*n**4/138 + 5041*n**3/69 - 6*n**2. Suppose x(q) = 0. Calculate q.
71
Let o(b) = b**3 - 7*b**2 - 10*b. Let k(w) = w**2. Let n(d) = 4*k(d) + o(d). Factor n(s).
s*(s - 5)*(s + 2)
Let g(y) be the second derivative of -5*y**4/12 + 355*y**3/6 + 180*y**2 + 417*y. Let g(j) = 0. What is j?
-1, 72
Let i(o) be the first derivative of o**5/60 + 5*o**4/24 + 2*o**3/3 + 13*o**2/2 + 24. Let c(j) be the second derivative of i(j). What is y in c(y) = 0?
-4, -1
Let d be (-400)/(-28) + -6 - 8. Let t(b) be the first derivative of -1/21*b**3 - d*b**2 - 4/7*b + 7. Solve t(s) = 0 for s.
-2
Let o be (-854)/287 + (-1)/(3/(-9)). Let n = o - -37/164. Factor -1/2*j + n*j**2 + 0.
j*(j - 2)/4
Let t be ((-905)/60 + 15)/(-1*1/4). Factor -t*j**4 + 1/3*j**2 + 0 + 0*j - 1/3*j**5 + 1/3*j**3.
-j**2*(j - 1)*(j + 1)**2/3
Let n(c) be the first derivative of 2/3*c**2 + 0*c + 2/3*c**3 + 13 + 1/6*c**4. Suppose n(g) = 0. Calculate g.
-2, -1, 0
Let u(z) = 4*z**5 - 16*z**4 + 12*z**3 - 10*z**2 - 2*z. Let o(f) = f**4 + f**3 + f**2 + f. Suppose 3 + 7 = -5*s. Let h(w) = s*u(w) - 6*o(w). Factor h(v).
-2*v*(v - 1)**3*(4*v - 1)
Factor 1/4*u**3 + 0 + 14*u**2 + 196*u.
u*(u + 28)**2/4
Let p = 854 - 854. Determine j so that 2/9*j**4 - 2/9*j**2 + p + 0*j + 0*j**3 = 0.
-1, 0, 1
Suppose -53 + 67 = 83*p - 152. Factor 0 - 4/3*t - 28/3*t**p.
-4*t*(7*t + 1)/3
Let p(d) be the third derivative of -d**6/840 - d**5/42 + 13*d**4/56 + d**2 - 59. Determine u, given that p(u) = 0.
-13, 0, 3
Suppose 1484 = 9*z - 1684. Let m be z/110 - (1 - (-2)/1). Factor -1/5 + 1/5*p**3 + 1/5*p**2 - m*p.
(p - 1)*(p + 1)**2/5
Let b = 18/121 - -291/484. What is k in -1/4*k**2 + b*k**3 + 1/4 - 3/4*k = 0?
-1, 1/3, 1
Let u(m) = -52*m**2 - 166*m - 14. Let x be u(-3). Factor 1/4*r**5 - 17/4*r**4 - x*r**2 + 20*r**3 + 0 + 0*r.
r**2*(r - 8)**2*(r - 1)/4
Let g(l) be the second derivative of 0 - 3/4*l**2 + 9*l + 3/4*l**3 - 3/8*l**4 + 3/40*l**5. Solve g(z) = 0 for z.
1
Factor 4/15 + 2/15*g**2 + 2/5*g.
2*(g + 1)*(g + 2)/15
Suppose -4*f + 11 + 13 = 2*d, 4*f = 3*d + 4. Let t(v) = -4*v**3 - 4*v**2 + 8*v - 12. Let g(n) = -n**2 - n - 1. Let p(l) = d*g(l) - t(l). Solve p(q) = 0 for q.
-2, 1
Factor 797*z + 4*z**4 + 483*z - 60*z**3 + z**4 + 0*z + 0*z**4.
5*z*(z - 8)**2*(z + 4)
Let v be ((-5)/(-10))/(-3 + 6). Let s(t) be the first derivative of -v*t**6 - 4 - 1/3*t**5 + 0*t**3 + 1/6*t**4 + 0*t**2 + 0*t. Factor s(c).
-c**3*(c + 2)*(3*c - 1)/3
Let -3/8*c**2 - 20667/8 - 249/4*c = 0. Calculate c.
-83
Let t(a) be the second derivative of -a**7/1512 - a**6/216 + 3*a**4/4 + 15*a. Let f(p) be the third derivative of t(p). Determine d, given that f(d) = 0.
-2, 0
Let j(x) = -46*x**4 - 31*x**3 + 24*x**2 - 13*x. Let r(a) = 34*a**4 + 23*a**3 - 18*a**2 + 9*a. Let p(f) = 8*j(f) + 11*r(f). Factor p(t).
t*(t - 1)*(t + 1)*(6*t + 5)
Determine h so that 24*h**3 - 75*h - 6*h**2 - 4*h**4 + 0*h + 48 + 23*h + 18*h**2 - 28*h = 0.
-2, 1, 6
Suppose q = 3*v - q - 34, -17 = -v - 5*q. Factor v + 3*z**2 - 2*z + 5*z + 2*z + 10*z.
3*(z + 1)*(z + 4)
Let q be (8 - 4)/(0/3 + -1). Let n be (4 + q)/((-2 - -3)/1). Factor -2/11*a**2 + n*a + 2/11.
-2*(a - 1)*(a + 1)/11
Let w(y) = -3*y**2 + 3*y + 7. Let n be w(-3). Let p = 48 + n. Factor -4*a + 24*a**2 - 19*a**2 + p*a + 10.
5*(a + 1)*(a + 2)
Suppose 0 = -5*r + 5*x, 0*r = -4*r - 5*x + 27. Let d = 14 + -10. Solve 6*o**d + 3*o**3 - 3*o**2 + r*o**5 + 3*o**2 = 0.
-1, 0
Let z(k) be the first derivative of k**8/10080 + k**7/1260 + k**6/432 + k**5/360 + 17*k**3/3 + 8. Let t(a) be the third derivative of z(a). Factor t(d).
d*(d + 1)**2*(d + 2)/6
Suppose -6*w - w = -14. Suppose w*z**4 + z**2 - 3*z**4 + 2*z**3 - 81*z + 79*z = 0. What is z?
-1, 0, 1, 2
Let r(a) be the third derivative of 40*a**2 + 1/18*a**4 + 1/30*a**5 + 0*a**3 + 0*a + 1/180*a**6 + 0. Find t, given that r(t) = 0.
-2, -1, 0
Let s = -472 - -4729/10. Let c(h) be the third derivative of s*h**5 + 6*h**2 - 1/5*h**6 - 27/2*h**3 + 0*h + 0*h**4 + 0 + 1/70*h**7. Factor c(t).
3*(t - 3)**3*(t + 1)
Let j(n) = -9*n**3 + n + 1. Let i be -1 + -3 + 4 + -1. Let g be j(i). Suppose 6*k - 4 + 7 + k + g*k**2 + 3*k**3 + 2*k = 0. Calculate k.
-1
Let p(b) be the third derivative of 1/90*b**5 + 0*b + 0 + 1/24*b**4 + 0*b**3 - 1/360*b**6 + 3*b**2. Suppose p(r) = 0. What is r?
-1, 0, 3
Let z(n) be the third derivative of -1/105*n**7 + 0 + 1/84*n**6 + 1/105*n**5 + 0*n**3 + 0*n**4 + 48*n**2 + 0*n. What is k in z(k) = 0?
-2/7, 0, 1
Let q(p) be the first derivative of p**6/2 - 6*p**5/5 - 33*p**4/4 + 12*p**3 + 54*p**2 - 41. Factor q(t).
3*t*(t - 3)**2*(t + 2)**2
Let f be 14 + (-11)/(-4 + 5). Factor -5/2*b + 5/2*b**f - 5/4*b**2 + 5/4*b**4 + 0.
5*b*(b - 1)*(b + 1)*(b + 2)/4
Factor -3/5*k**2 - 324/5*k - 8748/5.
-3*(k + 54)**2/5
Factor -8/5 - 1118/5*b**4 - 674/5*b**2 - 338/5*b**5 - 128/5*b - 1334/5*b**3.
-2*(b + 1)**3*(13*b + 2)**2/5
Determine u so that -3/2*u**3 + 3*u + 0 - 3/2*u**2 = 0.
-2, 0, 1
Let d(m) = 2*m**4 + 98*m**3 - 327*m**2 + 328*m - 113. Let l(w) = 10*w**4 + 492*w**3 - 1634*w**2 + 1640*w - 564. Let p(h) = -28*d(h) + 6*l(h). Factor p(n).
4*(n - 1)**3*(n + 55)
Let k(w) be the second derivative of 2*w**4 + 14*w**3/3 + 2*w**2 + 4*w - 3. Factor k(f).
4*(f + 1)*(6*f + 1)
Let k(u) be the first derivative of -u**4/30 + 2*u**3/9 + 14*u**2/15 - 38. Suppose k(y) = 0. What is y?
-2, 0, 7
Factor 60*o - 12*o + 313 - 125*o - 171*o - 4*o**2 - 557.
-4*(o + 1)*(o + 61)
Let d(s) = -3*s**2 + 7*s + 13. Let y(f) = -354*f + 6 + 715*f - 2*f**2 - 358*f. Let p(h) = -3*d(h) + 5*y(h). Determine i so that p(i) = 0.
-3
Let v(n) = -n**2 - 6*n - 1. Let s be v(-5). Factor 70 - 70 + 15*m**3 + 5*m**s + 10*m**2.
5*m**2*(m + 1)*(m + 2)
Let h be (-2)/(-4) - (-8)/(-16). Let l be 0/((h - -1) + -4). Find w, given that -w**2 + 2*w**2 + 4*w + l*w**2 - 2*w = 0.
-2, 0
Solve 7/5 + 1/5*j**4 + 2*j**3 + 22/5*j + 24/5*j**2 = 0 for j.
-7, -1
Let y(o) be the first derivative of -12 + 7*o - 25/2*o**2 - 2*o**3. Let t(q) = q**2 + 4*q - 1. Let z(m) = -39*t(m) - 6*y(m). Factor z(a).
-3*(a + 1)**2
Let p(b) be the third derivative of b**6/280 - 3*b**5/20 + 99*b**4/56 + 121*b**3/14 - 2*b**2 - 31. Determine z, given that p(z) = 0.
-1, 11
Find p such that -134*p + 150*p - 36*p**2 + 21 + 6*p**3 - 30*p**3 - 4*p**4 + 27 = 0.
-3, -2, 1
Factor 16/5*q**3 - 23/5*q**2 + 0 + 6/5*q - 3/5*q**4.
-q*(q - 3)*(q - 2)*(3*q - 1)/5
Let c(o) be the second derivative of -o**5/70 + 5*o**4/42 + 52*o - 2. Factor c(a).
-2*a**2*(a - 5)/7
Let i(f) = -f**4 + 2*f**3 + 4*f**2 - 6*f - 4. Let z(v) = -v + 2. Let k(q) = 3*i(q) + 6*z(q). Factor k(g).
-3*g*(g - 2)**2*(g + 2)
Let y(m) = 184*m**2 - 3*m - 2. Let j be y(-1). Let -2*b + 185*b**2 + 2*b**3 + 0*b**3 - j*b**2 = 0. Calculate b.
-1, 0, 1
Let t(n) be the first derivative of -6*n**5/25 - 4*n**4/5 - 14*n**3/15 - 2*n**2/5 - 165. Factor t(y).
-2*y*(y + 1)**2*(3*y + 2)/5
Let m(n) = 4*n**3 - 4*n**2 - 64 + 64 + 6*n**4 - 3*n + n**5. Let b(o) = o**2 + o. Let f(q) = 2*b(q) - m(q). Determine j, given that f(j) = 0.
-5, -1, 0, 1
Factor -52/7*m**2 - 2/7*m**3 - 338/7*m + 0.
-2*m*(m + 13)**2/7
Let k(c) = 19*c - 2. Let h be k(1). Factor 8 - 2*z + 16*z**2 + 5*z**3 - z**3 + h*z + 5*z.
4*(z + 1)**2*(z + 2)
Let m(b) be the first derivative of -b**7/490 - b**6/280 + 5*b**2 - 13. Let w(l) be the second derivative of m(l). Solve w(j) = 0.
-1, 0
Factor -556*y**2 + y**3 + 4*y**3 - 60*y + 584*y**2 + y**4 + 26*y**3.
y*(y - 1)*(y + 2)*(y + 30)
Suppose 0 = -5*n + 31 - 16. Suppose 5*f - 3*r - 30 = 0, -2*f = n*r - 6*r - 3. Suppose -9*u**3 - 1 - 3*u + 1 + f*u**2 + 3*u**4 = 0. Calculate u.
0, 1
Factor -27 + 4*w**2 + 132*w + 13*w + 27 - 25*w.
4*w*(w + 30)
Factor 0*i**2 + 0*i**3 + 1/3*i**5 - i**4 + 0*i + 0.
i**4*(i - 3)/3
Let o be 3 - (-3 - (12/3 - -2)). Suppose o*c - 26 + 2 = 0. Solve 192*y + 12*y**3 - 192 - 3/4*y**4 - 72*y**c = 0.
4
Let q(h) be the third derivative of -h**5/120 - 43*h**4/4 - 5547*h**3 - 104*h**2. Factor q(j).
-(j + 258)**2/2
Let l(c) be the second derivative of -c**6/30 - c**5/2 - 7*c**