f) = 16*f**4 + 34*f**3 + 26*f**2 + 4*f - 2. Let v(n) = 48*n**4 + 101*n**3 + 79*n**2 + 12*n - 7. Let h(m) = 2*v(m) - 7*y(m). Find s such that h(s) = 0.
-1, -1/4, 0
Let t(v) = v**3 - v + 4. Let w be t(0). Suppose 0 = 2*s - 3*d + 5, -3*d + 14 = s + d. Let 4*c**3 - 2*c**4 + 3*c**s + 5*c**w - 2*c**2 = 0. Calculate c.
-1, -1/3, 0
Factor -30*h**2 + 6*h - 12*h - 20 - 5*h**3 - 39*h.
-5*(h + 1)**2*(h + 4)
Let u(j) be the first derivative of j**4 + 4*j**3 + 4*j**2 + 18. Factor u(r).
4*r*(r + 1)*(r + 2)
Let o(y) be the first derivative of y**4/42 - 2*y**3/21 + y**2/7 - 2*y - 1. Let u(m) be the first derivative of o(m). Solve u(c) = 0 for c.
1
Let t be 2/(-6) + (-3)/(-3). Let c(z) be the first derivative of 2 - t*z**3 - 2*z**2 - 2*z. Factor c(q).
-2*(q + 1)**2
Let o(d) = 2*d**4 - 4*d**3 - 6*d**2 + 6*d. Let s(b) = -6*b**4 + 11*b**3 + 17*b**2 - 17*b. Let h(z) = 17*o(z) + 6*s(z). Solve h(y) = 0.
-1, 0
Let y(u) be the third derivative of u**7/105 - u**6/15 + u**5/10 + u**4/3 - 4*u**3/3 + 3*u**2. Factor y(w).
2*(w - 2)**2*(w - 1)*(w + 1)
Let h(v) be the first derivative of 0*v + 2 - v**4 + 2/3*v**3 + 2/5*v**5 + 0*v**2. Factor h(f).
2*f**2*(f - 1)**2
Determine u, given that 3/5*u**4 + 0 - 21/5*u + 21/5*u**3 - 3/5*u**2 = 0.
-7, -1, 0, 1
Factor 0 + 0*v + 4/3*v**2 + 2/3*v**3.
2*v**2*(v + 2)/3
Let d(m) be the first derivative of 9*m**5/5 - 3*m**4/2 - 3*m**3 + 3*m**2 + 12. Factor d(s).
3*s*(s - 1)*(s + 1)*(3*s - 2)
Factor 92*p**2 + 6*p + 8*p**4 + 65*p**3 - 71 + 6*p + 35 - 13*p**3.
4*(p + 1)*(p + 3)**2*(2*p - 1)
Let a be 29/(-2) + (-1)/(-2). Let n be 1/2 - 49/a. Factor -1/2*r**2 + 0*r - 3/2*r**n - 2*r**3 + 0.
-r**2*(r + 1)*(3*r + 1)/2
Let l = 265/4 - 66. Determine z, given that -l - z - 3/4*z**2 = 0.
-1, -1/3
Let b be (220/522)/(1 - -1). Let f = b + 1/87. Factor -2/9*m**2 + f + 0*m.
-2*(m - 1)*(m + 1)/9
Let u = -13 - -71/5. Factor 0 + 2/5*q**4 + 6/5*q**3 + 2/5*q + u*q**2.
2*q*(q + 1)**3/5
Let l(n) = 9*n - 68. Let h be l(8). Let v be (1 - 7)*2/(-4). Factor -7*q + h*q + 2*q - v*q + 2*q**2.
2*q*(q - 2)
Let b(a) be the first derivative of -a**4 + 8*a**3/3 + 2*a**2 - 8*a - 1. Factor b(f).
-4*(f - 2)*(f - 1)*(f + 1)
Let q(h) = h**2 - 13*h + 4. Let y be q(13). Suppose -b - y*b = 0. Suppose 0*j + 0*j**4 - 1/3*j**3 + 0 + b*j**2 + 1/3*j**5 = 0. What is j?
-1, 0, 1
Factor -3*k**3 + 5*k + 5 + 4 - 201*k**2 + 192*k**2 - 2*k.
-3*(k - 1)*(k + 1)*(k + 3)
Let q(g) = -11*g**3 - 6*g**2 + 11*g + 6. Let c(i) = -6*i**3 - 3*i**2 + 6*i + 3. Let k(p) = 5*c(p) - 3*q(p). Factor k(r).
3*(r - 1)*(r + 1)**2
Solve 28 - 3*t - t + 4*t**2 - 28 + 48*t**3 = 0.
-1/3, 0, 1/4
Suppose 0 = 7*u - 3*u + 4*n - 24, -4*u = -2*n. Factor -i**3 + 7*i**3 + 0*i + 2*i**u - 5*i**3 + i.
i*(i + 1)**2
Let n(q) be the third derivative of 3*q**8/392 + q**7/35 + q**6/60 - 17*q**5/210 - 4*q**4/21 - 4*q**3/21 + 10*q**2. Suppose n(v) = 0. Calculate v.
-1, -2/3, 1
Let r(h) be the first derivative of -1/18*h**3 + 1/3*h**2 - 2/3*h - 1. Factor r(q).
-(q - 2)**2/6
Let x(y) = 5*y - 27. Let d be x(6). Factor -3/2*u**5 + 0*u**3 + d*u**2 + 3/2*u + 0 - 3*u**4.
-3*u*(u - 1)*(u + 1)**3/2
Let w(j) = -8*j**5 - 12*j**4 + 4*j**3 - 4*j**2 + 4*j - 4. Let h(t) = 9*t**5 + 13*t**4 - 5*t**3 + 5*t**2 - 5*t + 5. Let d(u) = -4*h(u) - 5*w(u). Factor d(g).
4*g**4*(g + 2)
Let d be (9 + -4 + -5)/(2 - 1). Factor d + 2/3*n - 1/3*n**2.
-n*(n - 2)/3
Let o be (-15)/10 - 6/(-4). Factor -6/5*w**3 - 2/5*w**4 - 2/5*w - 6/5*w**2 + o.
-2*w*(w + 1)**3/5
Let s = 17 - 32. Let v be ((-6)/21)/(s/21). Find b, given that 2/5*b**2 + 0 + v*b = 0.
-1, 0
Let g(r) = 7*r**2 + 50*r + 123. Let a(c) = -c**2 + 1. Let s(o) = 2*a(o) + g(o). Factor s(k).
5*(k + 5)**2
Factor -18*p**2 - 4 - 25*p**4 + 139*p**4 - 101*p**3 - 61*p**3 + 156*p**4 + 26*p.
2*(3*p - 1)**3*(5*p + 2)
Solve 1/2*b**3 + 216*b + 18*b**2 + 864 = 0.
-12
Let i = -4 + 1. Let k(n) = n**5 + n + 1. Let t(h) = -6*h**5 + 6*h**4 - 3*h**3 - 3*h - 3. Let c(w) = i*k(w) - t(w). Solve c(l) = 0 for l.
0, 1
Let r(w) = 3*w - 9. Let x be r(3). What is p in x*p - p**2 + 1/2*p**3 + 0 = 0?
0, 2
Suppose 4*l - 24 = 4*q, -2*l + 5*l = -3*q + 6. Suppose -4*r = 3*i - 0*r - 4, -3*i + 18 = -3*r. Solve 2*u**i + l - 2*u**3 - 4 = 0.
0, 1
Solve 3/4*p**3 + 0 + 0*p + 3/2*p**2 = 0 for p.
-2, 0
Factor 0*l + 1/3*l**4 + 0*l**2 + 1/3*l**3 + 0.
l**3*(l + 1)/3
Let b(h) = -16*h**4 - 80*h**3 - 150*h**2 - 92*h + 8. Let i(p) = -63*p**4 - 319*p**3 - 600*p**2 - 368*p + 32. Let d(y) = -22*b(y) + 6*i(y). Factor d(g).
-2*(g + 2)**3*(13*g - 1)
Let 75*n - 37*n**3 - 33*n**3 - 35*n**4 + 3*n**5 + 9 + 36 - 8*n**5 - 10*n**2 = 0. Calculate n.
-3, -1, 1
Let u(y) = -y**3 - 7*y**2 - 2*y + 24. Let d be u(-6). Suppose 1/5*r**2 - 1/5*r + d = 0. What is r?
0, 1
Let w(i) be the third derivative of i**6/360 + i**5/180 - i**4/72 - i**3/18 - 10*i**2. Let w(c) = 0. Calculate c.
-1, 1
Let m = 27 + -9. Factor 10*r**5 - 3*r**2 - 24*r**4 + m*r**3 - 3*r**2 + 2*r**2.
2*r**2*(r - 1)**2*(5*r - 2)
Let o be 12/225 + (-8)/(-100). Factor 0 - 2/15*h**2 + o*h.
-2*h*(h - 1)/15
Let o(r) be the second derivative of -7*r**6/60 - 19*r**5/40 - 5*r**4/8 - r**3/12 + r**2/2 + 23*r. Find d such that o(d) = 0.
-1, 2/7
What is t in -4*t**2 - 8 + 9 + 2*t + t = 0?
-1/4, 1
Let y(h) = 2*h**3 - 2*h**2 + 6*h. Let w(s) = 3*s**3 - 3*s**2 + 12*s. Let o(k) = 3*w(k) - 5*y(k). Factor o(z).
-z*(z - 3)*(z + 2)
Let g = 322 + -322. Factor -1/3*v**3 + g - v**2 + 0*v.
-v**2*(v + 3)/3
Suppose 4*i + 0*i - 20 = 0. Suppose i*v = -g + 26, 4*g - 7 = -v + 2*g. Factor 2/3 + 2/3*c**v + 4/3*c**3 - 2*c**4 - 2*c + 4/3*c**2.
2*(c - 1)**4*(c + 1)/3
Suppose -3*d = -4*h + h + 9, -2*h + 5*d + 6 = 0. Suppose 4 = -p + h*p. Find c, given that 3*c**2 - 6*c**2 + c**p + 2*c**3 = 0.
0, 1
Suppose 1 = t - 2. Suppose 0 = 2*v - 3*x, -v - 4*x = t*v. Factor 0*u - 2/5*u**5 + v + 2/5*u**2 + 2/5*u**3 - 2/5*u**4.
-2*u**2*(u - 1)*(u + 1)**2/5
Let y = 603/490 + -3/98. Solve 2/5*k**2 - 8/5*k + y = 0.
1, 3
Let d(k) be the second derivative of k**4/12 + k**3/6 + 6*k. What is w in d(w) = 0?
-1, 0
Suppose -24 = 13*r - 50. Determine d, given that -1/2*d**4 - 1/2 - 3*d**2 - 2*d - r*d**3 = 0.
-1
Let f(s) be the second derivative of s**7/168 - 3*s**6/40 + 3*s**5/8 - 23*s**4/24 + 11*s**3/8 - 9*s**2/8 - s. Factor f(z).
(z - 3)**2*(z - 1)**3/4
Determine n so that 6/5*n + 8/5 - 2/5*n**2 = 0.
-1, 4
Let q(y) = -y**2 + 9*y - 6. Let m be q(8). Factor -m*g**4 - 8*g**2 + 0*g**4 + 4 + 6*g**4.
4*(g - 1)**2*(g + 1)**2
Let g be 5/(-1 + -4) + 1/1. Let x(m) be the third derivative of 1/120*m**4 + 0*m**3 + 0*m + 1/150*m**5 + g - 2*m**2 + 1/600*m**6. Factor x(q).
q*(q + 1)**2/5
Let c = -768 - -771. Determine i, given that 27/7*i - 6/7 - 18/7*i**4 + 3/7*i**5 + 6*i**c - 48/7*i**2 = 0.
1, 2
Let i(v) = 2*v**2 - v - 1. Let t be i(-1). Solve -2*c**t + 0*c - 3*c + 0*c**2 + c = 0 for c.
-1, 0
Suppose -117*k = -110*k - 28. Solve 0 + 64/3*i**2 + 12*i**k + 28*i**3 + 16/3*i = 0.
-1, -2/3, 0
Let r be 498/5 + 6/15. Determine w, given that -w**2 - r + 2*w + 100 = 0.
0, 2
Factor 6/7*d**2 + 2/7*d**4 + 0*d - 8/7*d**3 + 0.
2*d**2*(d - 3)*(d - 1)/7
Let c = 6 - 4. Solve 2*p**3 - c*p**3 + 15*p**5 - 2*p**3 + p**4 = 0.
-2/5, 0, 1/3
Suppose 5*u = -5*h, -4*h - 3*u + 2 = -2. Suppose -3*g = -7 - 8. Suppose 0*t + 4/5*t**h + 0*t**2 + 0*t**3 - 18/5*t**g + 0 = 0. Calculate t.
0, 2/9
Let v = -501/5 + 101. Let -2/5*r**3 + 0 - v*r**2 - 2/5*r = 0. Calculate r.
-1, 0
Suppose 7*o + 6*o = 5*o. Let w(i) be the second derivative of 0 + 0*i**3 + 2*i - 1/25*i**6 + 1/105*i**7 + o*i**2 - 1/30*i**4 + 3/50*i**5. Factor w(j).
2*j**2*(j - 1)**3/5
Let j(z) be the first derivative of -5*z**3/3 + 5*z + 6. Let j(i) = 0. Calculate i.
-1, 1
Suppose -2*a + 4*o + 16 = 0, -4*o - 18 = -3*a - 0*o. Let c(f) = 2*f**3 + 3*f**2 + 4*f + 2*f**2 + f**2. Let m(r) = r + 1. Let g(t) = a*m(t) + c(t). Factor g(k).
2*(k + 1)**3
Let z(r) be the first derivative of r**4/30 - 14*r**3/45 + 27. Factor z(s).
2*s**2*(s - 7)/15
Determine w, given that -1/2*w + 1/2*w**3 + 0*w**2 + 0 = 0.
-1, 0, 1
Let l = -77/39 - -30/13. Let i(y) be the third derivative of l*y**3 + 1/24*y**4 + 0 - 1/60*y**5 + y**2 + 0*y. Factor i(r).
-(r - 2)*(r + 1)
Let g be (-115)/(-15) + 8/((-2)/1). Find q, given that 4*q**2 + g*q**3 + q**4 + 0 + 4/3*q = 0.
-2, -1, -2/3, 0
Let w(b) be the third derivative of 0 - 1/120*b**5 - 1/48*b**4 + 1/336*b**8 + 0*b**3 + 0*b + 1/80*b**6 + 1/84*b**7 + b**2. Suppose w