w - 54. Let u(d) = d**4 - d**3 - d**2 - 2*d. Let t(q) = n(q) - 5*u(q). Suppose t(l) = 0. What is l?
-9, 1, 2
Suppose 16 = 3*d + 11*d - 12. Factor 3/7*c - 3/7*c**d + 0.
-3*c*(c - 1)/7
Let s(p) be the second derivative of -5*p - 1/4*p**5 - 40*p**3 - 160*p**2 - 5*p**4 + 6. Let s(a) = 0. Calculate a.
-4
Let a(f) be the first derivative of -f**3/21 + 8*f**2/7 + 57*f/7 - 418. Factor a(w).
-(w - 19)*(w + 3)/7
Let d be (-74)/(-333) + 220/225. Let 2/5*z**3 - 2/5*z - 4/5 - 2/5*z**4 + d*z**2 = 0. What is z?
-1, 1, 2
Let o(f) be the third derivative of -f**8/588 + 3*f**7/245 - f**6/42 + f**5/70 + 6*f**2 + 17*f. Suppose o(n) = 0. What is n?
0, 1/2, 1, 3
Let v(m) be the first derivative of 9*m**5/5 + 6*m**4 - 8*m**3 - 48*m**2 - 48*m - 986. Factor v(s).
3*(s - 2)*(s + 2)**2*(3*s + 2)
Suppose -4*x + 1364 = 7*x. Suppose 121*f = x*f - 6. Factor -2/5*j**f + 6/5*j - 4/5.
-2*(j - 2)*(j - 1)/5
Let i(x) = x**2 + 163*x + 1814. Let o be i(-12). Factor 64/7 + 16/7*d + 1/7*d**o.
(d + 8)**2/7
Let x = 4352 + -21759/5. Let p be ((-15)/50)/((-1)/2). Find j such that x - 2/5*j - p*j**2 = 0.
-1, 1/3
Let o be (-1656)/621*54*9/(-264). Let -122/11*f**3 + o*f**4 + 102/11*f**2 - 12/11 - 8/11*f**5 - 14/11*f = 0. Calculate f.
-1/4, 1, 2, 3
Let z(r) = r + 8. Let p be z(-3). Factor -11 + p*g**3 - 45*g - 14 + 0*g**2 - 15*g**2.
5*(g - 5)*(g + 1)**2
Let d(w) be the second derivative of -3/8*w**4 - 1/20*w**5 - 5/6*w**3 - 1/360*w**6 + 0 + 0*w**2 + 6*w. Let f(k) be the second derivative of d(k). Factor f(q).
-(q + 3)**2
Let l(y) be the third derivative of -y**7/70 + 11*y**6/60 + 17*y**5/60 - y**4/3 + 131*y**2. Factor l(i).
-i*(i - 8)*(i + 1)*(3*i - 1)
Let k be 1/((-5)/(4 - 14)). Factor -12*i - 4*i**4 + 2*i**5 - k*i**4 + 8*i**2 + 12*i.
2*i**2*(i - 2)**2*(i + 1)
Factor 2/9*g**2 - 2/9*g - 40/9.
2*(g - 5)*(g + 4)/9
Let u(j) be the second derivative of j**9/22680 - j**8/10080 - j**7/1890 + 2*j**4/3 - 16*j. Let c(x) be the third derivative of u(x). Factor c(h).
2*h**2*(h - 2)*(h + 1)/3
Let s be 1098/7320*((-170)/(-12) - 0) + -2. Factor s*u**2 + 0 + 1/4*u.
u*(u + 2)/8
Let k(n) = 10*n**2 - 242*n + 964. Let w(s) = 22*s**2 - 486*s + 1927. Let p(l) = 10*k(l) - 6*w(l). Factor p(h).
-2*(4*h - 31)**2
Let y(n) = -1. Let r(b) = b**2 - 11*b - 14. Let l(t) = r(t) - 2*y(t). Factor l(a).
(a - 12)*(a + 1)
Let l be (8/(-20))/((-2)/6). Let h be (-18)/4*36/(-54). Factor -2/5*g**4 + 0 + 0*g**h + l*g**2 + 4/5*g.
-2*g*(g - 2)*(g + 1)**2/5
Factor -10/11*d**3 + 0 - 14/11*d**2 - 6/11*d - 2/11*d**4.
-2*d*(d + 1)**2*(d + 3)/11
Let q(h) be the third derivative of -h**6/60 - 14*h**5/15 - 221*h**4/12 - 338*h**3/3 + 60*h**2. Factor q(r).
-2*(r + 2)*(r + 13)**2
Suppose 0 = -5*v - 1 + 21. Suppose 35 = a + v*a. Find q, given that 10*q**2 + 12*q**2 + 12*q**3 - a*q**2 + 3*q = 0.
-1, -1/4, 0
Factor 2*t**4 - 14 - 2*t**2 + 17 - 4*t + 10*t**3 - 3 - 6*t.
2*t*(t - 1)*(t + 1)*(t + 5)
Let o(d) = -d**4 - d**2 - 2*d + 1. Let z(s) = 24*s**5 - 29*s**4 + 3*s**3 - 2*s**2 - 4*s + 2. Let y(c) = -2*o(c) + z(c). Factor y(u).
3*u**3*(u - 1)*(8*u - 1)
Suppose -k + 5*l - 9 = 0, -k - 2*k + 3*l = -9. Suppose 3*p + k = 0, -2*n - 3*p = -3 - 3. Factor -j - n*j**3 + 3*j**2 + 7*j + 2 - 5*j**2.
-2*(j - 1)*(j + 1)*(3*j + 1)
Factor 3*r**3 + 241*r**2 - 487*r**2 + 249*r**2.
3*r**2*(r + 1)
Let y be 4*1 + (23 - 23). Let o be 6/(126/69) + y/(-14). Factor 0 - 1/2*v**4 + 0*v + 0*v**2 - 1/2*v**o.
-v**3*(v + 1)/2
Let n(j) = j**3 - 20*j**2 - 21*j. Suppose 7*d - 6*d = 21. Let p be n(d). Factor p + 3/4*i + 3/4*i**2.
3*i*(i + 1)/4
Let 54*z + 1/3*z**4 + 45 + 14/3*z**3 + 24*z**2 = 0. Calculate z.
-5, -3
Suppose -2*k - 6 = -0*k + 4*h, -12 = 4*h. Suppose 5*i + k*f - 27 = -0*f, 5*f = 3*i + 11. What is g in 2*g**3 - g**2 + 2*g**3 - 3*g**i = 0?
0, 1
Let u(z) = -z**3 - z**2 + z + 1. Let o(g) = 9*g**4 - 35*g**3 + 11*g**2 + 3*g + 12. Suppose i - 1 = -12. Let f = i + 9. Let a(s) = f*o(s) + 22*u(s). Factor a(c).
-2*(c - 1)**2*(3*c - 1)**2
Let o = 1/684 + 253/228. Let s(h) be the second derivative of 11/12*h**4 - o*h**3 + 0 - 11/30*h**5 - 7*h + 2/3*h**2 + 1/18*h**6. Factor s(q).
(q - 2)*(q - 1)**2*(5*q - 2)/3
Let q be (-2 - -36)*(-16)/(-8). Let z = -68 + q. Factor 0 - 2/3*p**3 + 0*p**4 + 0*p + 2/3*p**5 + z*p**2.
2*p**3*(p - 1)*(p + 1)/3
Let r(s) be the third derivative of s**8/84 - 8*s**7/105 + s**6/24 + 19*s**5/60 + s**4/4 - 51*s**2. Suppose r(q) = 0. Calculate q.
-1/2, 0, 2, 3
Let w = -47 - -63. What is y in -4*y - w*y + 8 - 13 + 25 + 5*y**2 = 0?
2
Let b(s) = -7*s**4 - 2*s**3 + 25*s**2 - 19*s. Let o(m) = -20*m**4 - 8*m**3 + 76*m**2 - 56*m. Let q(g) = -8*b(g) + 3*o(g). Suppose q(z) = 0. What is z?
-4, 0, 1
Let l(h) = h**2 - 190*h - 8. Let s(b) = 189*b + 6. Let c(o) = 3*l(o) + 4*s(o). Factor c(f).
3*f*(f + 62)
Let n(h) be the second derivative of -h**5/390 + h**4/78 + 10*h**2 - h. Let i(m) be the first derivative of n(m). Factor i(k).
-2*k*(k - 2)/13
Let i be (-1788)/1200*2 + 3*1. Let d(y) be the second derivative of 4*y - 1/30*y**4 + 0 + 0*y**3 + i*y**5 + 0*y**2. Find p such that d(p) = 0.
0, 1
Let b(r) be the second derivative of -r**7/105 + 4*r**6/75 - r**5/10 + r**4/15 + 82*r. Factor b(q).
-2*q**2*(q - 2)*(q - 1)**2/5
Solve -28/11*r**2 - 12/11 - 34/11*r - 6/11*r**3 = 0 for r.
-3, -1, -2/3
Let v(p) = -p**3 + 4*p**2 - p + 8. Suppose 2*o = -4*m - 8, -o + 4*m + 32 = 3*o. Let q be v(o). Factor 0*d + 0*d**2 + 4/7*d**q + 8/7*d**3 + 0.
4*d**3*(d + 2)/7
Let s(i) be the second derivative of 0 + 1/140*i**5 - 1/42*i**4 + 0*i**2 - 39*i - 1/14*i**3. Factor s(d).
d*(d - 3)*(d + 1)/7
Let j = -40 - -42. Suppose -5*q = 5*r - 45, -j*r = -r - q - 1. Factor 0 + 0*p - 1/2*p**3 - 1/2*p**r + 0*p**2 + p**4.
-p**3*(p - 1)**2/2
Let j = 21/22 - 26/33. Let l(x) be the second derivative of 0*x**5 + 0*x**2 + 1/15*x**6 + 0 - 1/42*x**7 - 2*x - 1/6*x**4 + j*x**3. Factor l(u).
-u*(u - 1)**3*(u + 1)
Let d(j) = 81*j - 2345. Let o be d(29). Factor -2/9*b**2 - 2/9*b**3 + 1/9 + 1/9*b**5 + 1/9*b**o + 1/9*b.
(b - 1)**2*(b + 1)**3/9
Let o = 122146/5 - 24423. Factor -o*y**3 + 83/5*y**2 - 10 + 3/5*y**4 - y.
(y - 5)**2*(y - 1)*(3*y + 2)/5
Let i(o) = -o**3 + o**2 + 1. Let n(l) = -2*l**3 - l**2 + 4*l + 3. Let j be (3*-1)/(87/58). Let k(d) = j*n(d) + 6*i(d). Determine s so that k(s) = 0.
0, 2
Suppose k - 3*s = -4, 4*s - 4 = 5*k + 16. Let r be ((-2)/k)/(8 - (-328)/(-48)). Factor 0*h - r*h**4 + 6/7*h**2 + 0 - 3/7*h**3.
-3*h**2*(h - 1)*(h + 2)/7
Let a(g) = -g**2 - 11*g - 28. Let j be a(-5). Let o(v) be the first derivative of -v**5 + v**j - 1 + 0*v + 5/3*v**3 - 9/4*v**4 + 7/6*v**6. Factor o(c).
c*(c - 1)**2*(c + 1)*(7*c + 2)
Let w(f) be the first derivative of f**7/112 - 3*f**5/40 + f + 13. Let l(n) be the first derivative of w(n). What is y in l(y) = 0?
-2, 0, 2
Suppose 4*c = -2*c + 13*c - 14. Let 0 + 3/2*h - 1/2*h**c = 0. What is h?
0, 3
Suppose -2*t = 13 - 3, -n + 5 = -t. Find b such that -4/5*b**3 + n + 0*b - 8/5*b**2 + 8/5*b**4 + 4/5*b**5 = 0.
-2, -1, 0, 1
Suppose 2*d = -4*p + 6, p - 4*p - 12 = -4*d. Factor -d*m**3 - 2 - m - 14*m + 8*m**3 - 8.
5*(m - 2)*(m + 1)**2
Suppose 8*c - 52*c = 242 - 330. What is x in 0 + 2/11*x**c - 4/11*x = 0?
0, 2
Let g be 723/(-4820) - 6/(-8). Suppose -6/5*k**2 + 0 + 6/5*k**4 - g*k**5 + 3/5*k + 0*k**3 = 0. What is k?
-1, 0, 1
Let x = -4989/4 - -1248. Suppose 3/4 + 3/4*u**3 - 3/4*u**2 - x*u = 0. Calculate u.
-1, 1
Let f(n) be the third derivative of 0 - 1/3*n**3 + 0*n + 1/18*n**4 - 18*n**2 + 1/90*n**5. Factor f(z).
2*(z - 1)*(z + 3)/3
Let s(d) = -d**3 + 2*d. Let f(r) = r**3 - 40*r**2 + 79*r - 42. Let v(x) = 3*f(x) + 6*s(x). Solve v(l) = 0 for l.
-42, 1
Let j = -71/2 - -36. Suppose -l - 3*d + 17 = 0, -4*l - 5 + 3 = -2*d. Factor j*c**3 + 3*c**l + 6*c + 4.
(c + 2)**3/2
Let j = -45352 - -272117/6. Suppose -j*w + 25/12 + 1/12*w**2 = 0. What is w?
5
Let v(i) be the third derivative of 0*i + 1/120*i**6 - 1/60*i**5 - 6*i**2 + 0 - 1/24*i**4 + 1/6*i**3. Solve v(r) = 0.
-1, 1
Let p(m) = m**3. Suppose 4*d - 25 = w, 2*d - 5*w - 2 = -3. Let g(t) = -11*t + 2*t + t + d*t. Let o(i) = 3*g(i) + 3*p(i). Factor o(h).
3*h*(h - 1)*(h + 1)
Let k(f) be the first derivative of -f**4/5 - 16*f**3/5 + 2*f**2/5 + 48*f/5 - 178. Determine z so that k(z) = 0.
-12, -1, 1
Let l = 96 + -92. Factor l*c**2 + 0*c**2 - 8*c + 28 - 40.
4*(c - 3)*(c + 1)
Let t(p) = -12*p**3 + 27*p - 27. Let b(x) = -x**3 + 2*x - 2. Let k = -40 - -42. Let i(