*3/27 + 13*d**2/18 + 14*d/9 + 50. Factor i(h).
-(h - 14)*(h + 1)/9
Suppose -u - 42 = -22. Let l be 5/(u/16) + 84/15. Determine n, given that -12/5*n**2 - 2/5*n**4 - 2/5 + l*n + 8/5*n**3 = 0.
1
Let q(w) be the third derivative of w**5/20 + 57*w**4/8 + 100*w**2 - w. What is s in q(s) = 0?
-57, 0
Let i(j) be the third derivative of 1/4*j**5 + 13/24*j**4 + 0 + 7/120*j**6 + 1/210*j**7 + 0*j + 2/3*j**3 - 19*j**2. Factor i(l).
(l + 1)**3*(l + 4)
Let v(s) be the third derivative of s**5/30 + 5*s**4/12 + 2*s**3 + s**2 - 11*s. Factor v(i).
2*(i + 2)*(i + 3)
Let z(f) be the second derivative of f**7/21 - 19*f**6/45 + 13*f**5/10 - 29*f**4/18 + 2*f**3/3 + 35*f. Solve z(l) = 0 for l.
0, 1/3, 1, 2, 3
Factor 1/4*n + 0 + 5/4*n**3 + 3/2*n**2.
n*(n + 1)*(5*n + 1)/4
Suppose 0 = m - 7 - 0. What is t in -15*t**4 + 2*t**3 + 13*t**4 - 5*t**2 - 2*t**5 + m*t**2 = 0?
-1, 0, 1
Let o be (3/(-4) - (-2)/4)*-12. Factor 3*q**3 + q**4 - 7*q**3 + o*q**3.
q**3*(q - 1)
Let o(x) = x**4 + 20*x**3 + 96*x**2 + 172*x + 112. Let z(b) = 2*b. Let s(u) = -o(u) - 2*z(u). Factor s(f).
-(f + 2)**3*(f + 14)
Let y be (-1568)/(-51480) - (-10)/25. Let p = y + 2/143. Factor -2/9*i**2 + p*i + 2/3.
-2*(i - 3)*(i + 1)/9
Solve -168*z + 292 + 1047 + 883 + 130 + 3*z**2 = 0 for z.
28
Find f such that -5000/3 - 2/3*f**3 - 1600*f + 66*f**2 = 0.
-1, 50
Let u(q) be the first derivative of 12*q - 9/4*q**4 - 11*q**3 + 42 - 12*q**2. Factor u(h).
-3*(h + 2)**2*(3*h - 1)
Let r = 228 - 135. Determine a so that 8*a + 2*a**4 - r*a**3 - 2*a**4 + 31*a**3 - 24*a**2 + 36*a**4 = 0.
-1/2, 0, 2/9, 2
Let d(y) = 2*y**3 + 20*y**2 - 120*y + 159. Let w(b) = -b**3 - 20*b**2 + 119*b - 160. Let q(l) = -2*d(l) - 3*w(l). Factor q(k).
-(k - 9)**2*(k - 2)
Let m(g) = g**2 + 16*g + 42. Let r be m(-13). Let u(k) = -k**2 - 6*k + 2. Let j be u(-6). Factor 36*s**j + 4*s**4 - r*s + 20*s**3 + 7 + 4 + 31*s - 3.
4*(s + 1)**3*(s + 2)
Let k(r) = -43*r**2 + 26*r + 23. Let t(h) = -85*h**2 + 55*h + 45. Let d(c) = 5*k(c) - 2*t(c). Factor d(l).
-5*(l - 1)*(9*l + 5)
Factor 51 + 3 - 30*y**2 - 3*y**4 - 134*y + 26*y + 69 + 45 + 27*y**3.
-3*(y - 7)*(y - 2)**2*(y + 2)
Let u(o) be the first derivative of o**3/4 + 93*o**2/8 - 24*o + 400. Let u(n) = 0. Calculate n.
-32, 1
Let m = 22525 + -22525. Factor 0*w + m + 1/8*w**2 - 1/8*w**3.
-w**2*(w - 1)/8
Let n(s) = 486*s**4 + 81*s**3 + 33*s**2 - 33*s - 33. Let r(c) = 61*c**4 + 10*c**3 + 4*c**2 - 4*c - 4. Let m(i) = 4*n(i) - 33*r(i). What is j in m(j) = 0?
-2/23, 0
Let q be (-6)/(-8) + (-13)/(-4). Factor s**4 + 8 - 8*s + 2*s**2 - 2*s**4 - q*s + 3*s**3.
-(s - 2)**2*(s - 1)*(s + 2)
Let n(l) = 2*l**4 - l**3 - l**2 + 3*l. Let k(p) = -p**4 + p**2 - 2*p. Let g be (12/9)/(1/3). Let r(f) = g*n(f) + 6*k(f). Factor r(m).
2*m**2*(m - 1)**2
Let w(t) be the third derivative of -5*t**2 + 1/60*t**5 + 0*t - 1/2*t**4 + 6*t**3 + 2. Solve w(d) = 0 for d.
6
Let g(p) be the first derivative of -3*p**4/16 + 6*p**2 + 84. Factor g(a).
-3*a*(a - 4)*(a + 4)/4
Let b be (2/4)/(1/4). Let j be (-8)/30*(3 - 9). Factor 2/5*h**b + 8/5 - j*h.
2*(h - 2)**2/5
Let t(q) = 2*q**4 - 8*q**3 - 12*q**2 + 5*q + 10. Let s(v) = 2*v**4 - 8*v**3 - 12*v**2 + 4*v + 10. Let k(d) = -3*s(d) + 4*t(d). Determine b, given that k(b) = 0.
-1, 1, 5
Let c = 25 - 23. Let y = 1 + 1. Find l such that l**3 - c*l**2 - 1 + 3*l**2 - y*l**3 + l = 0.
-1, 1
Suppose 3*w = -2*z, 4*w + 6*z - z = 0. Let i be (1 + -4)*(-15)/135 + w. Factor -1/3*c**5 + 1/3*c**2 + 0 - i*c**4 + 1/3*c**3 + 0*c.
-c**2*(c - 1)*(c + 1)**2/3
Let l be 340/(-16) - ((1 - 1) + 0). Let z = l - -259/12. Factor 2/3 - 1/3*f**2 + z*f.
-(f - 2)*(f + 1)/3
Let i(l) be the second derivative of -l**6/30 - l**5/90 + l**4/36 - 11*l**2/2 - 7*l. Let t(w) be the first derivative of i(w). Factor t(v).
-2*v*(2*v + 1)*(3*v - 1)/3
Let y be (-218)/(-14) - 3/(-7). What is b in -12*b**2 + y*b**2 - 8*b + 36*b**3 + 38 - 40 + 26*b**2 = 0?
-1, -1/6, 1/3
Suppose -4*g + 3*q = -23, -4*q + 5 = -5*g + 35. Let y be 56/16 - 2/4. Factor -o**3 - o**3 - 2*o**g + 0*o**3 + 0*o**y.
-2*o**2*(o + 1)
Let u(p) = -p**3 - 6*p**2 + 5*p - 10. Suppose 0 = -2*v - 12 - 2. Let n be u(v). Suppose -n*m**4 + 8*m - 2 + m**5 + 5*m**4 - 2 - 5*m**3 - m**2 = 0. Calculate m.
-2, 1
Let o = -269 - -549/2. Factor 25/2*j**4 - o*j**2 + 15*j**3 - 6*j + 2.
(j + 1)**2*(5*j - 2)**2/2
Suppose 2337 - 3009 + 6*g**2 + 246*g - 2*g**2 + 16*g + 66*g = 0. What is g?
-84, 2
Factor 2/3*c**3 + 0 + 128/3*c**2 + 2048/3*c.
2*c*(c + 32)**2/3
Determine w so that 9*w**2 - 14*w**2 + 12 + 3*w**3 - 2*w**2 - 2*w**2 = 0.
-1, 2
Let a be 39/(-52) + (-970)/(-56). Let j = 1290/77 - a. Factor -j*l**2 - 2/11*l + 0.
-2*l*(l + 1)/11
Let c(v) be the third derivative of v**7/105 - 7*v**6/30 + 23*v**5/10 - 35*v**4/3 + 100*v**3/3 - v**2 + 84*v. Solve c(i) = 0.
2, 5
Let p(g) be the third derivative of -g**8/28 + 38*g**7/105 - 13*g**6/30 - 33*g**5/5 + 18*g**4 + 72*g**3 - 429*g**2. Suppose p(z) = 0. What is z?
-2, -2/3, 3
Let b = 1/2 + 0. Let m be (-106)/(-56) - 100/700. Solve 3/4*z**5 - m*z + z**3 - 2*z**4 + b + 3/2*z**2 = 0 for z.
-1, 2/3, 1
Let c(f) be the first derivative of -867*f**5/5 + 816*f**4 - 888*f**3 - 384*f**2 - 48*f - 84. Factor c(h).
-3*(h - 2)**2*(17*h + 2)**2
Let q(l) be the first derivative of 2*l**3/51 - 155*l**2/17 + 308*l/17 - 82. Factor q(z).
2*(z - 154)*(z - 1)/17
Let s(x) = 48*x + 3028. Let y be s(-63). Find p such that 0 + 2/3*p**y + 1/3*p**5 - 2/3*p**2 - 4/3*p**3 + p = 0.
-3, -1, 0, 1
Let g = -245/8 + 7611/248. Let p = g - -89/62. Solve -5/2 + 9/2*a - 1/2*a**3 - p*a**2 = 0.
-5, 1
Let d = -195 + 197. Let a(v) be the second derivative of 0 + 3/2*v**2 + 0*v**5 + 0*v**3 + d*v - 1/2*v**4 + 1/10*v**6. Factor a(f).
3*(f - 1)**2*(f + 1)**2
Solve 16/9*g - 2/9*g**3 + 0 + 14/9*g**2 = 0 for g.
-1, 0, 8
Let r(n) = -5*n + 3*n**2 - 10 + 0 - 8*n**2 + 7*n**3 + n**2. Let p(b) = b**3 - 1. Let t(q) = 24*p(q) - 3*r(q). Find u such that t(u) = 0.
-2, -1
Let m be 2 - (-1)/(2/6). Let r(w) = -w**2 - 2*w + 3. Let q(l) = -2*l**2 - 3*l + 5. Let b(s) = m*r(s) - 3*q(s). Factor b(g).
g*(g - 1)
Let c = -51 + 80. What is a in -9*a - 29 + 2*a**3 - 4*a**4 + c + 12*a**2 - a**5 = 0?
-3, 0, 1
Let z(l) be the second derivative of l**5/15 + 2*l**4/3 + 8*l**3/3 + 27*l**2/2 + 3*l. Let c(o) be the first derivative of z(o). Factor c(j).
4*(j + 2)**2
Let q = 1718/5 - 5114/15. Factor -2/3*j**2 + q*j - 8/3.
-2*(j - 2)**2/3
Let j(s) be the first derivative of 3*s**3/10 - 23*s**2/4 - 13*s/5 - 534. Factor j(g).
(g - 13)*(9*g + 2)/10
Suppose -u + 9 = 2. Suppose -w + 2*w + u = 3*p, -5*p = 5*w - 25. Factor -f**3 + 11/2*f**w - 6*f - 9/2.
-(f - 3)**2*(2*f + 1)/2
Let x be (9/(-1) - -3)*2/(-4). Let w be 2*x - 231/42. Solve 0 - w*h - 1/2*h**2 = 0 for h.
-1, 0
Let x(m) be the second derivative of -m**5/5 - 44*m**4/3 - 328*m**3/3 - 320*m**2 + 77*m. Factor x(y).
-4*(y + 2)**2*(y + 40)
Let a be (1/2)/((-6)/(-4) + -2). Let v(z) = -z + 1. Let y(f) = -2*f**2 + 9*f + 1. Let o(q) = a*y(q) - 5*v(q). Factor o(h).
2*(h - 3)*(h + 1)
Let c be (44/7)/(1422/553). Let o(s) be the first derivative of -13*s**4 - c*s**6 - 4/3*s**2 + 2 - 28/3*s**5 - 68/9*s**3 + 0*s. Factor o(x).
-4*x*(x + 1)**3*(11*x + 2)/3
Let x(a) be the first derivative of 3*a**5/100 - 3*a**4/20 + a**3/5 + 3*a + 10. Let q(p) be the first derivative of x(p). Factor q(y).
3*y*(y - 2)*(y - 1)/5
Let f(b) = 3*b**3 - 10*b**2 + 8*b - 4. Let d(z) = z**3 - 2*z**2 - 1. Let y(g) = -4*d(g) + f(g). Factor y(a).
-a*(a - 2)*(a + 4)
Let n(q) = -35*q - 15. Let p(b) = b**2 - 2*b + 1. Let d(r) = -n(r) + 5*p(r). Factor d(t).
5*(t + 1)*(t + 4)
Let x be 5 - (-966)/(-108) - (-28)/7. Let b(v) be the third derivative of -1/90*v**5 - 4*v**2 + 0 + 0*v + x*v**4 - 1/9*v**3. Solve b(d) = 0.
1
Let 6/5*b**2 + 3*b - 1/5*b**3 - 20 = 0. Calculate b.
-4, 5
Let f(z) = 9*z**4 + 3*z**3 - 12*z**2 + 3*z. Let a = -14 + 12. Let g(t) = -t**5 - 9*t**4 - 2*t**3 + 12*t**2 - 2*t. Let m(j) = a*f(j) - 3*g(j). Factor m(s).
3*s**2*(s - 1)*(s + 2)**2
Suppose 2*l = 4*j - 18, 5*j + 263 - 248 = -5*l. Factor 4/11*i + 6/11*i**j + 0 + 2/11*i**3.
2*i*(i + 1)*(i + 2)/11
Let s(p) be the second derivative of -p**8/33600 + p**7/6300 - p**6/3600 + 2*p**4 - 2*p. Let j(z) be the third derivative of s(z). Factor j(n).
-n*(n - 1)**2/5
Suppose 7*j + 43 = 71. Let x(i) be the second derivative of -3/4*i**3 - 2*i + 9/4*i**2 - 1/120*i**5 + 0 + 1/8*i**j. Suppose x(f) = 0. 