 - 2)**2*(x - 1)
Let u(s) = s**2 - s + 1. Let v(b) be the third derivative of b**5/5 - 7*b**4/8 + 4*b**3 - 4*b**2. Let i(k) = -15*u(k) + v(k). Factor i(z).
-3*(z - 1)*(z + 3)
Let l(u) be the third derivative of -1/12*u**3 - 1/20*u**5 + 0*u - 1/12*u**4 + 0 - 3*u**2 - 1/420*u**7 - 1/60*u**6. Determine g so that l(g) = 0.
-1
Let n(g) be the third derivative of -5*g**2 + 0 + 1/150*g**5 + 1/20*g**4 + 0*g**3 + 0*g. Find s such that n(s) = 0.
-3, 0
Factor 2/3*c - 2/3*c**2 + 4/3.
-2*(c - 2)*(c + 1)/3
Let x = 260/1089 - 2/121. Factor 0*n + x*n**4 + 0 - 2/9*n**2 - 2/9*n**3 + 2/9*n**5.
2*n**2*(n - 1)*(n + 1)**2/9
Let q(y) be the first derivative of -y**5/60 + y**4/3 - 8*y**3/3 + y**2/2 + 8. Let d(i) be the second derivative of q(i). Factor d(f).
-(f - 4)**2
Let o(r) = r**2 - 8*r - 15. Let i be o(9). Let b be (-16)/i*36/84. What is t in 2*t**3 - 4/7*t**2 + 0 - 2/7*t - b*t**4 = 0?
-1/4, 0, 1
Let x(v) be the first derivative of 47/16*v**4 + 7/2*v**2 + 59/12*v**3 + 3/5*v**5 - 1 + v. What is b in x(b) = 0?
-2, -1, -2/3, -1/4
Let x(u) = -5*u**4 - 4*u**3 - 6*u**2 - 2*u - 7. Let o(b) = -4*b**4 - 3*b**3 - 5*b**2 - 2*b - 6. Let i(l) = 6*o(l) - 5*x(l). Factor i(w).
(w - 1)*(w + 1)**3
Let d(k) = 9*k**4 + 4*k**3 + 5*k**2 + 5. Let q(p) = -14*p**4 - 6*p**3 - 7*p**2 - 7. Let b(x) = -7*d(x) - 5*q(x). Find c such that b(c) = 0.
-2/7, 0
Let q(i) be the second derivative of i**4/16 + 5*i**3/8 + 3*i**2/2 + 21*i. What is j in q(j) = 0?
-4, -1
Let l(p) = -6*p**5 + 5*p**4 - 6*p**3 + 7*p. Let x(u) = u**5 - u**4 + u**3 - u. Let k(c) = -5*l(c) - 35*x(c). Solve k(w) = 0.
0, 1
Let x(m) be the first derivative of -1/24*m**4 + 0*m**3 - 3*m - 1/40*m**5 - 3 + 0*m**2. Let w(d) be the first derivative of x(d). Factor w(g).
-g**2*(g + 1)/2
What is m in -5/4*m**5 - 5/2*m**2 + 25/4*m + 5*m**4 - 5/2 - 5*m**3 = 0?
-1, 1, 2
Let r(j) = j**2 - 6*j. Let x be r(6). Let z(h) = 13*h + 405. Let p be z(-31). Find c, given that -4/7*c**4 + 2/7*c**p + x + 0*c + 2/7*c**3 = 0.
-1/2, 0, 1
Determine o so that 0 + 8*o**3 + 46/5*o**4 + 0*o + 14/5*o**5 + 8/5*o**2 = 0.
-2, -1, -2/7, 0
Factor -2*d**4 - 16*d**2 + 8*d**3 + 16*d + 1/5*d**5 - 32/5.
(d - 2)**5/5
Let x(v) be the first derivative of -v**7/147 - 2*v**6/105 + v**4/21 + v**3/21 + 3*v + 3. Let a(o) be the first derivative of x(o). Factor a(k).
-2*k*(k - 1)*(k + 1)**3/7
Let g be (0 - 1)/(3/(-18)). Suppose 2*v = g*v - 16. Factor 2*a**3 - a**v + a**2 - a**4 + a**2 - 2*a.
-2*a*(a - 1)**2*(a + 1)
Let b(k) be the third derivative of -1/6*k**4 + 1/3*k**3 - 2*k**2 + 1/30*k**5 + 0*k + 0. Find n such that b(n) = 0.
1
Let h = 5 - 2. Let j(k) = -2*k**2 + 5. Let o(z) = 2*z**2 - 6. Let r(q) = h*o(q) + 2*j(q). Factor r(y).
2*(y - 2)*(y + 2)
Determine z so that 1 - 8*z - 4 - z + 0*z - 9*z**2 - 3*z**3 = 0.
-1
Factor -10*b**4 + 10*b**4 + 6*b + 36*b**3 - 27*b**4 + 33*b**2.
-3*b*(b - 2)*(3*b + 1)**2
Determine r, given that 3*r**2 - 14*r**4 + r + 13*r**4 - 3*r = 0.
-2, 0, 1
Let i(l) be the second derivative of l**8/10080 + l**7/1890 - l**4/3 + 4*l. Let y(b) be the third derivative of i(b). Factor y(j).
2*j**2*(j + 2)/3
Let j(x) = 7*x**2 + 12*x - 15. Let k(q) = 50*q**2 + 85*q - 105. Let w(h) = -15*j(h) + 2*k(h). Let w(l) = 0. What is l?
-3, 1
Let d(q) = 105*q**2 - 135*q + 54. Let o(m) = 21*m**2 - 27*m + 11. Let y(p) = 5*d(p) - 24*o(p). Factor y(h).
3*(h - 1)*(7*h - 2)
Let i be 68/18 - (-6)/27. Suppose -x + i = -0*x. Factor x - p**3 + 3*p**2 + 0*p**3 - 6*p**2.
-(p - 1)*(p + 2)**2
Suppose 0 = 5*a - 2*m - 8, -5 = 2*a + 5*m - 14. Solve k**2 + 3*k**2 + 0*k - 3*k**a - k = 0.
0, 1
Let d(p) be the second derivative of 0 + 4/9*p**3 - 2*p + 1/18*p**4 + 4/3*p**2. Let d(f) = 0. Calculate f.
-2
Suppose 0 = -4*q - 3*y + 15, 2*y + 3*y = 4*q - 7. Suppose -3*d + 0*d**4 + 3 - 4 - 7*d**5 - 2*d**2 + q*d**4 + 2*d**3 + 8*d**5 = 0. Calculate d.
-1, 1
Let q(p) be the second derivative of -1/150*p**6 + 0*p**2 + 3*p + 0*p**5 + 0*p**4 + 0 + 0*p**3. What is y in q(y) = 0?
0
Let m(d) be the first derivative of -d**5/25 - d**4/4 - 2*d**3/5 + 33. What is q in m(q) = 0?
-3, -2, 0
Suppose 2*b - b - 3 = 0. Suppose b*h + 1 - 10 = 0. Factor -2/5*k**h + 0 + 0*k + 2/5*k**5 - 2/5*k**4 + 2/5*k**2.
2*k**2*(k - 1)**2*(k + 1)/5
Let v(n) = -6*n**3 + 9*n**2 + 4*n + 1. Let b(r) = r**3 - r**2 - 1. Let w(c) = -12*b(c) - 3*v(c). What is f in w(f) = 0?
-1, 1/2, 3
Factor 1/5*y + 2/5*y**4 + 0 + 0*y**3 - 1/5*y**5 - 2/5*y**2.
-y*(y - 1)**3*(y + 1)/5
Suppose 0*i**2 - 2/7*i**5 + 0 - 2/7*i**3 + 4/7*i**4 + 0*i = 0. Calculate i.
0, 1
Let 1 + 3*x**3 - 15*x**3 - 12*x**2 - 3*x**4 - 1 = 0. What is x?
-2, 0
Let g(d) be the second derivative of -d**5/130 - 2*d**4/13 + 9*d**3/13 - 14*d**2/13 - 49*d. Factor g(a).
-2*(a - 1)**2*(a + 14)/13
Let m(j) be the third derivative of j**8/12 - 19*j**7/70 + 7*j**6/30 + j**5/20 - j**4/12 - 2*j**2. What is l in m(l) = 0?
-1/4, 0, 2/7, 1
Let b(h) be the second derivative of 3/10*h**5 + 0 - 1/6*h**4 + 1/21*h**7 - 1/5*h**6 + 0*h**2 + 0*h**3 + 2*h. Let b(d) = 0. Calculate d.
0, 1
Solve k**5 - 12/5*k - 26/5*k**2 + 8/5 + 7/5*k**3 + 18/5*k**4 = 0.
-2, -1, 2/5, 1
Let g be ((-4)/6)/(4/(-18)). Factor g*h**2 - 6*h**2 + 2*h**2 + 2*h**2 + h.
h*(h + 1)
Let r(k) be the third derivative of k**6/1980 - k**3/6 - 4*k**2. Let f(c) be the first derivative of r(c). Suppose f(p) = 0. What is p?
0
Factor 4*l**5 + 28*l**3 + 20*l - 40*l**2 - 7 - 20*l**4 + 3 - 14*l**3 + 26*l**3.
4*(l - 1)**5
Let n(v) be the third derivative of v**6/180 - v**5/20 - 2*v**3/3 - 4*v**2. Let c(j) be the first derivative of n(j). Factor c(t).
2*t*(t - 3)
Let w(s) = s**3 + 7*s**2 - s - 3. Let c be w(-7). Suppose 0 = i + c*i. Factor -2/5*r**3 + 0*r - 2/5*r**2 + i.
-2*r**2*(r + 1)/5
Let p(q) be the third derivative of -7*q**6/160 + 3*q**5/8 - 9*q**4/8 + q**3 - 5*q**2. Factor p(n).
-3*(n - 2)**2*(7*n - 2)/4
Let u = -11 + 15. Suppose 16 = v + 3*v + u*p, -14 = -4*v - 3*p. Suppose -2/3*b**v - 2/3*b + 0 = 0. What is b?
-1, 0
Let r(p) be the second derivative of p**7/12600 + p**6/1800 - 7*p**4/12 - 6*p. Let x(c) be the third derivative of r(c). Factor x(b).
b*(b + 2)/5
Let q(b) be the third derivative of b**7/735 + b**6/210 - b**4/42 - b**3/21 + 4*b**2. Solve q(f) = 0 for f.
-1, 1
Let u = -12 - -14. What is f in -6*f - u*f**2 + f**2 + 2 + 5*f = 0?
-2, 1
Let c = -7 - -6. Let d(s) = 14*s**2 + 16*s. Let a(k) = k**2 + k. Let g(f) = c*d(f) + 12*a(f). Factor g(z).
-2*z*(z + 2)
Let k = -132 + 135. Factor 5/3*d**k - 5/3*d + 7/3*d**4 - 3*d**2 + 2/3.
(d - 1)*(d + 1)**2*(7*d - 2)/3
Let x(b) be the second derivative of b**7/840 - b**6/360 - b**5/120 + b**4/24 + b**3/3 + 4*b. Let z(p) be the second derivative of x(p). Factor z(q).
(q - 1)**2*(q + 1)
Factor -2*z**4 - 9*z**2 + 3*z**2 - 8*z**3 + 0*z**4.
-2*z**2*(z + 1)*(z + 3)
Let w = -44 + 68. Suppose 84*o**3 - w*o**4 - 3 + 57/2*o - 171/2*o**2 = 0. Calculate o.
1/4, 1, 2
Let k be 2/8 + (-9)/(-6). Let y = 21/46 - -1/23. What is j in 5/4*j**2 + y + k*j = 0?
-1, -2/5
Let n be (1 - (-6)/2) + -2. Let d(l) = -l**3 + 4*l**2 - 4*l + 3. Let q be d(n). Factor 9*u + 41 - 35 - 3*u**3 + 0*u**q.
-3*(u - 2)*(u + 1)**2
Let w(o) = 5*o**4 + 12*o**3 - 2*o**2 - 8*o + 1. Let y(f) = 36*f**4 + 84*f**3 - 15*f**2 - 57*f + 6. Let j(s) = -27*w(s) + 4*y(s). Factor j(u).
3*(u - 1)*(u + 1)**2*(3*u + 1)
Let i(c) be the third derivative of -c**5/60 - c**4/12 + 16*c**2. Factor i(k).
-k*(k + 2)
Let m be (1*(7 - 5))/1. Let -1/4*r**m - 1/4*r**3 + 1/4*r**4 + 0 + 1/4*r = 0. What is r?
-1, 0, 1
Let r(m) be the second derivative of 5*m**7/42 - m**5/2 + 5*m**3/6 + 2*m. Let r(d) = 0. What is d?
-1, 0, 1
Let o be 1/1 + (3 - 2). Let d be 6/18 - o/(-6). Find j, given that 2/3 + 4/3*j + d*j**2 = 0.
-1
Suppose 3*i = -i. Suppose 3*x + 5*x**5 + 2*x**5 - 6*x**3 + i*x - 4*x**5 = 0. What is x?
-1, 0, 1
Let s(c) = c - 12. Let m be s(15). Let i(p) be the first derivative of 0*p - 1/8*p**2 - 1 - 1/12*p**m. Factor i(a).
-a*(a + 1)/4
Let t = -59/78 + 37/26. What is u in -t*u**4 + 2/9 + 28/9*u**3 - 2*u**5 - 10/9*u + 4/9*u**2 = 0?
-1, 1/3, 1
Suppose -3 + 7 = 2*v. Solve 7*g + 4*g**4 + 7*g**3 - 6*g**v - 5*g + 6*g**3 + 17*g**2 = 0 for g.
-2, -1, -1/4, 0
Let n(r) = -r**5 - r**4 - r**3 + r**2 + r - 1. Let v(q) = 9*q**4 + 12*q**3 - 27*q**2 + 9*q + 3. Let f(d) = 3*n(d) + v(d). Solve f(g) = 0.
-2, 0, 1, 2
Let t(f) be the first derivative of 0*f + 0*f**2 - 1/6*f**4 - 1/180*f**6 + 1/20*f**5 -