).
2*t**2*(t - 1)/3
Suppose 3 = -n + 6. Factor 0*i + 2*i**2 + 1/2*i**4 + 2*i**n + 0.
i**2*(i + 2)**2/2
Let k be (-8)/(-12) - (-20)/6. Factor -o**5 + o + 2*o**2 + 3*o**5 - 2*o**k - 3*o**5.
-o*(o - 1)*(o + 1)**3
Let z(o) = o**2 + 1. Let y(a) = -a**5 - 3*a**4 - 3*a**3 - 6*a**2 - 5. Let j(q) = y(q) + 5*z(q). Factor j(v).
-v**2*(v + 1)**3
Let i be 20/8 - (5 - 10)/1. Factor -3/2 - 27/2*d**2 - 21/2*d**3 - 3*d**4 - i*d.
-3*(d + 1)**3*(2*d + 1)/2
Let x(f) be the third derivative of f**6/960 - f**5/120 + f**4/192 + f**3/8 - 37*f**2. Solve x(n) = 0 for n.
-1, 2, 3
Let l(d) be the third derivative of 13*d**5/60 + d**4/12 + 6*d**2. Factor l(h).
h*(13*h + 2)
Let v(p) = 24*p**2 - 80*p + 31. Suppose g - 3 = -b + 7, -3*b = -5*g + 58. Let r(l) = -5*l**2 + 16*l - 6. Let h(n) = g*r(n) + 2*v(n). Factor h(z).
-(z - 2)*(7*z - 2)
Suppose 0 = -0*i + 4*i - 5*u + 1, -2*i = 2*u - 22. Let k be 3*(-4 - (-28)/i). Factor 2/7*w**k + 2/7*w + 0.
2*w*(w + 1)/7
Suppose w + w - c = 0, 4*c = 4*w. What is n in -4/7*n**4 + w*n**3 + 0 - 2/7*n**5 + 2/7*n + 4/7*n**2 = 0?
-1, 0, 1
Let k(o) be the third derivative of 0 + 1/336*o**8 - 1/6*o**3 + 5/24*o**4 + o**2 + 1/12*o**6 - 1/6*o**5 - 1/42*o**7 + 0*o. Factor k(w).
(w - 1)**5
Let j(r) be the second derivative of 1/8*r**3 + 1/8*r**2 - 1/40*r**5 - 1/40*r**6 + 2*r + 1/24*r**4 + 0 - 1/168*r**7. Suppose j(g) = 0. What is g?
-1, 1
Let r = 172 + -343/2. Factor -a**2 + 0 - r*a**3 - 1/2*a.
-a*(a + 1)**2/2
Factor 2*a**4 + 1/2*a**2 + 3/4*a**5 + 7/4*a**3 + 0*a + 0.
a**2*(a + 1)**2*(3*a + 2)/4
Let n(x) be the first derivative of -1 + 0*x + 0*x**2 + 2/3*x**3. Factor n(u).
2*u**2
Suppose -4*f - 2*o = 2, 5*o = -2 - 3. Let x(g) be the second derivative of f - 3*g - 1/12*g**3 - 1/24*g**4 + 0*g**2. Suppose x(d) = 0. Calculate d.
-1, 0
Let m(j) = -j**2 - j. Let o(t) = -12*t**2 - 24*t - 16. Let d(k) = 8*m(k) - o(k). Find z, given that d(z) = 0.
-2
Let a(s) be the first derivative of -s**5/15 + s**4/3 - s**3/3 + 10. Factor a(w).
-w**2*(w - 3)*(w - 1)/3
Let l = -40 - -40. Let x(i) be the third derivative of -1/30*i**5 + 0*i - 1/12*i**4 + 0 - i**2 + l*i**3. Factor x(a).
-2*a*(a + 1)
Factor 1/2*u**4 + 2/3*u**3 - 5/6*u**2 + 0 - 1/3*u.
u*(u - 1)*(u + 2)*(3*u + 1)/6
Let h(s) = 4*s**3 + 10*s**2 - 16*s + 2. Let k(y) = y**3 - 1. Let z(c) = -h(c) + 6*k(c). Find b such that z(b) = 0.
1, 2
Let b(u) be the second derivative of 5*u**7/42 + u**6/2 - 3*u**5/2 - 25*u**4/6 + 35*u**3/2 - 45*u**2/2 - 11*u. Factor b(f).
5*(f - 1)**3*(f + 3)**2
Let o = 279/4 - 69. Factor -1/2*z**2 + 1/2 - o*z.
-(z + 2)*(2*z - 1)/4
Let t(z) = 3*z**2 - 1. Let x be t(1). Suppose 5*s - 5 = -5*g, 0 = g + x*g + 2*s - 2. Factor -2*y + 0*y**2 + 4*y**2 + g*y**2 - 3*y**2.
y*(y - 2)
Find p, given that -3*p**4 + 6*p**3 + 0*p**4 - 2*p**3 + p**4 = 0.
0, 2
Let p(m) be the third derivative of -m**6/210 + m**5/28 + m**4/7 + 5*m**3/42 + 29*m**2. Determine u so that p(u) = 0.
-1, -1/4, 5
Let u = 57 - 54. Find l, given that -2/3*l**2 + 2/3 + 1/3*l**u - 1/3*l = 0.
-1, 1, 2
Let r(m) be the third derivative of 4*m**7/105 - m**6/10 - 2*m**5/15 + 8*m**2. Solve r(a) = 0.
-1/2, 0, 2
Let c be 5 + -4 - (-1 + -1). Suppose 4*b - 25 = -c*w, 1 = -4*w - b + 17. Factor -6/7*o**2 - 2/7*o**4 + 6/7*o**w + 0 + 2/7*o.
-2*o*(o - 1)**3/7
Let z be 1*((-35)/10 - -5). What is s in 2 + 1/4*s**5 - z*s**4 - 1/2*s**2 - 3*s + 11/4*s**3 = 0?
-1, 1, 2
Let c = -19 - -55. Let u be (14/(-112))/((-2)/c). What is a in 3/2*a - 3/4*a**2 + u = 0?
-1, 3
Let f(d) = -130*d**2 + 150*d - 31. Let z(j) = -26*j**2 + 30*j - 6. Let l(g) = 4*f(g) - 22*z(g). Factor l(w).
4*(w - 1)*(13*w - 2)
Let j(s) be the first derivative of 2*s**3/9 + 4*s**2/3 + 8*s/3 - 10. Solve j(b) = 0.
-2
Let l = 432/455 + -6/65. Let -l*u + 24/7*u**2 - 4/7 - 2*u**3 = 0. What is u?
-2/7, 1
Let l be 12/(-42) - 16/(-7). Factor g**5 - 2*g**3 + g - g**4 + 1 - 2*g**l + 0*g**2 + 2*g**4.
(g - 1)**2*(g + 1)**3
Let a(b) be the third derivative of -b**8/336 + b**7/70 + b**6/120 - 7*b**5/60 + 2*b**3/3 + 21*b**2. Factor a(f).
-(f - 2)**2*(f - 1)*(f + 1)**2
Suppose 0 = -x - 3*t + 14, t - 22 = -5*x - 2*t. Suppose 4*q = -x*v + 3*v + 2, 0 = 3*v - 2*q - 4. Let 0 + 1/4*r**v - 1/4*r**4 + 1/4*r**3 - 1/4*r = 0. What is r?
-1, 0, 1
Let s(b) = 3*b**2. Let m be s(-1). Let k(p) be the second derivative of 3/8*p**5 - 1/20*p**6 - p**4 + p**3 + 0 - m*p + 0*p**2. Factor k(r).
-3*r*(r - 2)**2*(r - 1)/2
Let 65*n**3 - 59*n**3 + 5*n**4 + 4*n**2 - 3*n**4 = 0. Calculate n.
-2, -1, 0
Let b(s) be the third derivative of -s**7/350 + s**6/50 - 3*s**5/50 + s**4/10 - s**3/10 + 23*s**2. Factor b(k).
-3*(k - 1)**4/5
Let t(x) be the first derivative of x**7/210 - x**6/120 - x**5/60 + x**4/24 + 2*x**2 - 4. Let c(y) be the second derivative of t(y). Factor c(s).
s*(s - 1)**2*(s + 1)
Let q(m) be the first derivative of m**4/48 + m**3/8 + m**2/4 - m - 1. Let i(f) be the first derivative of q(f). Find d such that i(d) = 0.
-2, -1
Let w(q) be the third derivative of 3*q**6/40 + 4*q**5/5 + 15*q**4/8 - 9*q**3 - 6*q**2. What is u in w(u) = 0?
-3, 2/3
Let x = 13 + -7. Let r be 44/x + 12/18. Suppose -u - r + u**3 - u**4 + u**2 + 8 = 0. Calculate u.
-1, 0, 1
Let l(v) = v**2. Let d(r) be the third derivative of r**6/60 - r**5/30 - r**2. Let g(c) = -d(c) - 4*l(c). Suppose g(y) = 0. What is y?
-1, 0
Let p(v) be the third derivative of v**5/570 - 5*v**4/57 + 100*v**3/57 - 7*v**2. Factor p(t).
2*(t - 10)**2/19
Let d(u) = -u**2 + 8*u + 13. Let k be d(9). Let z(p) be the first derivative of 1/4*p**2 + 0*p**3 - 1/20*p**5 + 1/4*p - 1/8*p**k + 1. Factor z(f).
-(f - 1)*(f + 1)**3/4
Let k = 5 + -5. Determine w so that -w**4 + 0*w + k - 2/3*w**2 - 7/3*w**3 = 0.
-2, -1/3, 0
Let f = 99 + -53. Suppose f*p - 41*p = 0. Find s, given that -1/6*s**3 + 1/6*s + p - 1/6*s**2 + 1/6*s**4 = 0.
-1, 0, 1
Suppose 15*l - 58 - 17 = 0. Let a(x) be the third derivative of 3*x**2 + 0*x**4 + 0 - 1/180*x**l + 0*x + 0*x**3. Suppose a(t) = 0. What is t?
0
Find y such that 0 - 4/9*y - 2/3*y**2 - 2/9*y**3 = 0.
-2, -1, 0
Suppose 0 = t - 6*t + 50. Let d be ((-15)/t)/(9/(-49)). Factor -2/3 - 14/3*r - d*r**2.
-(7*r + 2)**2/6
Suppose 2/7*l**3 + 4/7*l**2 - 6/7*l + 0 = 0. Calculate l.
-3, 0, 1
Suppose 3*a - 9 = -0. Let c = 125/51 - -15/17. Solve c*b**4 - 4/3*b + 6*b**2 + 0 - 8*b**a = 0 for b.
0, 2/5, 1
Suppose -2*d + 20 = 4*s, -4*s + 2*d = s - 34. Determine n so that -21*n**5 - n**3 - 13*n**4 + 28*n**3 - 2*n**4 + 15*n**2 - s*n = 0.
-1, 0, 2/7, 1
Let b be 3/6 + 0/(-1). Let p = 29/50 - 2/25. Solve b*z - p*z**2 - 1/2*z**3 + 1/2 = 0 for z.
-1, 1
Let f = -6 + 11. Suppose 5*r = 25 - f. Factor 8*w**2 - 4*w - w + 3*w + r*w**4 - 10*w**3.
2*w*(w - 1)**2*(2*w - 1)
Let g(t) = -t**4 + 3*t**3 - 3*t - 3. Let a(s) be the first derivative of -2*s**5/5 + 5*s**4/4 - 5*s**2/2 - 5*s + 1. Let k(w) = -3*a(w) + 5*g(w). Factor k(o).
o**4
Let j(x) = -39*x**3 + 164*x**2 - 95*x - 30. Let p(h) = h**3 - h**2. Let m(a) = j(a) - 6*p(a). Factor m(q).
-5*(q - 3)*(q - 1)*(9*q + 2)
Let k(w) = -w**4 + 4*w**3 + 2*w**2 - 1. Let r(c) = c**4 - 5*c**3 - 2*c**2 + 1. Let y(v) = -5*k(v) - 4*r(v). Let y(f) = 0. Calculate f.
-1, 1
Find z such that -4 + 4*z**4 - 5*z**4 + z**3 + 5 - 3 - z + 3*z**2 = 0.
-1, 1, 2
Let n(w) be the third derivative of 0*w + 0*w**3 - 3*w**2 + 9/70*w**7 - 1/28*w**8 - 3/20*w**6 + 0 + 0*w**4 + 1/20*w**5. Factor n(r).
-3*r**2*(r - 1)**2*(4*r - 1)
Let z = -301 - -905/3. Factor 0 - 1/3*t**3 + z*t**2 + 0*t.
-t**2*(t - 2)/3
Let l = 6 + -1. Suppose -j + l = 3*m, 2*m - 2*j = 3 + 3. Suppose -3*d + 3*d**m - 2*d**2 + 2*d = 0. What is d?
0, 1
Let l(b) be the first derivative of -3/4*b**2 + 1/2*b + 1/4*b**4 + 1 - 3/10*b**5 + 1/12*b**6 + 1/3*b**3. Solve l(i) = 0.
-1, 1
Let l = 261/530 + 2/265. Factor 0 + 1/2*n + l*n**2.
n*(n + 1)/2
Suppose -60 = 10*b - 90. Factor -6*k - b - 15/4*k**2 - 3/4*k**3.
-3*(k + 1)*(k + 2)**2/4
Let k be -5*(110/(-25) + 4). What is l in -32/3*l + 27*l**3 - 4/3 - 15*l**k = 0?
-2/9, 1
Let j be 1/6 - 33/(-18). Factor -r**2 + 0*r - 4*r**3 + 5*r**4 - j*r - 4*r**4 + 6*r**2.
r*(r - 2)*(r - 1)**2
Let r = 4 + -1. Suppose j + r = 2*j. Determine k, given that k + 4*k**j - 5*k**3 + 0*k**3 = 0.
-1, 0, 1
Let v be (-1 + 1)/3 + 7. Find n, given that -4*n**5 + 3*n**5 - v*n**4 + 0*n**5 + 6*n**4 = 0.
-1, 0
Let r(j) = -3*j**2 + 28*j - 9. Let s be r(9). Let x(u) be the second derivative of u + 1/12*u**4 + 1/6*u**3 + 0*u**2 + 