405/24 - 25714. Let u = s + -13/24. What is j in -85/3*j**2 - 4/3 - u*j - 25*j**3 = 0?
-2/5, -1/3
Let p(q) = -q**3 + 10*q**2 + q - 8. Let a be p(10). Suppose 0*u**3 + u - u**2 + 4*u + 3*u**4 - 5*u**3 - a = 0. What is u?
-1, 2/3, 1
Let w(d) = -d - 10. Suppose -2*k - 25 = 1. Let s be w(k). Factor 6/11*b**2 - 6/11*b**s + 2/11*b**4 - 2/11*b + 0.
2*b*(b - 1)**3/11
Let x(g) be the second derivative of -g**5/50 - 7*g**4/30 - 5*g - 2. Factor x(d).
-2*d**2*(d + 7)/5
Let y be 8/(-164)*1/(-2). Let c = 37/164 + y. Suppose -1/2*p**4 - 3/4*p**5 - c*p + 0 + 1/2*p**2 + p**3 = 0. Calculate p.
-1, 0, 1/3, 1
Let d(u) = u**3 + u**2 - u - 1. Let h be -2*-15*3/6. Let w(p) = p - 5*p + 9*p**2 + 12*p**3 - 9 - 8*p + 0. Let n(z) = h*d(z) - w(z). Factor n(a).
3*(a - 1)*(a + 1)*(a + 2)
Determine r so that 0*r - 16/5*r**4 + 16/5*r**3 - 28*r**5 + 0 + 0*r**2 = 0.
-2/5, 0, 2/7
Let k(y) be the third derivative of -y**8/20160 + y**7/5040 - y**5/60 - 2*y**2. Let t(f) be the third derivative of k(f). Factor t(c).
-c*(c - 1)
Let q(m) be the first derivative of m**3 + 15*m**2/2 - 18*m + 2. Factor q(h).
3*(h - 1)*(h + 6)
Let p(i) = 2*i**2 - 2*i - 1. Let y(g) = g**3 + g - 1. Suppose -u = -5*f - 6, 3*f - 2*f + 2 = u. Let q(v) = u*p(v) + y(v). Factor q(r).
(r - 1)*(r + 1)*(r + 2)
Factor 0 + 1/5*s**2 + 3/5*s**3 + 3/5*s**4 + 0*s + 1/5*s**5.
s**2*(s + 1)**3/5
Determine r, given that 4*r**2 - 8*r - 5 - 2*r**2 + 11 = 0.
1, 3
Let w(i) be the third derivative of 0 + 1/60*i**6 + 2*i**2 + 0*i**3 - 1/168*i**8 + 0*i**7 + 0*i**5 + 0*i + 0*i**4. Factor w(k).
-2*k**3*(k - 1)*(k + 1)
Let r(q) be the third derivative of -7/20*q**5 + 0*q - 1/2*q**4 + 0*q**3 - 4*q**2 + 0. Factor r(l).
-3*l*(7*l + 4)
Factor -15*f**3 - 9*f**5 + 34*f + 24*f**4 - 3*f**3 - 31*f.
-3*f*(f - 1)**3*(3*f + 1)
Factor 3*n**3 + 12*n + 0*n - 12*n**2 + 0*n.
3*n*(n - 2)**2
Let u = 335/226 - -2/113. Factor 0 + u*v**2 + 3/2*v.
3*v*(v + 1)/2
Let u(w) = -19*w + 5 - 4 - 3 + 7*w**2 + 3. Let f(z) = -7*z**2 + 18*z - 2. Let h(g) = -3*f(g) - 2*u(g). Factor h(t).
(t - 2)*(7*t - 2)
Let p(y) be the third derivative of -y**8/8064 - y**7/5040 + y**5/20 - 4*y**2. Let k(r) be the third derivative of p(r). Let k(x) = 0. What is x?
-2/5, 0
Let m(g) = -5*g + 17. Let j be m(4). Let t be (6 + -6)/(j/3). Factor 2/5 + t*y**2 - 1/5*y**3 + 3/5*y.
-(y - 2)*(y + 1)**2/5
Let x be 87/(-189) + 12/21. Let r(t) be the first derivative of 1 - 1/6*t**2 + 0*t + x*t**3. Factor r(o).
o*(o - 1)/3
Let f(s) be the second derivative of s**4/12 + s**3/6 - s**2 - 22*s. Factor f(c).
(c - 1)*(c + 2)
Let k(u) be the second derivative of -u**4/20 + 3*u**3/10 - 3*u**2/5 + 7*u. Let k(r) = 0. Calculate r.
1, 2
Let x = 24 + -20. Let b(j) = -8*j**2 - j - 9. Let q(v) = -4*v**2 - 4. Let y(u) = x*b(u) - 9*q(u). Factor y(a).
4*a*(a - 1)
Suppose 11*k**2 - 2*k**4 - 3*k - 5*k**2 - 9*k**5 - 4*k**4 + 12*k**3 = 0. Calculate k.
-1, 0, 1/3, 1
Let c(y) = 3*y**2 - y. Let g be c(-1). Suppose 4 = 4*k - g. What is x in -3*x**3 - 1 + 4*x**k + 2*x - 3*x**2 + x**3 = 0?
-1, 1/2, 1
Let b(s) be the third derivative of -s**6/40 - 3*s**5/20 + 2*s**3 + 37*s**2. Factor b(l).
-3*(l - 1)*(l + 2)**2
Find y such that 0 + 9/2*y**4 + 3*y**3 + 0*y - 3/2*y**2 = 0.
-1, 0, 1/3
Suppose 5*p + 4*r + 20 = 0, -12*p + 5*r = -10*p - 25. Let -2/9*k**3 + p - 2/9*k**2 + 0*k = 0. Calculate k.
-1, 0
Suppose 15 - 66 = -17*i. Suppose 2/13*f**i + 2/13*f**2 - 4/13*f + 0 = 0. What is f?
-2, 0, 1
Let g be 259/(-49) + (-4)/(-14). Let r(a) = -5*a**3 + 10*a**2 - a - 4. Let w(y) = 4*y**3 - 9*y**2 + 3. Let b(v) = g*r(v) - 6*w(v). Solve b(o) = 0.
-2, -1
Suppose 5*y - 5*s = 20 + 25, 5*y - 4*s - 43 = 0. Suppose -y*d = -3*d. Find z, given that -2/7*z**3 - 4/7*z**4 - 2/7*z**5 + 0 + 0*z + d*z**2 = 0.
-1, 0
Suppose -y = 2*l + 4*y - 13, -1 = -y. Factor 2/7*x**l - 2/7*x**2 + 2/7*x**5 + 0*x - 2/7*x**3 + 0.
2*x**2*(x - 1)*(x + 1)**2/7
Let s(x) be the first derivative of 7*x**6/60 - x**5/15 - 7*x**4/12 + 2*x**3/3 + x**2 + 2. Let j(m) be the second derivative of s(m). Factor j(w).
2*(w - 1)*(w + 1)*(7*w - 2)
Let x(z) = z - 2. Let p be x(7). Let n(g) = -g + p + 0 - 4. Let k(r) = -r**3 - 4*r**2 - 10*r + 3. Let w(c) = -2*k(c) + 10*n(c). Find l, given that w(l) = 0.
-2, -1
Let a(g) be the first derivative of 0*g**4 + 0*g + 3/4*g**2 + 3/5*g**5 - 1/4*g**6 - g**3 + 11. Factor a(n).
-3*n*(n - 1)**3*(n + 1)/2
Let v be (-2 - 18/(-15))*-5. What is a in -3*a**2 - 24*a**3 + 12 + 2*a**4 - 9*a**4 + 24*a - 2*a**v = 0?
-2, -1, -2/3, 1
Let l(f) be the second derivative of -1/6*f**3 - 1/4*f**2 - 1/24*f**4 + 0 - 3*f. Factor l(u).
-(u + 1)**2/2
Suppose -5*y = -0*y. Let k(a) be the third derivative of -2*a**2 + 0*a + y + 0*a**3 - 1/60*a**6 + 0*a**4 + 1/30*a**5. Let k(i) = 0. What is i?
0, 1
Let s(q) be the third derivative of q**7/252 + q**6/180 + q**4/4 + 4*q**2. Let a(m) be the second derivative of s(m). Factor a(g).
2*g*(5*g + 2)
Let n be ((-8)/10)/((-42)/45). Let g be (-6)/9*(-4 - 5) - 4. Factor 0 - 8/7*p**g - n*p**3 + 8/7*p + 4/7*p**4 + 2/7*p**5.
2*p*(p - 1)**2*(p + 2)**2/7
Find o, given that -1/2 + 2*o**2 + 9/4*o - 15/4*o**3 = 0.
-2/3, 1/5, 1
Let t = 115 - 113. What is j in 0 + 0*j - 1/4*j**t = 0?
0
Factor 0 + 2/7*z**2 + 0*z.
2*z**2/7
Let z = 99 - 97. Factor -1/2*v**z - v + 0.
-v*(v + 2)/2
Let a(u) = -u - 3. Let v be a(5). Let i be 3/(-6)*v + -1. Find q, given that -8 + 3*q**i + 3*q**2 - 2*q - 7*q**4 + 8 + 3*q**5 = 0.
-2/3, 0, 1
Let g(j) be the second derivative of j**5/70 + j**4/42 + 26*j. Suppose g(d) = 0. What is d?
-1, 0
Suppose i - 5*i = -56. Suppose 3*p + 5 = i. Factor 0*a - 2/5*a**p + 1/5*a**4 + 1/5*a**2 + 0.
a**2*(a - 1)**2/5
Suppose -17*q + 15*q - 20*q = 0. Factor -1/5*v**4 + 0*v**3 + q + 0*v + 0*v**2.
-v**4/5
Let i(t) be the first derivative of 6/7*t**3 + 2 - t**2 + 4/7*t + 2/35*t**5 - 5/14*t**4. Let i(a) = 0. What is a?
1, 2
Let h(v) = v**3 - 5*v**2 - 6*v + 2. Let c = -3 + 9. Let r be h(c). Find g such that -6*g**3 - 7*g**2 - 4*g**4 - 2*g**4 - 2*g + g**r + 4*g**4 = 0.
-1, 0
Let x = 14 - 20. Let z = x + 8. Let -1/4*m**3 + 1/4*m**4 + 0 + 1/4*m**5 - 1/4*m**z + 0*m = 0. What is m?
-1, 0, 1
What is x in 0*x**2 - 4/9*x + 2/9 - 2/9*x**4 + 4/9*x**3 = 0?
-1, 1
Let y(o) be the second derivative of -o**4/6 + 2*o**3/3 - o**2 - 2*o. Factor y(u).
-2*(u - 1)**2
Let g(u) = u**3 - u**2 - u + 1. Let y be g(-2). Let s = 12 + y. Let -1/4*v**2 + 1/4 + 1/4*v**s - 1/4*v = 0. Calculate v.
-1, 1
Factor 1/4*d**2 - 1/4*d + 1/4*d**3 - 1/4.
(d - 1)*(d + 1)**2/4
Let p(r) be the first derivative of -r**6/120 - r**5/60 + r**4/24 + r**3/6 + 3*r**2/2 - 3. Let q(c) be the second derivative of p(c). Factor q(v).
-(v - 1)*(v + 1)**2
Factor 6*h - 2 + 2 - 5*h**2 + 4*h.
-5*h*(h - 2)
Suppose -4*c - 10 = -9*c. What is l in -2*l**4 + 2*l**2 - 3*l - l + c*l + 2*l**3 = 0?
-1, 0, 1
Let o(n) = -8*n**3 - 17*n**2 - 3*n + 2. Let y(h) = 135*h**3 + 290*h**2 + 50*h - 35. Let b(c) = -35*o(c) - 2*y(c). Determine i, given that b(i) = 0.
-1, -1/2, 0
Let a be (-3 - -3)/(-2 + 0). Let q = -1 + 3. Determine z so that 0 + 1/3*z**3 + a*z**q - 1/3*z**4 + 0*z = 0.
0, 1
Let m(t) = -t**2 + 6*t - 5. Let x be m(4). Suppose -2*y = o + 2, -4 + 7 = o - x*y. Solve -3/2*v**2 - 3/2*v + 3/2*v**4 + o + 3/2*v**3 = 0.
-1, 0, 1
Let c(y) = -y**2 - 9*y. Let m(p) = 5*p**2 + 53*p. Let f(k) = 34*c(k) + 6*m(k). Factor f(s).
-4*s*(s - 3)
Suppose 1/5*s**4 - 4/5*s**3 - 2/5*s + 0 + s**2 = 0. What is s?
0, 1, 2
Factor -32/3*k + 6*k**2 - 8/3.
2*(k - 2)*(9*k + 2)/3
Let i = 5 + -11/2. Let r = 1 - i. Factor 1/2 - 1/2*o**3 + 3/2*o**2 - r*o.
-(o - 1)**3/2
Let u = 9/8 - 5/8. Suppose 0 = -8*c + 25 - 1. Suppose -u*a**2 + 3/2*a**4 - 2*a**c + a + 0 = 0. What is a?
-2/3, 0, 1
Let i(g) be the second derivative of g**5/20 + 5*g**4/6 + 4*g**3/3 - 7*g**2/2 + 3*g. Let d be i(-9). Suppose -6*q + 8*q**d + 5 - 5 = 0. What is q?
0, 3/4
Determine n, given that 4*n**2 + 61*n**5 + 53*n**5 - 12*n**4 - 106*n**5 = 0.
-1/2, 0, 1
Let m(v) be the third derivative of v**2 + 0 - 1/240*v**5 - 1/32*v**4 + 0*v + 1/12*v**3 + 1/160*v**6 - 1/840*v**7. Suppose m(i) = 0. Calculate i.
-1, 1, 2
Let t = 273 - 270. Factor -1/6*g + 0 + 0*g**2 + 1/6*g**t.
g*(g - 1)*(g + 1)/6
Let l(f) be the third derivative of 0*f + 3*f**2 + 1/6*f**3 + 1/48*f**4 - 1/60*f**5 - 1/240*f**6 + 0. Factor l(h).
-(h - 1)*(h + 1)*(h + 2)/2
Let z be (-24)/(-126)*(5 + 2). Factor -z + 2*d - 2/3*d**2.
-2*(d - 2)*(d - 1)/3
