3
Factor 0 - 4/5*k**3 + 0*k - 4/5*k**4 + 4/5*k**5 + 4/5*k**2.
4*k**2*(k - 1)**2*(k + 1)/5
Let s(y) be the second derivative of -y**5/10 + y**3 - 2*y**2 + 6*y. Factor s(l).
-2*(l - 1)**2*(l + 2)
Factor -c - 7*c - c**3 - 4*c**2 + 4*c.
-c*(c + 2)**2
Let q = 47 + -47. Let i(k) be the first derivative of -k**4 + 0*k**2 + 7/3*k**6 - 2*k**5 + 0*k**3 - 3 + q*k. Suppose i(z) = 0. What is z?
-2/7, 0, 1
Suppose -3*b - 24 = y - 6*y, -21 = -4*y + 3*b. Factor -n**y + 1/2*n**5 + 0 + 0*n**2 + 0*n**4 + 1/2*n.
n*(n - 1)**2*(n + 1)**2/2
Let z(i) be the first derivative of 1/180*i**5 + 3 + 0*i**3 + 0*i + 1/72*i**4 + 2*i**2. Let f(q) be the second derivative of z(q). Solve f(a) = 0 for a.
-1, 0
What is d in -8/5 + 8/5*d - 2/5*d**2 = 0?
2
Factor 4 + 0*r**2 + 3 + 5 + 16*r + 4*r**2.
4*(r + 1)*(r + 3)
Factor 27/7*z**2 - 81/7*z - 3/7*z**3 + 81/7.
-3*(z - 3)**3/7
Let o(t) be the first derivative of 1/4*t**2 + 0*t**3 - 1/8*t**4 + 0*t + 1. Determine g so that o(g) = 0.
-1, 0, 1
Let o(k) be the second derivative of k**4/24 - k**3/24 - k**2/8 - 24*k. Factor o(f).
(f - 1)*(2*f + 1)/4
Let y(w) = w**2 + 1. Let m(i) = -3*i**2 - 6*i - 1. Let x(p) = -m(p) - 5*y(p). Factor x(r).
-2*(r - 2)*(r - 1)
Let p(d) be the first derivative of d**6/8 + 3*d**5/20 - 3*d**4/16 - d**3/4 + 3. Factor p(j).
3*j**2*(j - 1)*(j + 1)**2/4
Suppose -4*k + 20 = -4*z, 2*k - 6 = z - 1. Let n(y) be the third derivative of 0*y + 0 + k*y**3 + 1/30*y**5 + 1/6*y**4 + y**2. Solve n(g) = 0.
-2, 0
Let k be 1/(-5) - 55/(-25). Factor -2 - k*l - 4*l + 2*l**3 + 4*l + 2*l**2.
2*(l - 1)*(l + 1)**2
Factor c + 0*c + c**3 - 2*c**3 - c**2 - 13*c**4 + 14*c**4.
c*(c - 1)**2*(c + 1)
Let w be (-1)/5 - 14/(-90). Let o = w - -49/90. Factor 1/2*z + z**2 + o*z**3 + 0.
z*(z + 1)**2/2
Let k(w) be the second derivative of 0*w**4 - 1/4*w**3 + 1/40*w**5 + 5*w + 0 - 1/2*w**2. Let k(p) = 0. What is p?
-1, 2
Let l = -337/5 - -68. Factor -l*i**2 + 0 - 9/5*i**4 + 12/5*i**3 + 0*i.
-3*i**2*(i - 1)*(3*i - 1)/5
Let y be 1*(1 + -1) + (-6)/(-11). Find t such that -4/11*t**2 + 4/11 - y*t = 0.
-2, 1/2
Suppose 3*b - 3*m - 12 = 0, 5*m + 13 = -3*b - 7. Suppose 0*k - k = b. Factor k*i**2 + 9/4*i - 3/4*i**3 - 3/2.
-3*(i - 1)**2*(i + 2)/4
Let f(k) = -k + 5. Let g be f(0). Let t(v) = -5*v**2 - 2*v - 9. Let q(c) = -3*c**2 - c - 6. Let y(z) = g*t(z) - 8*q(z). Factor y(o).
-(o - 1)*(o + 3)
Let h(a) = -10*a**2 + 10*a + 6. Let u(r) = -3*r**2 + 3*r + 2. Let l(z) = -2*h(z) + 7*u(z). Factor l(x).
-(x - 2)*(x + 1)
Let x(n) be the second derivative of n**4/24 + n**3/3 - 10*n. Let x(u) = 0. What is u?
-4, 0
Let g = 35306/31 - 1139. Let a = 53/93 - g. Find i, given that -2/9*i + 0 - a*i**3 - 2/3*i**2 - 2/9*i**4 = 0.
-1, 0
Let y = -28 + 30. Let a(s) be the first derivative of y*s + 2*s**2 - 1 + 2/3*s**3. Let a(g) = 0. Calculate g.
-1
Factor 0 - 2/3*m**3 + 0*m + 1/3*m**2 + 1/3*m**4.
m**2*(m - 1)**2/3
Let l(u) be the first derivative of -2 - 1/18*u**3 + 0*u + 1/9*u**4 - u**2 - 4/45*u**5. Let o(i) be the second derivative of l(i). What is x in o(x) = 0?
1/4
Let f(o) = o**2. Let y(j) = -4*j**2 + 2*j. Let r(g) = 12*f(g) + 2*y(g). Factor r(n).
4*n*(n + 1)
Find f such that -3*f + 6*f + 2*f - 15*f**3 - 10 + 20*f**2 + 0*f = 0.
-2/3, 1
Determine f so that 10*f - 2*f**2 - 4*f**4 + 18*f**4 + 4 - 10*f**3 - 16*f**2 = 0.
-1, -2/7, 1
Suppose 4*v + 20 = r, -4*r - v = -3*r. Factor -k**2 + 9*k**3 - 5 - 2*k**2 + 5 + 3*k**5 - 9*k**r.
3*k**2*(k - 1)**3
Let x(u) = 6*u + 2*u**2 + 0*u**2 + 0*u**2. Let c be x(-4). Factor 2*j**2 - c*j**2 + 4*j + j**3 + 0*j + j**3.
2*j*(j - 2)*(j - 1)
Let m(z) be the second derivative of -z**6/45 + z**5/10 - z**4/6 + z**3/9 - z. Solve m(f) = 0.
0, 1
Suppose 0 = -2*j + 49*s - 48*s + 2, 0 = 3*j - 3*s. Find u, given that 3/5*u**j + 9/5*u - 12/5*u**3 + 0 = 0.
-3/4, 0, 1
Let o(r) = r**2 + 9*r + 10. Let h be o(-7). Let b be 15/(-4)*h/20. Factor -b*v + 1/4 + 3/4*v**2 - 1/4*v**3.
-(v - 1)**3/4
Let w(k) = -k**2 - 10*k - 8. Let g be w(-9). Suppose 2*u + t - 7 = 0, 3*u - 2*u + 5*t = -g. Let -u*i - 1 - 15/4*i**2 = 0. What is i?
-2/3, -2/5
Let w(p) = p + 8. Let u be w(-6). Suppose -u*c - 1 = -5. Suppose 2*o**2 + 3*o + 1 - 3*o**2 + 4*o**c + o**3 = 0. Calculate o.
-1
Let p(c) = -c**3 - c**2 + 3*c + 5. Let l be p(-2). Let g be l/15 - (-24)/5. Determine v so that 0*v**2 + 0*v + 0*v**4 + 0 + 0*v**3 - 3/4*v**g = 0.
0
Suppose -2*q - 5*h = -0*q - 3, -3*q + 17 = 5*h. Let d be (-2)/q + 170/14. Factor -3*r - 3 - 1 + 9*r**3 + d*r**2 - 2.
3*(r + 1)**2*(3*r - 2)
Let b = 2/171 + 74/171. Suppose 8/9*z**2 - 2/3*z**3 - b*z**4 + 8/9*z + 2/9*z**5 + 0 = 0. What is z?
-1, 0, 2
Let i(q) be the second derivative of -9*q + 0 - 1/3*q**3 - 1/6*q**4 + 0*q**2. Suppose i(l) = 0. Calculate l.
-1, 0
Let i(s) be the second derivative of 4*s**6/105 - s**5/14 + s**4/42 - 6*s. Factor i(a).
2*a**2*(a - 1)*(4*a - 1)/7
Let b be (-3)/((-9)/(-6)) - -2. Factor -i**2 - i**3 + 3*i**5 + i**4 + b*i**2 - 2*i**5.
i**2*(i - 1)*(i + 1)**2
Let u(l) be the third derivative of -2*l**7/315 + 7*l**6/360 + l**5/90 - 4*l**2. Factor u(x).
-x**2*(x - 2)*(4*x + 1)/3
Let t(a) be the first derivative of a**5/10 - a**4/3 + 7*a**3/18 - a**2/6 - 5. Let t(p) = 0. What is p?
0, 2/3, 1
Let a(p) be the third derivative of 0 + 2*p**2 + 0*p**7 + 0*p - 1/210*p**6 + 1/84*p**4 + 0*p**3 + 1/1176*p**8 + 0*p**5. Factor a(l).
2*l*(l - 1)**2*(l + 1)**2/7
What is m in 3/2*m**3 - m - 1/2*m**5 + 0 + 1/2*m**2 - 1/2*m**4 = 0?
-2, -1, 0, 1
Let o = 9081/10775 + -24781632/5570675. Let x = -3/517 - o. Factor x*a + 3/5*a**2 + 27/5.
3*(a + 3)**2/5
Let w(i) = 10*i - 27. Let o be w(3). Let t(g) be the third derivative of -1/60*g**5 + 1/24*g**4 + 0*g - 1/18*g**o - 3*g**2 + 0 + 1/360*g**6. Factor t(q).
(q - 1)**3/3
Let u(q) = q**2 - 5*q + 8. Let r be u(2). Let t be 16/9*9/6. Let 4/3 + 1/3*f**r - t*f + f**3 = 0. Calculate f.
-2, 2/3, 1
Let p(x) be the third derivative of -x**6/120 + x**5/10 - 11*x**4/24 + x**3 - 21*x**2. Suppose p(m) = 0. Calculate m.
1, 2, 3
Let v = 0 + 3. Suppose -6 = -5*n + 4*j, n + 1 = -4*j + 7. Suppose 11/3*q**v + 8/3 + 1/3*q**5 - 2*q**4 - 4*q - 2/3*q**n = 0. Calculate q.
-1, 1, 2
Factor 0 + 4/7*v**2 - 2/7*v**3 - 2/7*v.
-2*v*(v - 1)**2/7
Let f(s) be the first derivative of s**3/3 - s**2/2 - 2*s - 3. Solve f(m) = 0.
-1, 2
Suppose 4*k + 0*x - 5*x - 3 = 0, k + 4*x - 6 = 0. Let w be (-9)/(81/(-6))*1. Factor -1/3 - 1/3*j**k - w*j.
-(j + 1)**2/3
Let z(o) be the first derivative of o**7/1050 - o**6/900 + o**3 + 3. Let p(m) be the third derivative of z(m). Suppose p(t) = 0. What is t?
0, 1/2
Let c(g) be the first derivative of -1 - 1/3*g**3 + 2*g + 1/2*g**2. What is h in c(h) = 0?
-1, 2
Let m(r) be the second derivative of -3*r**5/20 + 3*r**4 - 11*r**3/2 + 2*r + 18. Factor m(q).
-3*q*(q - 11)*(q - 1)
Let u(f) be the third derivative of f**7/140 + f**6/16 + 7*f**5/40 + 3*f**4/16 + 10*f**2. Factor u(t).
3*t*(t + 1)**2*(t + 3)/2
Let x be 6/(0/(-3) + 2). Let k(y) = y**3 + 2*y**2 - 2*y - 2. Let u be k(-2). Factor -2*h**u - 2*h**x + 2*h + 2*h**2.
-2*h*(h - 1)*(h + 1)
Let g = 18 - 12. Let p be 3/(-3)*0 + 2. Solve 0*b**2 - 2*b**5 + 6*b**5 - g*b**4 + 2*b**p = 0 for b.
-1/2, 0, 1
Let h(r) be the second derivative of 1/2*r**3 + 3/4*r**4 + 9/20*r**5 - 2*r + 0 + 0*r**2 + 1/10*r**6. Factor h(a).
3*a*(a + 1)**3
Let u(t) = -4*t**4 + 7*t**3 + 4*t**2 - 8*t + 2. Let n(w) = w**3 - w**2 + w. Suppose -2*x - 3*x = -5. Let d(r) = x*u(r) + n(r). Factor d(o).
-(o - 2)*(o + 1)*(2*o - 1)**2
Suppose -4*v = -5*g + 25, -2*g = -3*v + g - 15. Solve -2/9*s + 2/9*s**3 + v + 2/9*s**2 - 2/9*s**4 = 0 for s.
-1, 0, 1
Let y(l) = l + 2. Let p be y(2). Let f be 1*-2 - (7 + -15). What is i in 15*i - 10*i**3 + 0*i**2 + 3*i**2 - 9*i**p + f - 5*i**3 = 0?
-1, -2/3, 1
Let z be (((-5)/(-39))/1)/(-1). Let s = z + 6/13. Factor -25/3*c**2 - s + 10/3*c.
-(5*c - 1)**2/3
Let a(h) be the first derivative of -h**8/840 + h**6/60 - h**5/30 - 5*h**3/3 - 5. Let f(i) be the third derivative of a(i). Solve f(b) = 0.
-2, 0, 1
Let s(t) be the third derivative of t**8/168 - t**6/30 + t**4/12 - 14*t**2. Find k such that s(k) = 0.
-1, 0, 1
Let k(l) = -20*l**3 + 11*l**2 - l - 18. Let q(h) = 9*h**3 - 6*h**2 + 9. Let s(m) = -3*k(m) - 7*q(m). Determine v so that s(v) = 0.
-1, 1, 3
Suppose 0 = -3*z - 2*z - 10. Let s be (-4)/z - 4/(-2). Factor 1/3*b**s + 0 - 1/3*b**2 + 0*b + 0*b**3.
b**2*(b - 1)*(b + 1)/3
Let n(s) = -2*s**2