/7
Let w(j) be the second derivative of -1/12*j**4 + 2*j + 0 + 0*j**2 + 1/18*j**3 - 1/15*j**5. Factor w(r).
-r*(r + 1)*(4*r - 1)/3
Let i = 13 + -11. Let y(f) be the second derivative of 0*f**i + 0*f**3 + 2/75*f**6 + 0*f**4 - 1/105*f**7 + 2*f + 0 - 1/50*f**5. Factor y(j).
-2*j**3*(j - 1)**2/5
Let p = -257/7 - -37. Factor 6/7*m**4 - 6/7*m + 2/7*m**5 + 4/7*m**3 - p - 4/7*m**2.
2*(m - 1)*(m + 1)**4/7
Suppose -32 = -4*g + 4*a, -g - 4*a = 4*g + 5. What is s in -12*s**3 + 15*s**g + 3*s**5 - 3*s**4 - 3*s**4 = 0?
0, 1
What is w in -8 + 2 - 1 + 2 + 10*w - 5*w**2 = 0?
1
Let x(z) be the third derivative of -z**5/15 + 8*z**3/3 - 5*z**2. Factor x(r).
-4*(r - 2)*(r + 2)
Suppose -14*u = -10*u - 8. Let 9/5*j + 0 - 6/5*j**u - 3/5*j**3 = 0. What is j?
-3, 0, 1
Let -2/7*b**4 - 4/7*b + 0 - 10/7*b**2 - 8/7*b**3 = 0. Calculate b.
-2, -1, 0
Factor 4/5*n**3 - 12/5*n**2 - 4/5 + 12/5*n.
4*(n - 1)**3/5
Let y = 38/13 + -1773/611. Let b = y - -87/329. Factor 0 - b*t**3 + 0*t + 0*t**2.
-2*t**3/7
Let i be (-160)/12 - 2/3. Let n = i - -17. What is v in 2*v + 4/5 - 2/5*v**4 + 6/5*v**2 - 2/5*v**n = 0?
-1, 2
Determine g so that 0*g + 2/5*g**2 - 2/5 = 0.
-1, 1
Let a(f) be the second derivative of -2/35*f**5 + 0*f**2 - 1/21*f**3 + 5/42*f**4 + f + 0. Solve a(c) = 0 for c.
0, 1/4, 1
Let s = 11/4 + -25/12. Factor -4*h + s*h**2 + 6.
2*(h - 3)**2/3
Let g(a) be the first derivative of -a**2 - 1 + a - 1/5*a**5 + 0*a**3 + 1/2*a**4. Solve g(v) = 0 for v.
-1, 1
Factor -20*k**4 - 11*k**2 - 4 + 40*k**3 - 14*k + 34*k + 4*k**5 - 29*k**2.
4*(k - 1)**5
Let u(o) be the second derivative of 0*o**3 + 4*o + 1/120*o**6 + 0*o**4 + 1/80*o**5 + 0 + 0*o**2. Solve u(c) = 0 for c.
-1, 0
Let t(i) = -i**3 + 4*i**2 + 3. Suppose -5*d + 4 = -4*d. Let r be t(d). Let l + 11 - 11 - l**2 - 2*l**r = 0. Calculate l.
-1, 0, 1/2
Let 4 - 2/3*k**2 - 2/3*k = 0. What is k?
-3, 2
Factor 0 - 9/2*c**3 - 3*c**2 - 3/2*c**4 + 0*c.
-3*c**2*(c + 1)*(c + 2)/2
Let i be ((-142)/90 - -1) + (-8)/(-10). Solve i*a**5 + 4/3*a**4 + 4/9 + 28/9*a**3 + 2*a + 32/9*a**2 = 0.
-2, -1
Let f(t) = -3 - 3*t**3 - 4 + 18*t - 21*t**2 + 25. Let i(q) = -q**3 - 6*q**2 + 5*q + 5. Let m(r) = -5*f(r) + 18*i(r). Solve m(w) = 0 for w.
-1, 0
Factor 0*o + 2/3*o**4 - 2/3*o**3 + 0 + 2/3*o**5 - 2/3*o**2.
2*o**2*(o - 1)*(o + 1)**2/3
Suppose 18/11*g**2 + 6/11*g**3 - 6/11*g - 12/11 - 6/11*g**4 = 0. Calculate g.
-1, 1, 2
Let z(s) be the third derivative of -s**5/60 - 3*s**4/8 - 3*s**3/2 - s**2. Let j(i) = i**2 + 8*i + 8. Let p(c) = -5*j(c) - 4*z(c). What is k in p(k) = 0?
-2
Factor 0 + 3/4*c**2 + 3/4*c.
3*c*(c + 1)/4
Let h(s) be the second derivative of 0 - 1/2*s**4 + 0*s**2 + 2*s - 1/10*s**5 - 2/3*s**3. Factor h(k).
-2*k*(k + 1)*(k + 2)
Factor -2/13*d + 2/13*d**2 + 2/13*d**3 - 2/13*d**4 + 0.
-2*d*(d - 1)**2*(d + 1)/13
Let v(h) be the first derivative of -h**5/5 - 3*h**4/4 - h**3 - h**2/2 - 7. Suppose v(q) = 0. Calculate q.
-1, 0
Let g(h) be the third derivative of -h**6/60 + h**5/30 + h**4/24 - 2*h**2. Let i be g(-1). What is r in 2/5*r**i - 2/5*r + 4/5*r**2 - 4/5 = 0?
-2, -1, 1
Let m(o) = -3*o**2 + 0 + o + 1 + 2*o**2. Let i(a) = 47*a**2 - 99*a**2 + 48*a**2 - 2*a. Let u(t) = i(t) - 2*m(t). Factor u(b).
-2*(b + 1)**2
Suppose -8 = -2*k + 12. Suppose 0 = 5*f - 0 - k. Factor 2*l - 5*l + f*l**4 + 2*l + 3*l**3.
l*(l + 1)**2*(2*l - 1)
Let d(t) = 27*t**3 + 27*t**2 + 15. Let j(n) = -7*n**3 - 7*n**2 - 4. Let c(o) = 4*d(o) + 15*j(o). Let c(b) = 0. What is b?
-1, 0
Let u(y) be the second derivative of -y**4/6 - 2*y**3/3 - 4*y. Determine c so that u(c) = 0.
-2, 0
Suppose 4*v - 25 = 3*d, -v + 3*d - 11 = 8*d. Determine k, given that -42*k**3 - 8*k - 2*k**4 + 0*k**3 - 32*k**2 - 16*k**v = 0.
-1, -2/3, 0
Let y be 20/(3 + -8) - 0. Let h = 6 + y. Let -2/9*d**h + 0 + 4/9*d = 0. What is d?
0, 2
Let c = -8/7 + 53/28. Suppose -3*i - 4*u + 2*u + 10 = 0, -4*i - 5*u + 18 = 0. Solve -1/2 - 7/4*f - c*f**3 - 2*f**i = 0 for f.
-1, -2/3
Factor 0*h**2 + 0*h**3 + 0*h + 1/6*h**4 + 1/6*h**5 + 0.
h**4*(h + 1)/6
Suppose -4*l = 5*t - 50, 2*t = 3*l + 2*l - 13. Let j(s) be the second derivative of 0*s**5 - 1/4*s**4 + 0*s**3 + 1/10*s**t + 0 + 0*s**2 + 3*s. Factor j(h).
3*h**2*(h - 1)*(h + 1)
Let y(h) be the second derivative of -h**4/48 - h**3/6 - h**2/2 - 25*h. Factor y(p).
-(p + 2)**2/4
Let x = -2 - -5. Suppose 0 = -2*t + 4*u + 24, u + 2 = -4*t + 14. Factor 2*h**x - h**3 + h**5 + 3*h**t + h**5.
h**3*(h + 1)*(2*h + 1)
Suppose g - 9 = -3. Let j(u) be the second derivative of 1/5*u**g + 2*u + 0 + 0*u**4 - 2/21*u**7 + 0*u**2 - 1/10*u**5 + 0*u**3. Find p such that j(p) = 0.
0, 1/2, 1
Let k(d) = 6*d**2 + 5*d + 7. Let w(n) = -2*n**2 - 2*n - 2. Let h(x) = 2*k(x) + 7*w(x). Factor h(m).
-2*m*(m + 2)
Suppose 0 = 4*s - 4, 4*r = -3*s + 8 + 3. Let o be r/4*(-20)/(-5). Factor -f - f + 2*f**o + 0*f.
2*f*(f - 1)
Let w(a) be the third derivative of -a**5/15 - a**4 - 16*a**3/3 + 16*a**2. Let w(v) = 0. What is v?
-4, -2
Let m(k) be the second derivative of k**7/14 + k**6/5 - k**4/2 - k**3/2 - 3*k. Factor m(j).
3*j*(j - 1)*(j + 1)**3
Let w(b) = -7*b**2 - 6*b - 3. Let p = 6 + 0. Let d(u) be the second derivative of -5*u**4/4 - 2*u**3 - 5*u**2/2 - 2*u. Let c(r) = p*d(r) - 13*w(r). Factor c(f).
(f + 3)**2
Let p be (2 - 8)/(-1 - 15/10). Determine a, given that 27/5 + 36/5*a + p*a**2 = 0.
-3/2
Let x(j) be the second derivative of -j**7/175 - j**6/60 - j**5/150 + j**4/60 + 3*j**2/2 + 2*j. Let o(y) be the first derivative of x(y). Factor o(i).
-2*i*(i + 1)**2*(3*i - 1)/5
Let i(p) = -8*p**2 - 2*p - 6. Let y(t) = t**2 - t. Let u(g) = i(g) + 6*y(g). Let u(x) = 0. Calculate x.
-3, -1
Let f(g) = 2*g**4 - 8*g**3 + 13*g**2 - 7*g - 3. Let h(u) = 6*u**4 - 24*u**3 + 38*u**2 - 20*u - 8. Let s(m) = -8*f(m) + 3*h(m). Factor s(j).
2*j*(j - 2)*(j - 1)**2
Let a = 43 - 43. Let d(q) be the third derivative of 0*q + 0*q**3 + 1/30*q**5 - q**2 + 0 + a*q**4 + 1/120*q**6 + 5/336*q**8 - 4/105*q**7. Factor d(s).
s**2*(s - 1)**2*(5*s + 2)
Let t(j) be the third derivative of -j**7/1575 - j**6/450 - j**5/450 + 7*j**2. Let t(x) = 0. What is x?
-1, 0
Let z(b) = b**2 + 12*b + 10. Let w(r) = -12*r - 9. Let a be (-1 + (-15)/(-6))*2. Let s(i) = a*z(i) + 2*w(i). Factor s(k).
3*(k + 2)**2
Suppose -4*m = 5*j + 5 - 15, 0 = 3*j + m - 6. Suppose 2*l + 2 = -3*v, -j*v = -l - v + 4. Find n, given that 0*n + n**l + 2*n - 4*n - 2*n**2 = 0.
-2, 0
Let f(t) be the third derivative of t**9/12096 - t**8/3360 + t**6/720 - t**5/480 + t**3 + 7*t**2. Let d(k) be the first derivative of f(k). Factor d(x).
x*(x - 1)**3*(x + 1)/4
Factor 0 + 1/2*o**3 + 1/2*o + 5/4*o**2.
o*(o + 2)*(2*o + 1)/4
Let d(j) = -j**3 - 3*j - 2. Suppose -5*y + 12 = -3. Let l(s) = -s**2 + 0*s**2 - 1 + 0. Let h(t) = y*l(t) - d(t). Solve h(r) = 0.
1
Let j(h) be the second derivative of 0*h**2 + 4*h - 1/66*h**4 + 0 - 1/33*h**3. Determine k, given that j(k) = 0.
-1, 0
Let d(q) be the third derivative of q**6/40 + q**5/5 + q**4/2 + 10*q**2. Determine z so that d(z) = 0.
-2, 0
Let z(g) be the first derivative of g**4/4 - 4*g**3/3 + 5*g**2/2 - 2*g - 14. Factor z(y).
(y - 2)*(y - 1)**2
Let l(h) be the third derivative of -2/3*h**3 + 0 + 4*h**2 - 1/30*h**5 + 0*h + 1/4*h**4. Determine d so that l(d) = 0.
1, 2
Suppose -14*s + 3*s**2 + 11*s - 6*s = 0. What is s?
0, 3
Let l(w) = -w**2 - 5*w - 9. Let q be l(-4). Let z = q + 5. Suppose -2/13 + z*t + 2/13*t**2 = 0. Calculate t.
-1, 1
Let z(a) be the first derivative of 2/15*a**5 + 0*a**2 + 5 + 0*a - 1/6*a**4 - 4/9*a**3. Factor z(v).
2*v**2*(v - 2)*(v + 1)/3
Factor -4/3 + 2/3*b**2 - 2*b**3 + 2*b + 2/3*b**4.
2*(b - 2)*(b - 1)**2*(b + 1)/3
Factor a**2 + 13*a**3 - 4*a**3 - 4*a + a**2 - 9*a**4 + 2*a**2.
-a*(a - 1)*(3*a - 2)*(3*a + 2)
What is l in 1/6*l**4 + 5/6*l**3 + 0 + 7/6*l**2 + 1/2*l = 0?
-3, -1, 0
Let w(m) be the first derivative of m**8/4200 - m**7/1050 + m**6/900 + m**3 + 4. Let o(u) be the third derivative of w(u). Find s, given that o(s) = 0.
0, 1
Let i(m) be the third derivative of m**5/60 + m**4/24 - m**3/3 - m**2. Suppose i(f) = 0. Calculate f.
-2, 1
Let g = 66 + -196/3. Let 0*s + 0*s**3 + 0 + 0*s**2 + g*s**4 = 0. What is s?
0
Solve 1/9*b**2 + 4/9 + 5/9*b = 0.
-4, -1
Let q(m) = m**2 + 19*m - 36. Let u(n) = -n**2 - 9*n + 18. Let x(f) = 3*q(f) + 5*u(f). What is v in x(v) = 0?
3
Let y(f) be the second derivative of f**8/6240 - f**7/1365 + f**6/1560 + f**5/390 - f**4/4 + 7*f. L