40 - x**4/16 - x**3/12 + 5*x - 1. Let k(v) be the first derivative of i(v). Suppose k(j) = 0. Calculate j.
-1, -2/3, 0, 1
Let k(g) be the second derivative of -g - 1/4*g**4 - 1/6*g**3 - 3/20*g**5 + 0*g**2 + 0 - 1/30*g**6. Factor k(w).
-w*(w + 1)**3
Let n(y) be the second derivative of -y**4/18 + y**3/9 + 2*y**2/3 + 6*y. What is z in n(z) = 0?
-1, 2
Let r be ((-2)/(-7))/((81/126)/3). Factor -1/3*c**4 + 2*c**3 - 13/3*c**2 + 4*c - r.
-(c - 2)**2*(c - 1)**2/3
Let x = 0 + 3. Let r(u) be the second derivative of 0 + 0*u**2 + 0*u**x + 0*u**4 - 1/80*u**5 - 2*u. Factor r(w).
-w**3/4
Factor 0*f + 4 - 3*f**2 - 6*f - f**4 - 4*f**3 + 10*f.
-(f - 1)*(f + 1)*(f + 2)**2
Determine f so that 1/2*f**2 + f + 0 = 0.
-2, 0
Let a = 92/11 - 1877/231. Let q(i) be the first derivative of -1 + 5/7*i**2 - 4/7*i + a*i**6 - 4/35*i**5 + 8/21*i**3 - 5/7*i**4. Find w, given that q(w) = 0.
-1, 2/5, 1
Determine r so that -r**2 + 30*r**3 - 52*r**5 - 35*r - 9*r**2 + 57*r**5 + 25*r**4 - 15 = 0.
-3, -1, 1
Factor 0 - 2/9*s**2 + 2/3*s - 2/3*s**3 + 2/9*s**4.
2*s*(s - 3)*(s - 1)*(s + 1)/9
Let y(c) be the third derivative of -2*c**7/15 - 13*c**6/90 + 4*c**5/15 + 2*c**4/9 + c**2. What is d in y(d) = 0?
-1, -2/7, 0, 2/3
Factor -10*u**2 - 10 + 8*u + u + 16*u.
-5*(u - 2)*(2*u - 1)
Suppose 33/2*o**4 + 0 + 3*o + 27/2*o**2 + 45/2*o**3 + 9/2*o**5 = 0. Calculate o.
-1, -2/3, 0
Let f = 3/2 - -1/6. Factor -t**2 + 0 - 2/3*t + f*t**3.
t*(t - 1)*(5*t + 2)/3
Let a = -61/2 - -31. Let g(n) be the first derivative of -1/10*n**5 + a*n + 0*n**3 + 1/2*n**2 + 2 - 1/4*n**4. Factor g(m).
-(m - 1)*(m + 1)**3/2
Let o(n) be the second derivative of 3*n**5/20 + n**4 + 3*n**3/2 + 4*n. Factor o(w).
3*w*(w + 1)*(w + 3)
Let o = 5 - 5. Suppose o = 2*i - 11 - 1. Factor 4*l**3 + 2*l**5 - 4*l**5 - 2*l + 2*l**2 - i*l**2 + 2 + 2*l**4.
-2*(l - 1)**3*(l + 1)**2
Determine c so that 0 + 0*c + 2/11*c**5 + 10/11*c**3 + 4/11*c**2 + 8/11*c**4 = 0.
-2, -1, 0
Let c(n) be the second derivative of -n**6/50 - 3*n**5/50 + 3*n**4/20 + 30*n. Solve c(o) = 0.
-3, 0, 1
Suppose -8/13*r**3 + 0*r - 6/13*r**2 + 0 = 0. What is r?
-3/4, 0
Let n(x) be the second derivative of x**5/30 - x**3/3 + 2*x**2 + x. Let z(m) be the first derivative of n(m). Factor z(c).
2*(c - 1)*(c + 1)
Let i(t) be the third derivative of -5/24*t**4 + t**2 + 0 + 1/20*t**5 + 0*t + 1/3*t**3. Factor i(m).
(m - 1)*(3*m - 2)
Factor -5*n**2 - 5*n**5 - 2*n**4 - 3*n**4 - 2*n**4 - 15*n**3 - 8*n**4.
-5*n**2*(n + 1)**3
Let j(k) be the third derivative of 1/60*k**5 + 0*k + 1/336*k**8 - 1/120*k**6 + 4*k**2 - 1/210*k**7 + 0 + 0*k**4 + 0*k**3. Factor j(r).
r**2*(r - 1)**2*(r + 1)
Let i = 24 - 22. Factor -18*c**i + 24*c**2 - 2*c**3 - 3*c - c.
-2*c*(c - 2)*(c - 1)
Let o(r) = r. Let s be o(3). Suppose 0 = -s*d + 7*d - 8. Factor 5*u**5 + 2*u - 3*u**5 - 2*u**3 - d*u**3.
2*u*(u - 1)**2*(u + 1)**2
Let c(v) be the third derivative of -4*v**2 - 1/21*v**3 + 0 - 1/84*v**4 + 0*v + 1/105*v**5. Factor c(i).
2*(i - 1)*(2*i + 1)/7
Let n = -2/853 - -1013/68240. Let u(z) be the second derivative of 0 + 1/24*z**3 + 3*z - 1/48*z**4 + 1/8*z**2 - n*z**5. Find w such that u(w) = 0.
-1, 1
Suppose -3*j = -2*a - 8, 3*a + 1 = 7. Factor 4*k + 2*k**2 + 0*k**2 - 2*k - j.
2*(k - 1)*(k + 2)
Let k(p) = p**3 - 4*p**2 + 8*p - 11. Let w be k(3). Let g(v) be the first derivative of 0*v - w + 4/21*v**3 + 1/7*v**2 + 1/14*v**4. Factor g(t).
2*t*(t + 1)**2/7
Let b(g) be the first derivative of -g**3/12 + 3*g**2/8 + g + 12. Factor b(t).
-(t - 4)*(t + 1)/4
Let r(o) = o**2 + 3*o + 1. Let f be r(-4). Let z be 6/21 - (-24)/14. Factor -12*l - 4 - 14*l**3 - 5*l - 46*l**z - f*l + 14*l**2.
-2*(l + 1)**2*(7*l + 2)
Let v = -4 + 7. Let o = -5 - -9. Find z, given that z**3 + 3*z - z - v*z**3 - 2*z**2 + 2*z**o = 0.
-1, 0, 1
Let o = 9/28 + -1/14. Factor 1/4*x**2 - o + 0*x.
(x - 1)*(x + 1)/4
Let k(d) be the third derivative of d**7/70 - 3*d**5/20 + d**4/4 - 5*d**2. Factor k(j).
3*j*(j - 1)**2*(j + 2)
Solve 6*a**3 + 0 - 96/5*a**2 - 3/5*a**4 + 96/5*a = 0.
0, 2, 4
Let n(g) = -g - 15. Let c be n(-15). Suppose c*j = 5*j. Factor j + 0*b**2 + 0*b + 2/7*b**4 + 2/7*b**3.
2*b**3*(b + 1)/7
Suppose 0 = 2*d - 4 - 0. Factor -2*l**2 - l**d + 3 + 6*l**2 - 6*l + 0*l.
3*(l - 1)**2
Let d(y) be the second derivative of -1/3*y**3 - 4*y + 1/2*y**2 + 0 + 1/12*y**4. Find i such that d(i) = 0.
1
Suppose 3*h + 3 = 12. Let g be 1/((-4 - -3) + h). Solve 0 - 1/2*s + g*s**3 + 0*s**2 = 0 for s.
-1, 0, 1
Let l(h) = h**3 - 21*h**2 + 22*h - 39. Let t be l(20). Let j(o) be the first derivative of 1/4*o**2 - 1/6*o**3 + 0*o - t. Factor j(i).
-i*(i - 1)/2
Let k(d) = 4*d**2 - 8*d - 7. Let w(b) = 5*b**2 - 9*b - 8. Let s = 7 + -12. Let v(l) = s*w(l) + 6*k(l). What is q in v(q) = 0?
-2, -1
Let a(y) be the second derivative of 3*y**5/70 + y**4/42 + 3*y**2 - 6*y. Let c(w) be the first derivative of a(w). Factor c(r).
2*r*(9*r + 2)/7
Let v(p) be the second derivative of -p**6/60 - 2*p. Factor v(u).
-u**4/2
Suppose 0 = z + 3*z + 44. Let r = z + 13. Factor 2/3 + 0*y - 2/3*y**r.
-2*(y - 1)*(y + 1)/3
Let o(c) = -c**3 + 10*c**2 - 5*c - 4. Let m be o(7). Let z be (-4)/(-18) + 30/m. Factor r**4 - r**2 - z*r + 0 + 0*r**3 + 1/2*r**5.
r*(r - 1)*(r + 1)**3/2
Let i(d) be the second derivative of d**9/1134 - d**7/420 + d**6/540 + 2*d**3/3 + 4*d. Let o(n) be the second derivative of i(n). Factor o(m).
2*m**2*(m + 1)*(2*m - 1)**2/3
Let u(n) be the third derivative of -7*n**5/120 + 3*n**4/16 - n**3/6 + 7*n**2. Factor u(m).
-(m - 1)*(7*m - 2)/2
Let d = 24 - 47/2. Determine p so that 1/2*p + d - 1/2*p**3 - 1/2*p**2 = 0.
-1, 1
Let s(g) be the third derivative of 0*g**7 + 4*g**2 + 0 + 0*g**3 - 1/180*g**6 + 0*g + 0*g**4 + 0*g**5 + 1/504*g**8. Solve s(b) = 0.
-1, 0, 1
Let f be (1/(-2))/((-1)/12). Let s(z) = -z**2 + 2. Let b be s(0). Factor b*o**2 - 2*o**3 + f*o + 4 + 2*o**2 - 4*o**2.
-2*(o - 2)*(o + 1)**2
Let s = 2747/9 + -305. Factor 0*n + 2/9*n**2 + 0 - s*n**3.
-2*n**2*(n - 1)/9
Let u(j) = j**2 - 5*j - 9. Let i be u(7). Let c(l) be the first derivative of -5/2*l**4 - 10*l**i + 32/3*l**3 - 1 + 0*l - 4*l**2. Determine a so that c(a) = 0.
-1, 0, 2/5
Factor -5/3*b - 4/3*b**2 - 1/3*b**3 - 2/3.
-(b + 1)**2*(b + 2)/3
Let l(f) be the second derivative of -f**8/1176 + f**7/735 + f**6/420 - f**5/210 - 3*f**2/2 + 3*f. Let h(d) be the first derivative of l(d). Factor h(k).
-2*k**2*(k - 1)**2*(k + 1)/7
Let 10 - 31*s + 5*s**2 + 30 - 14*s = 0. Calculate s.
1, 8
Let o(b) = b. Let i(j) = -2*j. Let d(l) = -2*i(l) - 5*o(l). Let x be d(-5). Let 0 - 4/11*n**2 + 0*n - 14/11*n**x - 2*n**3 - 32/11*n**4 = 0. What is n?
-1, -2/7, 0
Let l(c) = -c**4 + c**3 - c + 1. Let g(i) = -2*i**5 + 12*i**4 - 4*i**3 - 10*i**2 + 14*i - 10. Let w(t) = g(t) + 10*l(t). Find y such that w(y) = 0.
-2, 0, 1
Suppose -11*n = -n - 6*n. Factor 1/5*a**2 - 2/5*a + 2/5*a**3 + n - 1/5*a**4.
-a*(a - 2)*(a - 1)*(a + 1)/5
Suppose 5*t - 35 = -5*v, -2 = 2*v - 4*v + 2*t. Factor 2*k**3 + 18/11*k - 30/11*k**2 - 6/11*k**v - 4/11.
-2*(k - 1)**3*(3*k - 2)/11
Let g = 0 - 6. Let b(s) = s**3 + 7*s**2 + 5*s - 6. Let z be b(g). Factor 2/5*w + z + 2/5*w**2.
2*w*(w + 1)/5
Let l = -445 - -1783/4. Factor 0 - l*n**5 + 0*n**2 + 1/2*n**3 + 0*n - 1/4*n**4.
-n**3*(n + 1)*(3*n - 2)/4
Let v(m) be the second derivative of -m**4/4 - m**3 - 3*m**2/2 - 3*m. Suppose v(n) = 0. Calculate n.
-1
Let d = 13/7 + -11/7. Factor d*j**2 - 4/7*j + 0.
2*j*(j - 2)/7
Suppose -i + 4 = y + 3, y - i = 3. Determine u so that 1/2 + u + 1/2*u**y = 0.
-1
Let i(p) be the first derivative of -8*p**5/15 - 8*p**4/3 - 26*p**3/9 - p**2 - 11. Factor i(w).
-2*w*(w + 3)*(2*w + 1)**2/3
Let f(r) = -r. Let i(w) = 5*w**3. Let u(c) = -5*f(c) - i(c). Factor u(y).
-5*y*(y - 1)*(y + 1)
Let m(f) = 110*f**2 + 440*f + 330. Let t(k) = -5*k**2 - 20*k - 15. Let j(g) = -2*m(g) - 45*t(g). Factor j(o).
5*(o + 1)*(o + 3)
Suppose -5*i + 16 = -14. Let v(m) be the second derivative of m - 1/14*m**4 + 2/7*m**2 + 1/21*m**3 + 0 + 1/105*m**i - 1/70*m**5. Solve v(c) = 0.
-1, 1, 2
Let o(b) = b**3 - b**2 - 6. Let l be o(0). Let d = 10 + l. Determine t, given that 5*t**d + 4*t**5 - 3*t**5 - t - 2*t**2 - 3*t**4 = 0.
-1, 0, 1
Let i be (15/(-36))/(3/(-9)). Factor 1/2 + i*d**3 + 1/4*d**4 + 9/4*d**2 + 7/4*d.
(d + 1)**3*(d + 2)/4
Let l(g) be the second derivative of -8*g**6/15 + g**4 + 2*g**3/3 - 42*g. Factor l(f).
-4*f*(f - 1)*(2*f + 1)**2
Suppose 4*s +