/(-15)). Find a, given that 8*a + 3*a**3 + 2*a**4 + 12*a**2 + 1 + 1 + d*a**3 = 0.
-1
Let g(n) be the first derivative of n**4/4 + 2*n**3 + 9*n**2/2 - 6*n - 3. Let f(o) be the first derivative of g(o). Factor f(j).
3*(j + 1)*(j + 3)
Let i(k) be the third derivative of 23/210*k**5 + 0 - 1/35*k**7 - 5*k**2 + 1/420*k**6 + 0*k - 2/21*k**3 - 1/84*k**4. What is g in i(g) = 0?
-1, -2/7, 1/3, 1
Let c(y) be the second derivative of y**7/21 + y**6/15 - y**5/10 - y**4/6 + 3*y. Factor c(x).
2*x**2*(x - 1)*(x + 1)**2
Let -2*d + 11*d + 4*d - 5*d**2 - 18*d + 25*d**3 - 15*d**4 = 0. Calculate d.
-1/3, 0, 1
Let t be ((-2)/(-9))/(3/9). Factor 0*n**3 + t*n**2 - 2/3*n**4 + 0 + 0*n.
-2*n**2*(n - 1)*(n + 1)/3
Let m be 5/(-4)*6/(-135). Let r(f) be the second derivative of 1/3*f**2 - 1/30*f**5 + 0 + 1/9*f**3 + 2*f - m*f**4. Find n, given that r(n) = 0.
-1, 1
Suppose -4*c = -c + 9. Let d be 24/(-9)*c/5. Determine q so that 4/5 + 12/5*q**2 - 6/5*q**5 - d*q**3 - 16/5*q**4 + 14/5*q = 0.
-1, -2/3, 1
Let a be 4/3*(-9)/6. Let c be (-351)/(-364) + a/(-7). Factor f**2 + 1/4 - c*f.
(f - 1)*(4*f - 1)/4
Let v(z) be the first derivative of -3/4*z**4 + 3*z**2 + z**3 + 0*z + 6. Determine c, given that v(c) = 0.
-1, 0, 2
Let k(p) be the first derivative of 4*p - p**2 + 1/2*p**4 + 3 - 4/3*p**3. Factor k(g).
2*(g - 2)*(g - 1)*(g + 1)
Suppose -4*x - 4 + 0 = 0, 0 = 4*z - 2*x - 2. Let 2/3*w**4 - 2/3*w**2 + 0 + 0*w**3 + z*w = 0. Calculate w.
-1, 0, 1
Suppose 0*o = k + o + 38, -k = 4*o + 29. Let a = 165/4 + k. Factor -a*x**2 + 0 + 1/4*x.
-x*(x - 1)/4
Let w be (-5 + -9)/(2 - 3). Let j = -11 + w. Find f such that -2/11*f**j - 6/11*f**2 - 2/11 - 6/11*f = 0.
-1
Let m be 0 - (-5 + (1 - -4)). Let d(h) be the first derivative of m*h + 0*h**4 - 2/15*h**5 + 0*h**3 - 1 + 0*h**2 - 1/9*h**6. Let d(n) = 0. Calculate n.
-1, 0
Let c(v) = -v**4 + v. Let o(t) = 4*t**4 + 4*t**3 - 10*t + 2. Suppose -n + 1 + 0 = 0. Let i(x) = n*o(x) + 6*c(x). Let i(p) = 0. Calculate p.
-1, 1
Let d = -6 + 13/2. Let s(n) be the first derivative of 1/4*n - 1/2*n**3 - d*n**4 + 2 + 0*n**2 - 3/20*n**5. Factor s(i).
-(i + 1)**3*(3*i - 1)/4
Let z(h) be the second derivative of h**5/36 - 7*h**4/72 + h**3/9 - 2*h**2 + 5*h. Let q(b) be the first derivative of z(b). Solve q(d) = 0 for d.
2/5, 1
Let r be 1 + (0 - (4/(-16) - -1)). Factor -r*a**2 + 0 + 1/2*a.
-a*(a - 2)/4
Let p(b) be the third derivative of -1/9*b**4 + 0*b + 5*b**2 - 1/45*b**5 + 0*b**3 + 0. Factor p(d).
-4*d*(d + 2)/3
Let z(y) be the first derivative of 2 - 1/9*y**3 - 1/3*y + 1/3*y**2. Suppose z(r) = 0. What is r?
1
Let k = 3 - -5. Suppose -4*c + 29 = 21. Factor o**c + 6*o + 5 + k*o**2 - 3*o**2 - 3 + 2*o**3.
2*(o + 1)**3
Let r(l) = 4*l**3 + 3*l + 3. Suppose -2*d = -d + 34. Let s = -2 + 8. Let g(w) = 23*w**3 + 17*w + 17. Let o(b) = d*r(b) + s*g(b). Solve o(y) = 0 for y.
0
Let g = 3 + -13/7. Factor 22/7*j**2 - g*j - 8/7 - 18/7*j**4 + 12/7*j**3.
-2*(j - 1)**2*(3*j + 2)**2/7
Let y(u) = -u**2 - 8*u + 3. Let q = -16 - -8. Let n be y(q). Find o such that -2/3*o - 2/3 + 2/3*o**n + 2/3*o**2 = 0.
-1, 1
Let p = 71/5 - 14. Solve p - 1/5*d**3 + 1/5*d - 1/5*d**2 = 0.
-1, 1
Let w(s) = 5*s**3 - 3*s**2 - 5*s - 5. Let f(g) = 5*g**3 - 2*g**2 - 4*g - 4. Let r(h) = 5*f(h) - 4*w(h). Factor r(x).
x**2*(5*x + 2)
Let v(m) be the second derivative of -m**7/42 - 7*m**6/30 - 9*m**5/10 - 5*m**4/3 - 4*m**3/3 - 39*m. Factor v(c).
-c*(c + 1)*(c + 2)**3
Suppose 496 = 5*m - 4309. Find h such that 700*h**4 - 160*h + 16 + 68*h**3 + 580*h**2 - 196*h**5 - 47*h**3 - m*h**3 = 0.
2/7, 1
Let y(d) = d**3 - d**2 - 3*d - 3. Let s(w) = -w**3 + 3*w**2 + 5*w + 5. Let k(r) = -3*s(r) - 5*y(r). What is n in k(n) = 0?
-2, 0
Let y be ((-4)/24*-9)/3. Let g(k) be the second derivative of 0 + 1/12*k**4 + 1/20*k**5 - 1/6*k**3 - y*k**2 - k. Factor g(w).
(w - 1)*(w + 1)**2
Let h(r) be the first derivative of 1/24*r**4 + 0*r**2 + 0*r + 7 - 1/18*r**3. Suppose h(a) = 0. Calculate a.
0, 1
Let f(q) be the third derivative of -q**7/2520 + q**5/120 + q**4/36 - q**3/6 + 3*q**2. Let o(l) be the first derivative of f(l). Solve o(b) = 0.
-1, 2
Let d(j) = 0*j**2 + 1 + j**2 - 2 + 2. Let s(h) = -h**2 + h - 2. Let m(i) = 6*d(i) + 3*s(i). Factor m(u).
3*u*(u + 1)
Let f be (-64)/(-12) - 1/3. Let h = -1 + f. Factor -h*t**2 - 2*t**3 + 2*t - 2*t + 2*t**2.
-2*t**2*(t + 1)
Let p = -4 + 9. Suppose -6*a**5 + 4*a**3 + 2*a**4 - 5*a**2 + 2*a**p + 2*a**4 + a**2 = 0. Calculate a.
-1, 0, 1
Let v = -7 - -9. Suppose -2*n = v*n. Factor n*g - 1/3*g**3 + 0*g**2 + 0.
-g**3/3
Let t(v) be the third derivative of 4*v**8/105 + 8*v**7/75 - 17*v**6/150 - 83*v**5/300 - 23*v**4/120 - v**3/15 + 7*v**2. Solve t(p) = 0 for p.
-2, -1/4, 1
Let a(b) be the first derivative of 4 + 4 - 11 + b**3. Factor a(v).
3*v**2
Let f(s) be the second derivative of s**4/42 - 2*s**3/21 - 3*s**2/7 + 16*s. Let f(o) = 0. What is o?
-1, 3
Let y(d) = -1 + 0*d**2 + d**2 + 0*d**2. Let l(j) = -j**3 + 1. Let f(u) = -3*u**3 + 5*u**2. Let h(v) = f(v) - 4*l(v). Let q(s) = h(s) - 4*y(s). Factor q(t).
t**2*(t + 1)
Let k(z) be the first derivative of z**6/2 - 3*z**4/2 + 3*z**2/2 + 10. Factor k(t).
3*t*(t - 1)**2*(t + 1)**2
Let c = 10 + -22. Let v be (-4 - -5)*(-3)/c. Factor -1/2*l**4 - 1/4*l**3 + 0*l + 0*l**2 + 0 - v*l**5.
-l**3*(l + 1)**2/4
Let n(c) be the second derivative of -c**7/3780 + c**6/810 - c**3/6 + 3*c. Let d(p) be the second derivative of n(p). Find s such that d(s) = 0.
0, 2
Let n(b) be the first derivative of -b**6/6 - 3*b**5/5 - 3*b**4/4 - b**3/3 - 7. Factor n(v).
-v**2*(v + 1)**3
Factor -u + u**2 - 8*u + 16 + u.
(u - 4)**2
Find w such that -1/2*w**3 - 1/2*w**5 + 0*w - w**4 + 0 + 0*w**2 = 0.
-1, 0
Let n = -400/3 - -136. Find a such that 0 - n*a**2 - 2/3*a**3 - 8/3*a = 0.
-2, 0
Let l(w) be the third derivative of -w**8/280 - 3*w**7/280 + w**5/40 + w**3 - 5*w**2. Let j(m) be the first derivative of l(m). Factor j(a).
-3*a*(a + 1)**2*(2*a - 1)
Let i be 4 + 0 - 6/3. Let k(m) be the first derivative of -1/9*m**3 + 1/6*m**i - 1/12*m**4 - 1 + 1/3*m. Factor k(g).
-(g - 1)*(g + 1)**2/3
Let n(z) be the third derivative of 2*z**6/15 - 7*z**5/15 + z**4/3 + 2*z**3/3 - 3*z**2. Solve n(g) = 0.
-1/4, 1
Let -2/9*k**4 - 44/9*k**2 + 16/9*k**3 + 16/3*k - 2 = 0. What is k?
1, 3
Let x(j) = 30*j**2 - 32*j - 22. Suppose -3*m = -m - z + 5, 0 = -4*m - 2*z - 30. Let g(i) = -12*i**2 + 13*i + 9. Let y(h) = m*x(h) - 12*g(h). Factor y(f).
-2*(f - 1)*(3*f + 1)
Suppose 0 = 2*t + 3*t + 5*k - 15, -6 = -2*t + 4*k. Suppose -3 = -3*v - t*l + 4*l, -4*v + l = -5. Factor 0*q + 1/2*q**v - 1/2.
(q - 1)*(q + 1)/2
Let r(o) be the third derivative of o**7/840 - o**6/240 - o**5/240 + o**4/48 - 6*o**2. Suppose r(i) = 0. What is i?
-1, 0, 1, 2
Suppose -20 = -2*u - 0*u. Factor 3*k**3 - 4*k - k**3 + u*k + k**3 + 9*k**2.
3*k*(k + 1)*(k + 2)
Let h(u) be the third derivative of 5*u**8/336 - u**7/14 + u**6/12 + 4*u**2. Factor h(c).
5*c**3*(c - 2)*(c - 1)
Factor -2/5*s**5 + 0 + 2/5*s - 4/5*s**4 + 0*s**3 + 4/5*s**2.
-2*s*(s - 1)*(s + 1)**3/5
Factor 3/5*q**3 + 0 + 0*q + 0*q**2.
3*q**3/5
Let a(s) be the second derivative of -1/273*s**7 - 1/130*s**5 + 0 + 2/39*s**3 + 1/26*s**4 + 0*s**2 - 1/65*s**6 - 2*s. Suppose a(b) = 0. Calculate b.
-2, -1, 0, 1
Let z be (-4)/10 - 54/(-10). Let l be 4*(z/(-6) + 1). Find u, given that 0*u**2 - l*u + 0 + 2/3*u**3 = 0.
-1, 0, 1
Let y(o) be the first derivative of -4*o**3/3 + 4*o - 4. Solve y(w) = 0.
-1, 1
Let l(o) be the second derivative of -o**4/30 - 2*o**3/15 + 11*o. Factor l(c).
-2*c*(c + 2)/5
Let t(h) be the first derivative of -h**2/2 + 11*h + 2. Let p be t(9). Determine q so that -6*q - 2*q**3 - 3*q**p + 2 + 6*q**2 + 3*q**2 = 0.
1
Let h(y) = -y - 5. Let v be h(-7). Factor -4*m + 6*m**2 - 3*m**v - 2*m.
3*m*(m - 2)
Let j(x) be the second derivative of 0 - 2/35*x**5 + 1/42*x**4 - x + 0*x**2 + 0*x**3. Factor j(n).
-2*n**2*(4*n - 1)/7
Suppose g + 1 = -0*g. Let l be 12/10 + (-2 - g). Solve -1/5*s + l*s**2 + 0 = 0.
0, 1
Let x(w) be the third derivative of w**8/100800 - w**7/12600 + w**6/3600 - w**5/60 + 2*w**2. Let a(h) be the third derivative of x(h). Let a(o) = 0. What is o?
1
Let q(t) = t**2 + 3*t - 4. Suppose 7*j - 3*j = -16. Let y be q(j). Factor y*l - 1/3*l**3 + 0*l**2 - 1/3*l**5 - 2/3*l**4 + 0.
-l**3*(l + 1)**2/3
Let t(g) = -g**3 + 6*g**2 - 3*g - 1. Let p be t(5). Let z be (7/21)/(1/p). Find s, given that -4*s**