1
Let l(v) be the third derivative of 0*v**4 + 0 + 0*v + 2*v**2 + 1/3*v**3 + 1/180*v**6 + 0*v**5. Let o(i) be the first derivative of l(i). Factor o(w).
2*w**2
Suppose 0*z + 2*z - 6 = 0. Let j be (z - 0 - 3)/(-4). Factor 0 - 2/3*q**4 - 1/3*q**3 + j*q**2 + q**5 + 0*q.
q**3*(q - 1)*(3*q + 1)/3
Let y(j) be the third derivative of 1/300*j**5 - 1/30*j**3 + 0 + 0*j**4 + 0*j + 2*j**2. Factor y(h).
(h - 1)*(h + 1)/5
Let f(w) = -w + 5. Let d be f(5). Suppose -5*r - 5*m = d, 0 = -3*r - 4*m - m. Factor 0*v - v**2 + r - 21/4*v**4 + 49/4*v**5 - 6*v**3.
v**2*(v - 1)*(7*v + 2)**2/4
Let m be -3 - (5 - 0/(-2)). Let h = m + 8. Solve -1/3*u**2 + h - 2/3*u = 0 for u.
-2, 0
Suppose 0 = -9*k + 8*k + 2. What is g in -12 + 0*g**k + 0 + 3*g**2 = 0?
-2, 2
Let t(c) be the third derivative of -c**11/1829520 + c**9/332640 + c**5/30 + c**2. Let m(d) be the third derivative of t(d). Factor m(f).
-2*f**3*(f - 1)*(f + 1)/11
Factor 66*s - 8*s + 18*s**3 + 7*s**2 + 47*s**2 - 4*s + 2*s**4.
2*s*(s + 3)**3
Suppose 4*v = 2*f + 8, 0 = -5*v + f - 2 + 12. Suppose v - 4 = -2*d. Factor -8 + 1 + 2*s**3 - d + 6*s**2.
2*(s - 1)*(s + 2)**2
Factor -1/6 - 1/6*d**3 + 1/6*d + 1/6*d**2.
-(d - 1)**2*(d + 1)/6
Let y = 14/5 + 29/20. What is j in -9/4*j**5 + 4*j - 21/4*j**4 + y*j**2 - 7/4*j**3 + 1 = 0?
-1, -2/3, 1
Factor -1/2*p**3 + 0*p + 0 + 0*p**2 - 1/2*p**5 - p**4.
-p**3*(p + 1)**2/2
Let k(u) = 12*u**5 - 24*u**3 - 9*u**2 + 12*u. Let s(c) = 3*c**5 - 6*c**3 - 2*c**2 + 3*c. Let t(i) = 2*k(i) - 9*s(i). Factor t(n).
-3*n*(n - 1)**2*(n + 1)**2
Suppose 3*p = -0*p. Let x(i) be the second derivative of 0*i**4 + 0*i**3 + 0*i**2 - 1/40*i**5 + p + i. Factor x(h).
-h**3/2
Let b = -469 - -471. Factor 0*a + 0*a**b + 4/9*a**3 + 10/9*a**4 + 0.
2*a**3*(5*a + 2)/9
Factor 0*i + 0 - 1/5*i**2.
-i**2/5
Let g(n) be the third derivative of 2/945*n**7 + 0*n**3 - 5*n**2 - 1/108*n**4 + 1/1512*n**8 + 0*n**6 + 0 + 0*n - 1/135*n**5. Find x, given that g(x) = 0.
-1, 0, 1
Let q(m) = -4*m**4 + 40*m**3 + 50*m**2 + 6*m - 14. Let v(x) = -x**4 + 8*x**3 + 10*x**2 + x - 3. Let g(y) = 6*q(y) - 28*v(y). Suppose g(b) = 0. What is b?
-2, -1, 0
Let t(h) be the first derivative of -h**5/60 + h**3/18 + 4*h + 4. Let d(n) be the first derivative of t(n). Let d(o) = 0. Calculate o.
-1, 0, 1
Factor -12 + 5*i**2 + 0*i**2 - i**2 + 8.
4*(i - 1)*(i + 1)
Let s(p) be the first derivative of 3/8*p**2 - 5 - 3/2*p + 7*p**3. Let s(o) = 0. Calculate o.
-2/7, 1/4
Let o(k) be the first derivative of k**5/15 - 2*k**3/9 + k/3 - 6. Determine r, given that o(r) = 0.
-1, 1
Let d = 150 + -146. Let -5/2*s**2 + 0 - 1/2*s - 3/2*s**d - 7/2*s**3 = 0. Calculate s.
-1, -1/3, 0
Let v(c) be the first derivative of 0*c**4 - 1/60*c**5 + 2 + 0*c + 0*c**3 - c**2. Let u(l) be the second derivative of v(l). Factor u(t).
-t**2
Let k be 2/(-6) + 8/(-3). Let x be k/15 - 21/(-5). Factor -2*c**2 + c**2 + 0 + 2*c - x + 3*c**2.
2*(c - 1)*(c + 2)
Let p(b) be the first derivative of -2*b**4/3 + 4*b**3/9 + 7*b**2/12 + b/6 + 8. What is k in p(k) = 0?
-1/4, 1
Let a be (-24)/(-8) + 0/(-2). Let v be (-4)/(-3*2/a). Factor c**2 + v*c + 2*c**2 - 5*c**2.
-2*c*(c - 1)
Let m(r) = -4*r**3 - 24*r**2 - 44*r - 24. Let l(j) = -8*j**3 - 48*j**2 - 88*j - 48. Let w(t) = -2*l(t) + 5*m(t). Suppose w(v) = 0. What is v?
-3, -2, -1
Let v(m) = -m**4 - m**2. Let s be 3/(-2)*12/9. Let f(p) = -11*p**4 - 8*p**3 - 21*p**2 - 8*p - 2. Let w(d) = s*f(d) + 18*v(d). Let w(z) = 0. Calculate z.
-1
Let v(b) be the first derivative of 3*b**4/28 - b**3/7 + 7. Factor v(z).
3*z**2*(z - 1)/7
Let u be 3 + (288/(-171) - 1). Find g such that -2/19*g + 2/19*g**3 - u + 6/19*g**2 = 0.
-3, -1, 1
Let h be 5 - (60/(-25))/1 - 6. Suppose 3*y = 4*j + 4*y - 5, 3*j - 21 = 5*y. Factor a + h*a**j - 2/5.
(a + 1)*(7*a - 2)/5
Let 3/5*l**2 + 0 - 6/5*l = 0. Calculate l.
0, 2
Suppose 2*c = -0 + 4. Let 7*j**2 - 2*j**c - 8*j + 8*j**3 - 5*j**2 - 4 + 4*j**4 = 0. What is j?
-1, 1
Let r(s) = -5*s**3 + 5*s**2 + 7*s + 9. Let k(u) = 9*u**3 - 9*u**2 - 15*u - 17. Let v(c) = -6*k(c) - 10*r(c). Factor v(q).
-4*(q - 3)*(q + 1)**2
Let n(m) be the second derivative of m**5/4 - 5*m**3/6 + m. Solve n(y) = 0 for y.
-1, 0, 1
Let p(g) be the third derivative of g**7/21 - 37*g**6/210 + 13*g**5/70 + g**4/21 - 4*g**3/21 + 44*g**2. Let p(i) = 0. What is i?
-2/7, 2/5, 1
Let o(w) be the first derivative of -2*w**5/35 + w**4/7 + 2*w**3/21 - 2*w**2/7 - 2. Factor o(a).
-2*a*(a - 2)*(a - 1)*(a + 1)/7
Let a be (-9)/(-6)*4 - 2. Factor -11*c**2 - a*c - 4*c**2 - 14*c**3 - 3*c**2.
-2*c*(c + 1)*(7*c + 2)
Let y = -1 + 7. Let z(o) = -o**3 + 6*o**2 + o - 4. Let q be z(y). Factor 8*c + c**2 + c**2 + 0*c**q + 8.
2*(c + 2)**2
Let p(c) be the second derivative of -c**5/10 - c**4/6 + 2*c. Find v, given that p(v) = 0.
-1, 0
Let q(d) be the first derivative of 0*d + 0*d**2 + 1/10*d**5 + 0*d**4 - 1/6*d**3 - 2. Suppose q(i) = 0. What is i?
-1, 0, 1
Let b = -1/27 - -73/27. Factor 2/3*s - b*s**4 + 2/3*s**5 + 4*s**3 - 8/3*s**2 + 0.
2*s*(s - 1)**4/3
Let c = 6007/3 - 1958. Let m = c - 44. Find p, given that -1/3*p**4 + 0 + 1/3*p**5 - m*p**3 + 0*p + 1/3*p**2 = 0.
-1, 0, 1
Let i(o) be the first derivative of -o**3/9 - o**2/6 + 2*o/3 + 8. Factor i(l).
-(l - 1)*(l + 2)/3
Let a = 1/54 + 11/135. Let g(r) be the first derivative of 1 - 1/15*r**3 + 1/5*r + a*r**2 - 1/20*r**4. Solve g(h) = 0.
-1, 1
Suppose u - 6*u = 4*m - 16, 2*u + m = 4. Factor u*p + 1/3*p**3 + p**2 - 4/3.
(p - 1)*(p + 2)**2/3
Let d = -17/234 - -5/39. Let w(k) be the second derivative of -k - 1/60*k**5 + 0*k**2 - d*k**3 + 0 + 1/18*k**4. Factor w(y).
-y*(y - 1)**2/3
Let x(q) be the first derivative of 2*q**5/35 - 4*q**4/7 + 44*q**3/21 - 24*q**2/7 + 18*q/7 + 37. Factor x(n).
2*(n - 3)**2*(n - 1)**2/7
Factor -93*g**2 + 99*g**2 + 9*g + g**3 - g**3 - 14 - g**3.
-(g - 7)*(g - 1)*(g + 2)
Factor -r**4 + 3 - 3 + r**5.
r**4*(r - 1)
Let q(i) = -i**2 - 8*i - 2. Let u be q(-7). Factor 6/5*w**4 - 2/5*w**u - 4/5*w**3 + 6/5*w - 4/5*w**2 - 2/5.
-2*(w - 1)**4*(w + 1)/5
Let f(p) be the third derivative of 3*p**6/160 - 11*p**5/160 + p**4/16 - p**3/2 - 8*p**2. Let q(d) be the first derivative of f(d). Let q(l) = 0. What is l?
2/9, 1
Solve 8*l**2 + 4*l**2 + 5*l**4 - 1 - 14*l**3 - 2*l + 0*l**2 = 0 for l.
-1/5, 1
Let n(b) be the first derivative of 4*b**3/3 - 4*b + 3. Solve n(a) = 0 for a.
-1, 1
Let y(v) = 6*v**2 - 24*v + 41. Let k(j) be the first derivative of j**3/3 - 2*j**2 + 7*j - 4. Let d(c) = -34*k(c) + 6*y(c). Suppose d(l) = 0. Calculate l.
2
Let d(x) be the first derivative of -15*x**4/4 + 3*x**3 + 3*x**2 - 4. Let d(m) = 0. What is m?
-2/5, 0, 1
Let p(j) = -5*j**3 - 6*j**2 + 6. Let r(y) = 11*y**3 + 13*y**2 - 13. Let z(g) = -13*p(g) - 6*r(g). Factor z(u).
-u**3
Let f be 0 + -2 - 0 - -5. Let c be -2*((-6)/f + 1). Factor -2*b**2 + b**3 + 3*b**2 + c*b - 3*b - b**4.
-b*(b - 1)**2*(b + 1)
Suppose 3 = -5*s + 8. Let j be -3 - -5 - s*-1. Factor 1/4*q**j + 1/4*q + 1/2*q**2 + 0.
q*(q + 1)**2/4
Let b(t) be the first derivative of -t**4/4 + t**3/3 + t**2 + 11. Factor b(p).
-p*(p - 2)*(p + 1)
Let j(l) be the second derivative of -l**5/80 - l**4/24 - l**3/24 - 7*l + 1. Determine p, given that j(p) = 0.
-1, 0
Let b(t) be the first derivative of t**5/5 + 4*t**4/3 + 2*t**3 - 6*t + 3. Let l(x) be the first derivative of b(x). Determine n so that l(n) = 0.
-3, -1, 0
Let o(b) be the third derivative of b**8/40320 - b**7/10080 - b**5/60 + b**2. Let g(c) be the third derivative of o(c). Determine n, given that g(n) = 0.
0, 1
Let n(y) = 24 + 14*y**2 + 10*y**3 - 39*y - 4*y - 5*y. Let p(j) = -3*j**3 - 5*j**2 + 16*j - 8. Let w = -13 - -8. Let k(m) = w*n(m) - 16*p(m). Factor k(g).
-2*(g - 2)**2*(g - 1)
Let n(t) be the second derivative of -t**7/840 - t**6/80 - t**5/20 + t**4/6 + 6*t. Let g(p) be the third derivative of n(p). Find b such that g(b) = 0.
-2, -1
Let v be (-2 - (-1 - 0)) + 3. Suppose 1 = -b + 5*g, 0 = -5*b + v*b + 5*g + 7. Factor 3*m**5 + 4*m**b + 2*m**3 + 0*m**4 - m**3.
m**3*(m + 1)*(3*m + 1)
Let n(v) be the first derivative of 2*v**6/3 + 4*v**5/5 - v**4 - 4*v**3/3 + 5. Solve n(g) = 0 for g.
-1, 0, 1
Let o(g) be the third derivative of -9*g**6/40 + 7*g**5/20 + 5*g**4/2 + 2*g**3 + 20*g**2. Factor o(h).
-3*(h - 2)*(h + 1)*(9*h + 2)
Let p(s) be the first derivative of s**8/84 + 2*s**7/35 + s**6/30 - s**5/5 - s**4/3 - 2*s**2 - 5. Let k(n) be the second derivative of p(n). Fact