/180 - y**5/90 + y**4/72 + y**3/18 + 3*y**2. Factor m(l).
(l - 1)**2*(l + 1)**3/3
Let c = -53 - -55. Let h(p) be the first derivative of 1/8*p**4 + 0*p - 1/10*p**5 + 0*p**c - 1 - 1/12*p**6 + 1/6*p**3. Factor h(r).
-r**2*(r - 1)*(r + 1)**2/2
Suppose -2 = -n - m + 3, 4*n + 2*m = 10. Let p(a) be the first derivative of 0*a + n*a**2 + 0*a**3 + 2/5*a**5 + 0*a**4 + 3. Find d, given that p(d) = 0.
0
Let r(x) be the second derivative of 3*x + 1/30*x**6 + 0*x**3 + 0*x**2 + 0*x**4 + 1/20*x**5 + 0. Solve r(p) = 0 for p.
-1, 0
Let p(s) be the third derivative of s**6/180 + s**5/60 + s**3/6 + s**2. Let h(j) be the first derivative of p(j). Factor h(t).
2*t*(t + 1)
Let t(o) be the first derivative of -2*o**7/105 - o**6/15 - o**5/15 - o**2/2 + 9. Let q(r) be the second derivative of t(r). Determine b so that q(b) = 0.
-1, 0
Let d(g) be the third derivative of g**5/450 - g**4/9 + 20*g**3/9 - 10*g**2. Factor d(o).
2*(o - 10)**2/15
Let s = -5/2188 - 7919/5470. Let d = -6/5 - s. Let 0*a + 1/4 - d*a**2 = 0. Calculate a.
-1, 1
Suppose 2*v + 2 = 3*v. Find l, given that -1 + 5*l**v - 2*l**2 + l - 3*l - 4*l**2 = 0.
-1
Let d be (-27)/4 + 1/(-4). Let l be d/(-15) - 12/(-60). Factor l*p**3 - 2/3 - 2*p**2 + 2*p.
2*(p - 1)**3/3
Let z be (2 + 3 - 5)/(-1). Factor 0*n + 2/5*n**2 + z.
2*n**2/5
Let n = -6 + 9. Let a(j) be the first derivative of 2/3*j**n - 2/5*j**5 + 0*j + 0*j**4 + 1/6*j**6 - 1/2*j**2 - 1. Factor a(w).
w*(w - 1)**3*(w + 1)
Let m(v) = -v**3 - 12*v**2 + 10*v - 19. Let q be m(-13). Factor -6*x**4 + 12*x + 5*x**3 - 14*x**3 - 8*x**2 + 3*x**5 + q*x**2.
3*x*(x - 2)**2*(x + 1)**2
Let d(z) be the second derivative of z**5/10 - 4*z**3/3 + 5*z. Let d(k) = 0. What is k?
-2, 0, 2
Let -23*c**5 + 18*c**4 + 32*c**3 + 9*c**5 - 8*c**2 - 4*c**3 - 4*c**3 = 0. Calculate c.
-1, 0, 2/7, 2
Let y = 20/9 - -28/9. Factor y*f**2 - 14/3*f + 4/3 - 2*f**3.
-2*(f - 1)**2*(3*f - 2)/3
Let i(l) be the first derivative of 3*l**4/4 + 3*l**3 - 6*l**2 - 6. Suppose i(t) = 0. What is t?
-4, 0, 1
Suppose 0 = a - 1 - 2. Let l be ((-1)/a)/(2/(-12)). Let 18/7*o**l + 4/7*o + 2*o**3 + 0 = 0. Calculate o.
-1, -2/7, 0
Find m such that -2/5*m**5 + 0*m + 0*m**2 - 2/5*m**3 + 4/5*m**4 + 0 = 0.
0, 1
Find p such that 1/5*p**3 + p + 10 - 8/5*p**2 = 0.
-2, 5
Let z(q) = -4*q**4 + q**3 - q - 2. Let i(l) = 5*l**4 - 2*l**3 + l**2 + 2*l + 3. Let f(n) = 2*i(n) + 3*z(n). Factor f(x).
-x*(x - 1)*(x + 1)*(2*x + 1)
Factor 0 + 0*l + 2/7*l**2.
2*l**2/7
Let u = -4/7 - -6/7. Solve -u*l**2 + 2/7*l - 2/7*l**3 + 2/7 = 0 for l.
-1, 1
Let i(h) be the third derivative of h**8/5040 - h**5/15 - 2*h**2. Let t(j) be the third derivative of i(j). Solve t(c) = 0 for c.
0
Find r such that -6 - 8/3*r**2 + 7*r + 1/3*r**3 = 0.
2, 3
Let d(i) be the third derivative of -1/12*i**4 + 1/30*i**5 - 1/3*i**3 + 1/60*i**6 + 0*i + 0 + 5*i**2. Let d(v) = 0. What is v?
-1, 1
Let b be (1/3)/(2/386). Let p = 65 - b. What is n in p*n**2 + 0*n + 0 = 0?
0
Let y be (-4)/10 - 36/(-15). What is k in -k**3 - 4*k**y - 4*k - 4*k**3 + 2*k**3 + 2*k**3 = 0?
-2, 0
Let y = -5 - 4. Let m = y + 11. Suppose 6*a - 3 + 5*a - 7*a + 12*a**m + 5*a = 0. Calculate a.
-1, 1/4
Find r, given that 5*r**2 - 2*r**2 - r**2 - 6*r + 2*r + 2*r**3 = 0.
-2, 0, 1
Let w(c) be the first derivative of -c**6/10 - 3*c**5/25 + 3*c**4/20 + c**3/5 + 16. Factor w(u).
-3*u**2*(u - 1)*(u + 1)**2/5
Let r(f) be the first derivative of f**5/15 + f**4/12 - f**3/9 - f**2/6 + 2. Factor r(x).
x*(x - 1)*(x + 1)**2/3
Determine g, given that -60/7*g**3 + 0 - 46/7*g**4 - 2*g**2 - 8/7*g**5 + 8/7*g = 0.
-4, -1, 0, 1/4
Let c = -15 - -46/3. Let h = -5/21 + 4/7. What is n in 0 + c*n + h*n**2 = 0?
-1, 0
Let 4*g**2 + 4 - g**2 - 18*g**3 + 12*g + 13*g**3 = 0. What is g?
-1, -2/5, 2
Let y(s) be the first derivative of s**3/9 - s/3 - 9. Factor y(l).
(l - 1)*(l + 1)/3
Suppose -20/11*m**4 - 4/11 + 2*m**3 - 10/11*m + 12/11*m**2 = 0. What is m?
-1/2, -2/5, 1
Factor 10/9*c - 4/9 + 14/9*c**2.
2*(c + 1)*(7*c - 2)/9
Let r(w) be the first derivative of 1/20*w**4 - 1/15*w**3 + 0*w**2 + 2 + 0*w. Suppose r(u) = 0. Calculate u.
0, 1
Let d(x) be the second derivative of -x**6/90 + x**5/60 + x**4/9 - 2*x**3/9 - 8*x - 4. Let d(n) = 0. What is n?
-2, 0, 1, 2
Let v(g) be the second derivative of g**4/12 + 7*g**3/6 - 9*g**2/2 - 2*g. Let m be v(-9). Factor m*a**2 - 3*a**2 + 6*a + 3*a**2 + 1.
(3*a + 1)**2
Factor 8/5*w**2 + 32/5*w + 2/15*w**3 + 128/15.
2*(w + 4)**3/15
Let o(i) be the first derivative of -i**5/45 - i**4/36 + 2*i**3/9 + 2*i**2/9 - 8*i/9 + 1. Solve o(b) = 0 for b.
-2, 1, 2
Let l(o) be the second derivative of 1/20*o**5 + 7/60*o**6 + 0*o**2 - 1/6*o**3 + o - 7/24*o**4 + 0. Find c such that l(c) = 0.
-1, -2/7, 0, 1
Let j(h) be the second derivative of h**4/6 - 48*h. Suppose j(r) = 0. What is r?
0
Suppose -13*v = -9*v. Let f(j) be the second derivative of 0*j**3 + 1/10*j**5 - j + v*j**2 + 1/6*j**4 + 0. Find l such that f(l) = 0.
-1, 0
Let k(t) be the second derivative of 3*t + 0 - 1/66*t**4 + 0*t**2 + 1/33*t**3. Factor k(s).
-2*s*(s - 1)/11
Let k = 3 - 4. Let s(l) = 4 - 2*l**3 - 5 + 3*l**3. Let a(q) = q**5 - q**4 - q**3 - 1. Let p(f) = k*s(f) + a(f). Factor p(d).
d**3*(d - 2)*(d + 1)
Let h(d) be the second derivative of 0*d**4 + 0 + 0*d**2 + 0*d**3 + 1/45*d**6 - 1/63*d**7 + 0*d**5 + 2*d. Factor h(r).
-2*r**4*(r - 1)/3
Let g = 22 - 22. Let i(l) be the third derivative of -1/60*l**6 + 0 + 0*l**3 + 0*l - 4/525*l**7 - 1/75*l**5 + g*l**4 - 1/840*l**8 + 2*l**2. Factor i(t).
-2*t**2*(t + 1)**2*(t + 2)/5
Let o = 115/186 - -3/62. Let 7/3*i**4 - 3*i**3 + 0*i + o*i**2 + 0 = 0. What is i?
0, 2/7, 1
Let o(m) be the first derivative of m**3/3 - 2*m**2 - 5*m - 2. Let o(x) = 0. Calculate x.
-1, 5
Let h(s) be the first derivative of -s**7/210 + s**6/60 - s**4/12 + s**3/6 + 3*s**2/2 - 6. Let v(x) be the second derivative of h(x). Factor v(u).
-(u - 1)**3*(u + 1)
Let h(f) be the first derivative of f**3/12 - f**2/8 - f/2 + 43. Factor h(t).
(t - 2)*(t + 1)/4
Factor -5/6*w**4 + 5/6*w**3 - 5/6*w**5 + 5/6*w**2 + 0*w + 0.
-5*w**2*(w - 1)*(w + 1)**2/6
Determine h so that 5 - 22*h + 5*h - 15*h**2 + 7*h = 0.
-1, 1/3
Factor 2/5 - 2/5*r - 2/5*r**2 + 2/5*r**3.
2*(r - 1)**2*(r + 1)/5
Solve -4/5*g - 4/5*g**3 + 0 + 8/5*g**2 = 0 for g.
0, 1
Let x be (-18)/(-9)*(1 + 0). Let b(y) be the first derivative of -16/3*y**3 + x - y**2 - 8*y**4 + 0*y. Factor b(f).
-2*f*(4*f + 1)**2
Let h(k) = 2*k + 18. Suppose -36 + 9 = 3*s. Let b be h(s). Determine y so that -2/7*y**2 + b + 2/7*y**4 + 2/7*y - 2/7*y**3 = 0.
-1, 0, 1
Suppose -4*f - p = -5, -2*f - p = p + 2. Let -1 - 9/2*z**f - 11/2*z = 0. What is z?
-1, -2/9
Suppose 0 = -j + 3*s - 3 - 6, 5*s = -5*j + 15. Let g(q) = -q**3 - q. Let a be g(j). Factor a - 6*k**2 + 2*k - 7/2*k**3.
-k*(k + 2)*(7*k - 2)/2
Factor 0 - 1/3*m - 1/3*m**2.
-m*(m + 1)/3
Suppose 2*j - 2*o + 5*o - 12 = 0, -2*o = 5*j - 8. Find x such that j + 0*x**2 + 0*x - 2/7*x**4 - 2/7*x**3 = 0.
-1, 0
What is b in 3*b**3 + 8*b**2 + b - 14*b**2 + 2*b = 0?
0, 1
Let i(p) = -p**2 - p + 1. Let g(l) = 6*l**3 - 33*l**2 + 9*l + 6. Let n(j) = g(j) - 12*i(j). Factor n(a).
3*(a - 2)*(a - 1)*(2*a - 1)
Factor -11*r + 3*r**4 + 2*r + 0 + 3*r**2 - 3 + 9*r**3 - 3.
3*(r - 1)*(r + 1)**2*(r + 2)
Let z be (-12)/(-7) - (-4)/14. Let a = 1 + 1. Factor 4 - 4 + z*w - 2*w**a.
-2*w*(w - 1)
Let p(n) be the second derivative of n**9/5400 + n**8/8400 - n**7/900 - n**6/900 + n**4/6 - 2*n. Let o(m) be the third derivative of p(m). Solve o(a) = 0 for a.
-1, -2/7, 0, 1
Let y(n) be the first derivative of 5*n**4/4 + 5*n**3 - 45*n**2/2 + 25*n - 4. Factor y(f).
5*(f - 1)**2*(f + 5)
Let f(s) = s**2 + 2*s + 1. Let k be f(-3). Suppose -n + w = -1, k*w = -5*n + 6 + 8. Factor -5*m**3 - m + n*m**2 + 4*m**3 + 0*m**3.
-m*(m - 1)**2
Factor 4 - 15*r**3 - 5*r**5 - 4 + 0*r**5 + 5*r**2 + 15*r**4.
-5*r**2*(r - 1)**3
Let s = 8 + -4. Factor 2*t**2 + 2*t**3 - 4*t**2 + 2*t**3 - s*t + 2*t**3.
2*t*(t - 1)*(3*t + 2)
Let d(q) be the third derivative of q**5/30 - 5*q**4/12 + 4*q**3/3 + 9*q**2. Determine w so that d(w) = 0.
1, 4
Let x(n) be the first derivative of -n**6/7 + 8*n**5/35 + n**4/14 - 4*n**3/21 - 14. Factor x(j).
-2*j**2*(j - 1)**2*(3*j + 2)/7
Factor 1/5*x**2 + 4/5*x + 3/5.
(x + 1)*(x + 3)/5
Let z = 1264/385 - -8/55. Suppose -18/7*q**2 - z*q - 8/7 = 0. Calculate q.
-2/3
Let i(w) be the first derivative of -2/3*w**3 + 0*w + 0*w