
Let z(d) be the second derivative of d**7/980 + d**6/420 + d**5/420 + 2*d**4/3 + 4*d. Let t(m) be the third derivative of z(m). Factor t(j).
2*(3*j + 1)**2/7
Let j = 2253/10 - 225. Let m(l) be the second derivative of 3/25*l**5 + 2/5*l**3 + j*l**4 + 1/50*l**6 + 0 + 3/10*l**2 + 5*l. Solve m(r) = 0 for r.
-1
Let a be (2/(-16))/((-3)/6). Suppose -2 = -14*w + 13*w. Factor 1/2 - a*p**w - 1/4*p.
-(p - 1)*(p + 2)/4
Suppose 3*s - 4*y + 9*y = 27, -3*s + 6 = -2*y. Let m(v) be the third derivative of 0 + 0*v + 1/16*v**s + 3/80*v**5 + 0*v**3 - 2*v**2. Find k such that m(k) = 0.
-2/3, 0
Let t be ((-63)/6)/3 - (-2 - 3). Factor 3/4 - t*r + 3/4*r**2.
3*(r - 1)**2/4
Let c(z) be the first derivative of z**5/35 + 3*z**4/28 + 2*z**3/21 + 2. Factor c(w).
w**2*(w + 1)*(w + 2)/7
Let v = 90 + -5492/61. Let c = 69/244 + v. Let -1/2*z + 1/4 + c*z**2 = 0. What is z?
1
Let w(k) be the first derivative of -5 + 0*k**2 - 1/2*k**3 + 3/2*k. Factor w(i).
-3*(i - 1)*(i + 1)/2
Let y(i) be the second derivative of i**6/11 - 51*i**5/110 + 8*i**4/11 - 4*i**3/11 - 13*i. Solve y(f) = 0 for f.
0, 2/5, 1, 2
Let p(c) be the first derivative of -9/16*c**4 + 0*c - 27/8*c**2 - 1/20*c**5 + 10 - 9/4*c**3. Factor p(d).
-d*(d + 3)**3/4
Let f(a) be the first derivative of 3/10*a**2 - 2/5*a + 1/5*a**3 + 2 - 1/10*a**4. Determine n so that f(n) = 0.
-1, 1/2, 2
Suppose -4*k + 6 + 2 = 0. Factor -6*q**3 - 4*q**4 - k*q**2 + 2*q**3 + 0*q**3 - 2*q**3.
-2*q**2*(q + 1)*(2*q + 1)
Let i(d) be the third derivative of d**8/6720 - d**7/1260 - d**6/720 + d**5/60 - d**4/12 - 6*d**2. Let v(l) be the second derivative of i(l). Factor v(y).
(y - 2)*(y - 1)*(y + 1)
Let z be 15*((-72)/15)/(-4). Suppose w**2 + w**4 + 2*w**3 - z + 18 = 0. What is w?
-1, 0
Let x(c) be the third derivative of 0*c**3 + 0*c**4 + 1/180*c**6 - 1/90*c**5 - c**2 + 0*c + 0. Factor x(z).
2*z**2*(z - 1)/3
Let g(n) be the third derivative of n**6/40 + 23*n**5/100 + n**4/4 - 4*n**3/5 - 2*n**2. Factor g(y).
3*(y + 1)*(y + 4)*(5*y - 2)/5
Suppose 0 = 4*p - 5*h + 5, -36*p - 3 = -39*p - 3*h. Suppose p - 1/2*t**2 - t = 0. What is t?
-2, 0
Let d be ((-3)/(-12))/((-3)/(-4)). Factor 0 - d*c - 1/3*c**4 + 1/3*c**3 + 1/3*c**2.
-c*(c - 1)**2*(c + 1)/3
Factor -24/5*x**2 - 48/5*x - 4/5*x**3 - 32/5.
-4*(x + 2)**3/5
Let w(l) be the third derivative of 1/70*l**6 + 0*l - 4/735*l**7 + l**2 + 0*l**3 + 1/1176*l**8 + 0 + 1/84*l**4 - 2/105*l**5. Factor w(s).
2*s*(s - 1)**4/7
Let p = 54 - 38. Let i be (-8)/(-20)*10/p. Determine a so that 0 - i*a**2 + 1/4*a = 0.
0, 1
Let m be 4 - (-2)/(-3)*3. Suppose m*d - 5*x = d + 5, 5 = -4*d - 5*x. Determine p, given that -2/5*p**2 + d + 0*p = 0.
0
Suppose 184 = -2*j - 374. Let o = j - -1401/5. Factor o*g + 3/5*g**2 + 3/5.
3*(g + 1)**2/5
Let j = -9 + 9. Let y(s) be the third derivative of 0*s**3 + 1/210*s**7 + 0*s**6 + j*s**4 + 2*s**2 + 0*s + 0 - 1/60*s**5. What is b in y(b) = 0?
-1, 0, 1
Let d be ((-3)/(-2))/((-6)/8). Let n = 0 - d. Solve 0*x - x + x**2 + 0*x**n = 0 for x.
0, 1
Let r(m) be the second derivative of 0 + 32/15*m**3 + 139/50*m**5 + 97/30*m**4 + 4/5*m**2 + 19/15*m**6 + 3*m + 5/21*m**7. Factor r(c).
2*(c + 1)**3*(5*c + 2)**2/5
Let d(w) = -4*w**4 + 21*w**3 - 51*w**2 + 37*w - 15. Let b(s) = 12*s**4 - 62*s**3 + 154*s**2 - 110*s + 46. Let k(p) = -3*b(p) - 10*d(p). Solve k(a) = 0.
1, 3
Let t(k) = k**2 - k - 8. Let d be t(0). Let j = -6 - d. Solve -l**j + 0*l**2 - 7*l + 2 + 8*l = 0.
-1, 2
Let c(a) be the second derivative of -3*a**5/20 - 13*a**4/12 - 8*a**3/3 - 2*a**2 + 35*a. Factor c(d).
-(d + 2)**2*(3*d + 1)
Let g(f) be the first derivative of f**7/1890 - f**6/1080 - f**2 - 5. Let x(p) be the second derivative of g(p). Factor x(o).
o**3*(o - 1)/9
Let h(m) = m**3 + 2*m**2 - 4*m. Let y be h(-3). Factor -1/3*k**y + 0*k + 0 + 0*k**2.
-k**3/3
Suppose -4*a**2 + a + 2 + 1 - 3*a + 3*a**2 = 0. What is a?
-3, 1
Let f(r) be the third derivative of 8*r**2 + 1/105*r**7 + 0*r**5 + 0*r**6 + 0 + 0*r**3 + 0*r**4 + 0*r + 1/168*r**8. Factor f(t).
2*t**4*(t + 1)
Let n(z) = z. Let b be n(2). Let o(d) be the first derivative of d**2 + 2/5*d + b + 8/15*d**3. Determine g, given that o(g) = 0.
-1, -1/4
Let d = -11 + 40. Let k = -27 + d. Let -2*g - k*g**2 - 2/3 - 2/3*g**3 = 0. Calculate g.
-1
Let l(t) be the third derivative of -t**10/15120 - t**4/12 - t**2. Let v(y) be the second derivative of l(y). Factor v(f).
-2*f**5
Let q = 10/29 - -47/116. Factor -1/4*f**2 - 1/2 - q*f.
-(f + 1)*(f + 2)/4
Let r(m) be the first derivative of -14*m**5/5 - 2*m**4 + 2*m**3 - 1. Factor r(h).
-2*h**2*(h + 1)*(7*h - 3)
Let u be -1 - (2 - 0) - (-30)/9. Let y(f) be the second derivative of 1/8*f**4 + 2*f + 0 - u*f**3 + 1/4*f**2. Solve y(o) = 0 for o.
1/3, 1
Let b(m) = -m**3 + m - 1. Let v be 1/(-4) - 27/(-12). Let f(d) = -d**4 - 2*d**3 + 3*d**2 - 2. Let g(s) = v*b(s) - f(s). Factor g(y).
y*(y - 1)**2*(y + 2)
Let b(h) be the second derivative of -h**6/15 + h**4/2 + 2*h**3/3 - 5*h. Suppose b(p) = 0. Calculate p.
-1, 0, 2
Let a be ((-1)/3 - -1)*-3. Let b(n) = -2*n**3 + 0*n + n**4 + 3*n**3 + n. Let g(l) = -l**4 - 4*l - 1. Let h(w) = a*b(w) - g(w). Factor h(i).
-(i - 1)*(i + 1)**3
Suppose -3*l = -5*d + 47, -4*l - 61 = d - 6. Let j be (14/49)/((-6)/l). Factor 8/3*x + j*x**3 - 8/3*x**2 + 0.
2*x*(x - 2)**2/3
Suppose g - 8*g + 14 = 0. Find s, given that -3/5*s**3 + 2/5*s**4 + 1/5*s + 0 + 0*s**g = 0.
-1/2, 0, 1
Let p be -3*(-8)/(-36)*-3. Let v = 1 - 0. Suppose 19*u**2 + v + 22*u + 5*u**p + 3 = 0. What is u?
-2/3, -1/4
Let r be (-3576)/10 + (-4)/10. Let h = 1796/5 + r. Factor -6/5*n**3 + 2/5*n**4 + 0 - 2/5*n + h*n**2.
2*n*(n - 1)**3/5
Suppose g = -3*w + 5*w - 10, 2*g = 5*w - 24. Let k(o) be the first derivative of 1/20*o**w + 0*o**2 - 4 + 0*o - 1/15*o**3. Determine p so that k(p) = 0.
0, 1
Let s(o) be the third derivative of -o**8/252 - 4*o**7/315 + o**6/90 + 2*o**5/45 - o**2 - 58*o. Suppose s(p) = 0. What is p?
-2, -1, 0, 1
Let 6*b**3 - 16*b**2 + 12*b - 3*b**3 + 5*b**3 - 4*b**3 = 0. What is b?
0, 1, 3
Let a(j) be the third derivative of 1/210*j**5 - 1/420*j**6 + 0 + 1/84*j**4 - 1/21*j**3 + 0*j + 3*j**2. Let a(n) = 0. What is n?
-1, 1
Let q(p) be the third derivative of -p**5/390 + p**4/156 - 11*p**2. Factor q(b).
-2*b*(b - 1)/13
Factor -1/9*k**2 - 1/9 + 2/9*k.
-(k - 1)**2/9
Let u = -18 - -18. Let o(j) be the second derivative of -1/8*j**2 - 1/40*j**5 - j + 0*j**4 + 1/120*j**6 + 1/12*j**3 + u. Factor o(p).
(p - 1)**3*(p + 1)/4
Let s(l) be the third derivative of -1/54*l**4 + 0 + 0*l + 1/270*l**5 - 2*l**2 - 1/27*l**3 + 1/270*l**6. Factor s(g).
2*(g - 1)*(g + 1)*(2*g + 1)/9
Suppose 2*c - 9 = u, -3*c + 7*c = -5*u + 25. Let d = 8 - c. Determine r, given that -2*r + d + 3*r**2 - 2 - 2*r**2 = 0.
1
Let p(h) be the first derivative of 0*h - 7 + 0*h**2 + 2/21*h**3. Solve p(b) = 0 for b.
0
Suppose 0 = -5*m + 3*c - 5, 3*m + 2*c = c - 3. Let a be 1/(m/(-1 + -2)). Suppose 6/7*t**2 + 2/7*t**4 + 2/7*t + 6/7*t**a + 0 = 0. Calculate t.
-1, 0
Let i(p) be the first derivative of -5*p**3/9 + 5*p/3 - 25. Factor i(f).
-5*(f - 1)*(f + 1)/3
Let q(p) = p**3 + p**2. Let v(s) = -s**4 + s**3 + 2*s**2. Let u = 8 - 3. Suppose -2*d - 2*x - 3 = 3*d, -d = -4*x + u. Let f(g) = d*v(g) + q(g). Factor f(c).
c**2*(c - 1)*(c + 1)
Suppose -2*d + 15*d = 8*d. Find o, given that d - 1/2*o - 1/2*o**2 = 0.
-1, 0
Let h(i) be the second derivative of -i**7/42 + i**6/10 + i**5/20 - 7*i**4/12 + 2*i**2 - 39*i. Factor h(q).
-(q - 2)**2*(q - 1)*(q + 1)**2
Let l(y) = -y**2 - y - 2. Let r(t) = -2*t**2 - t - 3. Suppose -2*c = 2*c + 4, 0 = -2*z + c - 3. Let u(w) = z*r(w) + 3*l(w). Factor u(b).
b*(b - 1)
Suppose 0 = -5*d - 4*s - 138, 0*s = 4*d + 5*s + 114. Let h = 28 + d. Factor 22/7*v + 32/7*v**2 + 4/7 + h*v**3.
2*(v + 1)**2*(7*v + 2)/7
Let x(b) be the second derivative of 4/7*b**7 - 1/6*b**4 + 2*b**5 - b + 0*b**2 - 2/3*b**3 - 29/15*b**6 + 0. Determine l, given that x(l) = 0.
-1/4, 0, 2/3, 1
Let s(p) be the third derivative of -p**9/52920 + p**8/23520 + p**7/8820 - p**6/2520 + p**4/8 + 5*p**2. Let f(l) be the second derivative of s(l). Factor f(w).
-2*w*(w - 1)**2*(w + 1)/7
Let b be 3/(1*(-3)/(-6)). Suppose -14 - b = -4*m. Solve -3*d**m + 3*d**3 + 2*d**5 + 0*d**3 - 2*d**3 = 0 for d.
-1, 0, 1
Suppose 7*n = -n + n. Let l(v) be the second derivative of 0*v**2 - 4/35*v**7 + 5*v + 0 + 7/75*v**6 - 1/50*v**5 + 0*v**4 + n*v**3. Find i, given t