Let z = 7 + -3. Factor -2*s**5 + 4*s**5 + l*s**z - 4*s**2 + 4*s**2.
2*s**4*(s + 1)
Let n(y) be the first derivative of -4*y**3/3 - 64*y**2 - 1024*y - 29. Factor n(o).
-4*(o + 16)**2
Let i(x) be the second derivative of -x**8/1008 - x**7/2520 + x**6/1080 + x**4/12 + 3*x. Let k(j) be the third derivative of i(j). Factor k(v).
-v*(4*v - 1)*(5*v + 2)/3
Let a(z) = 10*z. Let t be a(0). Solve 3/4*j**5 + 3/2*j**4 + 0 + 0*j + 3/4*j**3 + t*j**2 = 0.
-1, 0
Let s(t) be the second derivative of t**6/5 + t**5/5 - t**4/6 - 24*t. Find r such that s(r) = 0.
-1, 0, 1/3
Let b be (-18)/90*(-4)/6. Factor 0 + b*k**3 + 2/15*k + 4/15*k**2.
2*k*(k + 1)**2/15
Suppose -70*n - 2 = -71*n. Determine g so that -11/3*g**3 + 0 - 2/3*g**n + 0*g = 0.
-2/11, 0
Let r(q) be the third derivative of q**6/30 - q**4/6 + 4*q**2. Factor r(i).
4*i*(i - 1)*(i + 1)
Let r be (12/3*-1)/(-1). Let i = -1 + r. Let 0*a + 0 + a**4 + 1/3*a**i + 0*a**2 = 0. What is a?
-1/3, 0
Suppose 5/4 + 11/4*i + 1/4*i**3 + 7/4*i**2 = 0. What is i?
-5, -1
Let c(g) be the first derivative of -g**6/3 + 2*g**5 - 5*g**4 + 20*g**3/3 - 5*g**2 + 2*g - 6. Factor c(r).
-2*(r - 1)**5
Find q such that -1/2*q**2 - 1/2 - q = 0.
-1
Let t = 581 - 579. Solve 2/11*x + 0 - 2/11*x**t = 0.
0, 1
Let x(k) be the second derivative of 1/24*k**4 + 1/84*k**7 + 0*k**2 - 1/40*k**5 - 2*k - 1/60*k**6 + 0 + 0*k**3. Factor x(z).
z**2*(z - 1)**2*(z + 1)/2
Let n = 4 - -4. Find t such that -24*t + 0*t**2 + 12*t**3 + 2*t**3 - 18*t**2 + n = 0.
-1, 2/7, 2
Find h, given that -4*h**2 + 2*h**2 + 0*h**2 - h**3 - h + 0*h = 0.
-1, 0
Suppose -5*w = -17 - 8. Let f(o) be the second derivative of 0*o**4 + 2*o + 0 + 0*o**3 + 1/80*o**w - 1/120*o**6 + 0*o**2. Factor f(s).
-s**3*(s - 1)/4
Factor 4*g**3 + 3*g**2 - 8 - 4*g**4 - 54*g + 108*g + 9*g**2 - 58*g.
-4*(g - 2)*(g - 1)*(g + 1)**2
Suppose -3*j + 50 = 7*j. Let h(q) be the second derivative of 1/75*q**6 + 1/25*q**j + 0 - 1/10*q**4 - 2*q + 4/5*q**2 - 4/15*q**3. Factor h(g).
2*(g - 1)**2*(g + 2)**2/5
Let b = -4 + 6. Determine v so that -3*v**3 + b*v**4 - 4*v**4 + 0*v**3 + 5*v**3 = 0.
0, 1
Let h(z) be the third derivative of -1/20*z**6 + 5/12*z**4 + 2*z**2 - 2/15*z**5 + 0 + 0*z + 2/3*z**3. Factor h(r).
-2*(r - 1)*(r + 2)*(3*r + 1)
Let o(y) = 13*y**3 + 13*y**2 + 7*y + 2. Let t(q) = 7*q**3 + 6*q**2 + 3*q + 1. Let z(s) = -6*o(s) + 10*t(s). Factor z(p).
-2*(p + 1)**2*(4*p + 1)
Let v(l) be the third derivative of -l**7/1470 + l**6/420 - l**4/84 + l**3/42 + 11*l**2. Let v(r) = 0. Calculate r.
-1, 1
Let r(q) be the first derivative of q**6/40 + 3*q**5/20 + 3*q**4/8 + q**3/2 - 2*q**2 - 4. Let a(p) be the second derivative of r(p). Find b such that a(b) = 0.
-1
Let w = 32 + -20. Suppose -w*v = -14*v + 8. Find l such that 0*l**v + 0*l**3 + 0 - 1/4*l**5 + 0*l + 0*l**2 = 0.
0
Let r = -2 - -2. Suppose -12 = 3*d, -13 = 3*t - 2*t + 4*d. Factor -2*c**2 + 3*c**3 - 2*c**4 + r*c**t + c**4.
-c**2*(c - 2)*(c - 1)
Let y(j) = -j**4 + j**2 - j. Let d(i) = -7*i**4 + 3*i**3 + 4*i**2 - 6*i. Let z(k) = d(k) - 6*y(k). Factor z(u).
-u**2*(u - 2)*(u - 1)
Let b be ((-4)/(-18))/((-2)/(-6)). Let x = 1/21 - -13/21. Factor -2/9*z**3 + 2/9 - x*z + b*z**2.
-2*(z - 1)**3/9
What is p in 3/2*p - 9/4*p**2 + 0*p**3 + 0 + 3/4*p**4 = 0?
-2, 0, 1
Let u(t) = 2*t**2 - 2*t - 2. Let a be u(3). Suppose 3*s + s = 2*x - 20, x = -3*s - a. Factor -48*w**3 - 4*w**2 + 10*w**4 - 7*w**2 - w**x - 31*w**4.
-3*w**2*(w + 2)*(7*w + 2)
Let n(l) be the third derivative of l**8/28 - 8*l**7/21 + 4*l**6/5 + 2*l**5/3 - 9*l**4/2 + 20*l**3/3 + 5*l**2. Find h such that n(h) = 0.
-1, 2/3, 1, 5
Let s = -1075 - -1077. Find v such that 2/13*v**4 - 4/13*v**s + 0*v**3 + 2/13 + 0*v = 0.
-1, 1
Suppose -c - 3 + 23 = 0. Suppose -4*b + 0 = -c. What is k in 7*k**4 - 49/3*k**b + 0*k + 8*k**3 + 0 + 4/3*k**2 = 0?
-2/7, 0, 1
Let o be 10/4*(-78)/(-65). Suppose 5*k = 4*m - 16, -4*k = m + o*m - 16. Determine w, given that -2/7*w**5 + 4/7*w**3 + 0*w**2 - 2/7*w + 0 + k*w**4 = 0.
-1, 0, 1
Factor 2/5*c**4 + 26/5*c + 14/5*c**3 + 6*c**2 + 8/5.
2*(c + 1)**3*(c + 4)/5
Let x(s) be the third derivative of s**8/16800 - s**6/600 - s**5/150 + s**4/8 + 3*s**2. Let r(o) be the second derivative of x(o). Let r(p) = 0. What is p?
-1, 2
Let b be (-2 + (-1)/(-1))*-1. Let c be (3 - 3)*b/(-2). Suppose -2/7*p**2 + 4/7*p**3 + c - 2/7*p**4 + 0*p = 0. What is p?
0, 1
Suppose t - 4 = -3*w, 0*t - 3*w + 70 = -5*t. Let z = t - -15. Solve -6*m**2 + 2*m**4 - m**3 - m - m - z*m**4 - 5*m**3 = 0.
-1, 0
Let i(z) be the third derivative of -25*z**8/168 - 26*z**7/21 - 46*z**6/15 + 8*z**5/15 + 28*z**4/3 - 32*z**3/3 + 7*z**2. Factor i(x).
-2*(x + 2)**3*(5*x - 2)**2
Determine l, given that 12*l**2 - 2*l**4 - l - 15*l + 6 + 0*l**4 = 0.
-3, 1
Let 0 - 4*w**4 + 24*w**5 - 5*w**2 - 29/2*w**3 - 1/2*w = 0. What is w?
-1/3, -1/4, 0, 1
Determine q, given that -q**2 - 21*q + 2*q**2 - 43 + 2*q**2 + 61 = 0.
1, 6
Solve -3/2*v**2 - 3/8*v**4 + 0*v - 3/2*v**3 + 0 = 0 for v.
-2, 0
Let j(z) be the second derivative of z**4/18 - 20*z**3/9 + 100*z**2/3 + 7*z. Factor j(k).
2*(k - 10)**2/3
Let d(n) be the first derivative of -n**3/5 + 33*n**2/5 - 363*n/5 + 24. Determine m, given that d(m) = 0.
11
Let u(j) = 7*j**5 + 16*j**4 + 5*j**3 + 4*j**2 + 4. Let g(t) = -8*t**5 - 17*t**4 - 4*t**3 - 5*t**2 - 5. Let i(r) = -4*g(r) - 5*u(r). Find l, given that i(l) = 0.
-3, -1, 0
Let h(a) = 2*a**2 - 2. Suppose -2*v + 3*j - 33 = 0, 2*j = -v - 0*j - 27. Let d(g) = -9*g**2 + 9. Let l(w) = v*h(w) - 5*d(w). Factor l(i).
3*(i - 1)*(i + 1)
Let j(v) = v**3 - 5*v**2 + 2*v - 1. Let f(m) = 4*m**2 - 2*m. Let l = 9 + -9. Suppose l*n - 6 = 3*n. Let r(s) = n*j(s) - 3*f(s). Factor r(x).
-2*(x - 1)*(x + 1)**2
Let h(m) = m**2 - m. Let w(u) = -11*u**2 + 9*u. Let f(r) = 5*h(r) + w(r). Let f(z) = 0. Calculate z.
0, 2/3
Let n(z) be the third derivative of z**5/27 - 7*z**4/108 + z**3/27 + 13*z**2. Suppose n(c) = 0. Calculate c.
1/5, 1/2
Let y(z) = -4*z**2 + 6*z - 5. Let m be y(4). Let g = m + 226/5. Factor 2/5*p**4 + 0*p - g*p**2 + 1/5*p**3 + 0.
p**2*(p + 1)*(2*p - 1)/5
Let n(l) be the third derivative of l**8/336 + l**7/105 + l**6/120 - 4*l**2. Solve n(q) = 0.
-1, 0
Let i(y) be the third derivative of -y**5/100 + 3*y**4/40 - y**3/5 + 6*y**2. Find o such that i(o) = 0.
1, 2
Let l = -1 - -3. Let x be (-1 + (l - -1))*1. Factor z**2 - 2*z - 4*z**4 + 5*z**2 + 2*z**5 + 7*z**x - 9*z**2.
2*z*(z - 1)**3*(z + 1)
Let y(m) be the second derivative of m**6/60 - 2*m. Factor y(v).
v**4/2
Let s(a) be the third derivative of 0 + 5*a**2 - 1/210*a**5 + 0*a + 2/21*a**3 - 1/84*a**4. Suppose s(w) = 0. What is w?
-2, 1
Let o be 16/(-136) + 65/119. Factor 0*x - 1/7*x**5 + 0 - o*x**4 - 3/7*x**3 - 1/7*x**2.
-x**2*(x + 1)**3/7
Suppose 1/2*w**2 + 0 - w**3 + w - 1/2*w**4 = 0. Calculate w.
-2, -1, 0, 1
Let f(i) be the second derivative of -i**4/42 - i**3/21 - 5*i. Factor f(n).
-2*n*(n + 1)/7
Let d be (2 + -1 + -1)/(-2). Factor 0 + d*m + 0*m**2 + 3/5*m**3.
3*m**3/5
Let r = -16 - -21. Let o(c) be the second derivative of 0 - 1/105*c**6 + 0*c**3 + 0*c**2 - 2*c + 1/70*c**r + 0*c**4. Factor o(i).
-2*i**3*(i - 1)/7
Let f = -8/7 + 54/35. Determine s so that 2/5*s**3 + 0 - f*s + 0*s**2 = 0.
-1, 0, 1
Let j be (2 - 0) + 174/(-15). Let b = j + 346/35. Factor 2/7*m - 2/7*m**3 - b*m**4 + 0 + 2/7*m**2.
-2*m*(m - 1)*(m + 1)**2/7
Solve -2*z + 2*z**2 - z - 3*z + 8*z - 4 = 0 for z.
-2, 1
Let x(i) be the first derivative of i**7/840 - i**6/180 + i**5/120 + 4*i**3/3 + 1. Let a(r) be the third derivative of x(r). Suppose a(n) = 0. What is n?
0, 1
Let q = -1/427 + 2567/2135. What is b in -1/5*b**3 - 9/5*b + 0 - q*b**2 = 0?
-3, 0
Let g = 32 - 30. Suppose 5*a - 3*r = -12, g*r = 2*a - 2*r + 16. Factor a + 2/9*m - 2/9*m**3 - 2/9*m**2 + 2/9*m**4.
2*m*(m - 1)**2*(m + 1)/9
Factor -16/3*d**4 - 3*d**2 - 1/3*d - 8*d**3 + 0.
-d*(d + 1)*(4*d + 1)**2/3
Let n(k) be the third derivative of 5*k**7/168 + k**6/96 - 11*k**5/40 + 11*k**4/24 - k**3/3 - 2*k**2. Factor n(b).
(b - 1)*(b + 2)*(5*b - 2)**2/4
Suppose 2*f - 2*s = -f - 12, -5*f - 2*s - 20 = 0. Let u = f - -6. Factor -4*n**u + 2 - 2*n + 3*n + 0 - 3*n**3.
-(n + 1)**2*(3*n - 2)
Suppose 5*v - 3*k - 25 = 0, 9 = -3*v - 4*k - 5. What is h in h**2 - 4 + v*h**2 + h**2 - 2*h + 2*h**3 = 0?
-2, -1, 1
Let f = -20/3 + 7. Let m = -8 - -8. Find o such that m*o**2 + 0*o**3 + 0 - f*o**4 + 0*o = 0.
0
Let z(y) be the second derivat