/(-759). Let r = 3057/3542 + k. Factor 4/7*u**3 - r*u - 6/7*u**4 + 2/7 + 4/7*u**2 + 2/7*u**5.
2*(u - 1)**4*(u + 1)/7
Find q such that 1/5*q**3 + 3/5*q - 1/5 - 3/5*q**2 = 0.
1
Let p = 1/3 + -2/15. Let s(f) be the first derivative of 2/15*f**3 - 2 - p*f**4 + 0*f + 1/5*f**2. Factor s(m).
-2*m*(m - 1)*(2*m + 1)/5
Let q(s) = -24*s**2 - 207*s - 600. Let t(b) = 3*b**2 + 26*b + 75. Let y(w) = -4*q(w) - 33*t(w). Factor y(c).
-3*(c + 5)**2
Determine h, given that h**4 + 25 + 3*h**2 + 6*h**3 + 2*h**4 - 25 = 0.
-1, 0
Suppose -4 = 4*q + 8. Let y be (q - -2) + 22/18. Suppose 10/9*u**2 + y - 4/3*u = 0. Calculate u.
1/5, 1
Let s be (-12)/(-21)*(693/(-18))/(-11). Factor 1/2*c**s - 1/2 + 1/2*c - 1/2*c**3.
-(c - 1)**2*(c + 1)/2
Suppose 2*z - 125 = -121. Factor -4/13*t + 0 + 2/13*t**3 + 2/13*t**z.
2*t*(t - 1)*(t + 2)/13
Let m = 7 + -7. Suppose 2*x = -10, -c + m*x + 5*x + 25 = 0. What is d in -1/2*d + 1/2*d**2 + c = 0?
0, 1
Suppose -2*p - 4*f = -8, -6 = -2*f - 0. Let g be (8/p)/(2/(-1)). Let 2*r**4 + 5*r**2 + g*r**3 - 5*r**2 = 0. What is r?
-1, 0
Let j(i) be the second derivative of 0*i**4 - 1/105*i**6 + 0*i**2 + 0 - 4*i - 1/147*i**7 + 0*i**5 + 0*i**3. Determine d, given that j(d) = 0.
-1, 0
Let i(t) be the third derivative of t**7/90 + t**6/72 - 4*t**5/45 + t**4/18 - 4*t**2. Factor i(u).
u*(u - 1)*(u + 2)*(7*u - 2)/3
Suppose -y = 4*c - 9 + 26, -11 = -2*y + c. Factor -3*v - 13*v**3 - 52*v**2 + 93*v**y + 10*v + v.
4*v*(4*v - 1)*(5*v - 2)
Let q(p) = 4*p**4 + 18*p**3 + 23*p**2 + 13*p + 4. Let l(w) = -6*w**4 - 27*w**3 - 34*w**2 - 19*w - 6. Let a(m) = -5*l(m) - 8*q(m). Factor a(f).
-(f + 1)**2*(f + 2)*(2*f + 1)
Let c be (7/(-336))/(2/(-10)). Let o(h) be the third derivative of 0 + 3*h**2 - 1/60*h**5 - 1/6*h**3 - c*h**4 + 0*h. Factor o(m).
-(m + 2)*(2*m + 1)/2
Let p(a) be the first derivative of -2*a**5/5 + 3*a**4 - 8*a**3/3 - 6*a**2 + 10*a + 54. Determine f, given that p(f) = 0.
-1, 1, 5
Let w(m) = -m + 12. Let q be w(10). Factor -6*c**q - 2*c + 12 + 2*c**3 + 2*c - 4.
2*(c - 2)**2*(c + 1)
Let n = 12 + -12. Let p be -1 + (n - 1)*-1. Factor 1/3*q**4 + 1/3*q**3 + p + 0*q + 0*q**2.
q**3*(q + 1)/3
Let l(y) = -y**3 - 5*y**2 - 5*y - 5. Let q(c) = c**3 + 3*c**2 + 3*c + 3. Let t(g) = -3*l(g) - 5*q(g). Let t(p) = 0. Calculate p.
0
Let m = 1/172 + 857/516. Let v(z) be the first derivative of -2 - 13/9*z**3 + 0*z - 3/5*z**5 - m*z**4 - 1/3*z**2. Find g such that v(g) = 0.
-1, -2/9, 0
Let o(u) be the second derivative of -u**8/1680 + u**7/140 - u**6/30 + u**5/15 + u**3/3 - 3*u. Let c(l) be the second derivative of o(l). Factor c(v).
-v*(v - 2)**3
Let v(n) be the third derivative of n**7/420 - n**6/240 + 9*n**2. Solve v(r) = 0.
0, 1
Suppose 2*x - 7*x + 15 = 0. Suppose -1 = -4*m + 15. Find b such that 7*b**3 + 0*b**2 - 8*b**4 + 4*b**2 + m - 2*b**5 - 15*b**x + 10*b = 0.
-2, -1, 1
Let b(s) be the first derivative of -s**6/105 + s**5/35 + s**4/42 - 2*s**3/21 + 4*s - 3. Let f(m) be the first derivative of b(m). Factor f(h).
-2*h*(h - 2)*(h - 1)*(h + 1)/7
Let k(p) be the first derivative of -p**3 + 27*p**2/2 - 63. Find c such that k(c) = 0.
0, 9
Let z(x) be the third derivative of x**6/540 - x**5/90 - x**4/108 + x**3/9 + 30*x**2. Suppose z(q) = 0. What is q?
-1, 1, 3
Let z(l) be the first derivative of -l**6/1620 - l**5/540 - l**3 - 3. Let u(n) be the third derivative of z(n). Factor u(y).
-2*y*(y + 1)/9
Solve 87 + 75*g + 165*g + 153 + 80 + 5*g**3 - 75*g**2 = 0 for g.
-1, 8
Let p(o) be the second derivative of -2*o**6/15 + o**5/5 + o**4/3 - 2*o**3/3 - 10*o. Solve p(k) = 0 for k.
-1, 0, 1
Let m be 37/(-74) + (-2)/(-4). Factor -2/9*z**4 + m*z + 2/9*z**2 + 0 + 0*z**3.
-2*z**2*(z - 1)*(z + 1)/9
Suppose 2 = k + 5*b, 6*k = 5*k + 2*b + 2. Let g(j) be the first derivative of 12/7*j**k - 10/21*j**3 - 8/7*j + 1. Determine y so that g(y) = 0.
2/5, 2
Find u such that 47*u**3 + 6*u**4 - 6*u**2 + 2*u + u - 47*u**3 - 3*u**5 = 0.
-1, 0, 1
Let x be (-6)/(-48)*-4 - (-2 + 1). Suppose -h**2 - x*h + 1/2*h**3 + 1 = 0. What is h?
-1, 1, 2
Let x(o) be the third derivative of -2*o**7/15 + 9*o**6/40 + o**5/20 - o**4/12 + 6*o**2. Factor x(u).
-u*(u - 1)*(4*u - 1)*(7*u + 2)
Let t(h) = h**3 + 6*h**2 + h + 3. Let w be t(-6). Let z be -1*((w - 0) + 0). Factor -x**2 - 2*x**4 + 6*x**2 - z*x**2 + 0*x**2.
-2*x**2*(x - 1)*(x + 1)
Let g(p) be the first derivative of -p**4/4 + p**3/3 + 5*p**2/2 + 3*p - 18. Solve g(h) = 0 for h.
-1, 3
Let s(y) be the third derivative of -y**8/60480 - y**7/15120 + y**6/1080 + y**5/12 + 5*y**2. Let m(b) be the third derivative of s(b). Factor m(g).
-(g - 1)*(g + 2)/3
Let y = 97 + -289/3. What is l in 2/9*l**2 - y*l + 4/9 = 0?
1, 2
Let g(t) be the second derivative of 2/7*t**3 + 0 + t - 9/7*t**2 - 1/42*t**4. Solve g(p) = 0.
3
Let m = -1 + 6. Suppose w + 7 = -i - w, 16 = -3*i - m*w. Factor -12*q + i*q**2 + 5 + 5 + 2.
3*(q - 2)**2
Let y(g) be the first derivative of -g**6/1800 - g**5/300 - g**4/120 + g**3/3 - 3. Let o(j) be the third derivative of y(j). Let o(h) = 0. Calculate h.
-1
Let s be ((-62)/15)/((-42)/(-5)). Let i = 5/7 + s. Factor 2/9*n**2 + 0 + i*n.
2*n*(n + 1)/9
Let i(p) be the second derivative of p**4/12 - p**3/2 + p**2 - 13*p. Factor i(w).
(w - 2)*(w - 1)
Let p(c) = 3 + 2 - 6 + 2 + c. Let d be p(1). Determine g, given that g**2 - 10*g**3 - 2*g**2 + 2*g + 10*g**d - 4*g = 0.
0, 2/5, 1/2
Let i(n) be the second derivative of -1/105*n**6 + 2/35*n**5 - 1/7*n**4 + 0 + 4/21*n**3 - 8*n - 1/7*n**2. Factor i(g).
-2*(g - 1)**4/7
Let q(z) be the first derivative of -z**7/280 - z**6/60 - z**5/40 + 2*z**3/3 - 1. Let m(a) be the third derivative of q(a). Find g such that m(g) = 0.
-1, 0
Let d = 468 + -2328/5. Factor -9/5*x**5 - 3/5*x**3 + 0 + d*x**4 + 0*x**2 + 0*x.
-3*x**3*(x - 1)*(3*x - 1)/5
Let c(q) be the second derivative of 3/2*q**2 + 0 + 4/33*q**3 + 0*q**4 + 1/220*q**6 - 3*q - 7/330*q**5. Let b(h) be the first derivative of c(h). Factor b(p).
2*(p - 2)*(p - 1)*(3*p + 2)/11
Let a be 5/20 + (-6732)/(-80). Let r = -84 + a. Find w, given that -r - 8/5*w**3 - 12/5*w**2 - 2/5*w**4 - 8/5*w = 0.
-1
Let z be (-70 + 70)/((-2)/((-2)/(-3))). Let z*c - 2/5*c**5 - 32/5*c**2 + 32/5 + 8/5*c**3 + 6/5*c**4 = 0. What is c?
-2, -1, 2
Let n(v) = -v**3 - 2*v**2 + 3*v - 2. Let w be n(-3). Let s(u) = 3*u**2 + 3*u. Let x be s(w). Let 2*r**3 + 3*r**3 + 3*r - x*r**3 + 4 - 2 = 0. Calculate r.
-1, 2
Let v(h) be the third derivative of h**4/24 + h**3 + 6*h**2. Let u be v(4). Determine s, given that 12*s + 8/3 + u*s**2 - 25/3*s**3 = 0.
-2/5, 2
Determine b, given that -1/3*b**3 + 0 - 2/3*b**2 - 1/3*b = 0.
-1, 0
Let q(l) be the third derivative of -l**6/24 + l**5/12 + 5*l**4/6 - 10*l**3/3 - 10*l**2. Factor q(i).
-5*(i - 2)*(i - 1)*(i + 2)
Factor 1/4*v**2 + 1/4*v**3 - 1/4*v**4 + 0*v - 1/4*v**5 + 0.
-v**2*(v - 1)*(v + 1)**2/4
Let c = -4 - -7. What is u in 2 - u + u**2 - 1 - c = 0?
-1, 2
Let v(b) = b + 2. Let m be v(0). Let p(d) be the first derivative of -2/15*d**3 + 0*d + 1 - 1/10*d**4 + 2/25*d**5 + 1/5*d**m. Find u, given that p(u) = 0.
-1, 0, 1
Let h be 0 - 15/20 - -1. Find q, given that -1/4*q**2 - h*q + 1/2 = 0.
-2, 1
Let x(a) be the second derivative of -a**7/2520 + a**4/3 - 3*a. Let o(g) be the third derivative of x(g). Factor o(q).
-q**2
Let v(x) = -x**2 + 7*x. Let m(i) = i**2 - 3*i + 3. Let c be m(4). Let b be v(c). Let 0 + 1/4*u**2 + 1/4*u**4 + b*u - 1/2*u**3 = 0. Calculate u.
0, 1
Factor -3/2*f**3 + 3/2*f**2 + 0 + 0*f.
-3*f**2*(f - 1)/2
Determine w so that -1 + 2*w**2 + 4 + 8*w**2 - w**2 + 12*w = 0.
-1, -1/3
Let a(b) be the second derivative of -b**7/420 + b**6/72 - b**5/30 - b**4/4 + 3*b. Let v(i) be the third derivative of a(i). Factor v(f).
-2*(f - 1)*(3*f - 2)
Let f(r) = -11*r**2 + 18*r - 7. Let q(u) = -6*u**2 + 9*u - 3. Let x(d) = 3*f(d) - 5*q(d). Factor x(p).
-3*(p - 2)*(p - 1)
Factor 2*w - 2*w + 16*w**4 + 100*w**3 - 104*w**3.
4*w**3*(4*w - 1)
Let v(q) = q**3 + 9*q**2 - 4*q - 12. Let n be v(-9). Let u be (4/n)/(1/3). Determine g so that u + 9/4*g**2 - 3*g**5 + 11/4*g - 19/4*g**3 - 31/4*g**4 = 0.
-1, -1/4, 2/3
Let q(i) = -23*i**4 - 23*i**3 + 30*i**2 + 8. Let s(p) = 8*p**4 + 8*p**3 - 10*p**2 - 3. Let f(x) = 3*q(x) + 8*s(x). Factor f(l).
-5*l**2*(l - 1)*(l + 2)
Suppose -4*n = 5*d + 11, -3*d + 5*n + 7 = 4*n. Let u be 0/5 + d/2. Solve -u*v**2 + 0 + 1/2*v**4 - 1/2*v + 1/2*v**3 = 0.
-1, 0, 1
Let c = -101 - -298/3. 