uppose -12 = -j*f + 3*k, -6 - 3 = -3*f - 2*k. Factor 0*s - 9*s**4 - 6*s**2 - 6*s**f - 2*s + 7*s**4.
-2*s*(s + 1)**3
Determine t, given that -3/7*t + 13/7*t**3 - 10/7*t**5 + 2/7 - 11/7*t**2 + 9/7*t**4 = 0.
-1, -1/2, 2/5, 1
Let g = -49 + 491/10. Let i(s) be the second derivative of 0*s**2 + 1/9*s**4 + 2*s + 0*s**3 + g*s**5 + 0. Solve i(u) = 0.
-2/3, 0
Let g(h) = -3*h**5 + 2*h**4 - 6*h**3 - 4*h**2 + 5*h. Let y(l) = -16*l**5 + 9*l**4 - 31*l**3 - 21*l**2 + 25*l + 1. Let k(a) = 11*g(a) - 2*y(a). Factor k(q).
-(q - 2)*(q - 1)**3*(q + 1)
Let k(p) = p**2 + 4*p + 13. Let o(a) = -2*a - 6. Let g(l) = -2*k(l) - 5*o(l). Suppose g(c) = 0. What is c?
-1, 2
Let h be (-2)/6 + (-63)/(-108). Find c such that 0*c**2 + 0*c + 1/4*c**3 - h*c**4 + 0 = 0.
0, 1
Suppose 44*j - 4 = 42*j. Let f(h) be the third derivative of 0 + 0*h + h**j + 1/24*h**4 + 1/24*h**3 + 1/60*h**5. Factor f(a).
(2*a + 1)**2/4
Let n(r) be the first derivative of r**3/4 + 3*r**2/4 - 9*r/4 + 6. Factor n(k).
3*(k - 1)*(k + 3)/4
Suppose -u + 3*u = 4*v + 4, 10 = -2*v - 3*u. Let r(g) = -2*g**3 - 2*g**2 + g - 2. Let p be r(v). Factor -3*q**p + 0*q**4 - q**3 + 0*q**3.
-q**3*(3*q + 1)
Let j(m) be the third derivative of -m**8/28 + 3*m**7/70 + m**6/8 - 3*m**5/20 - m**4/8 - 8*m**2. Determine k so that j(k) = 0.
-1, -1/4, 0, 1
Let q(h) be the second derivative of h**7/231 + h**6/55 + h**5/55 + 7*h. Factor q(o).
2*o**3*(o + 1)*(o + 2)/11
Let f(v) = 3*v**3 + v**2 + 2*v. Let c(x) = 8*x**3 + 2*x**2 + 4*x. Let u(r) = 6*c(r) - 15*f(r). What is b in u(b) = 0?
-1, 0, 2
Let m(v) = -3*v**2 + 6. Let r(o) = 4*o**2 - 7. Let c(b) = 3*m(b) + 2*r(b). Solve c(a) = 0 for a.
-2, 2
Let b(q) be the third derivative of 0 + 0*q**3 + 0*q - 1/10*q**5 - 1/8*q**4 - 1/40*q**6 + 5*q**2. Factor b(x).
-3*x*(x + 1)**2
Let z(c) = -c**3 + 3*c**2 - c. Let w = 8 - 6. Let x be z(w). Suppose 2/5*n**4 + 0*n + 2/5*n**3 - 2/5*n**5 + 0 - 2/5*n**x = 0. Calculate n.
-1, 0, 1
Factor -15*n**4 + 4*n**2 + 25*n**3 - 20*n - 2*n**2 - 4*n**2 + 22*n**2.
-5*n*(n - 2)*(n + 1)*(3*n - 2)
Let j(s) be the second derivative of -s**5/5 - s**4/12 + 2*s**3/3 + s**2/2 + 7*s. Factor j(y).
-(y - 1)*(y + 1)*(4*y + 1)
Let c(t) = t**2 + 2*t + 3. Let g be c(-1). Factor -1/4*f**g - 1 + f.
-(f - 2)**2/4
Let j = 1848/13 - 27538/195. Let l = 73/30 - j. Factor l*g**3 - 3/2*g + g**2 - 1.
(g - 1)*(g + 1)*(3*g + 2)/2
Suppose 0*g = -2*g + 6. Suppose -7*l**2 - 9*l**2 + 4*l - 2*l**4 + 0*l**4 + 6*l**2 + 8*l**g = 0. Calculate l.
0, 1, 2
Let i be 8/(-36) - (25/9 + -3). Let o(s) be the second derivative of 0 + 0*s**3 + i*s**2 + 2*s + 1/36*s**4 + 0*s**5 - 1/90*s**6. Suppose o(y) = 0. What is y?
-1, 0, 1
Let i(j) = -2*j**5 - j**4 - 3. Let p(o) = -o**5 - 1. Let l(v) = -i(v) + 3*p(v). Let l(u) = 0. Calculate u.
0, 1
Let s(f) be the first derivative of -3*f**5/5 - 3*f**4/4 + 3*f**3 + 3*f**2/2 - 6*f + 3. Factor s(t).
-3*(t - 1)**2*(t + 1)*(t + 2)
Let y(g) be the third derivative of 0*g**4 - 1/240*g**6 + 0*g + 0*g**3 - 2*g**2 + 0 + 1/120*g**5. Determine n so that y(n) = 0.
0, 1
Let p be 0/((-208)/96 + 1/6). Factor 6/5*g**3 - 3/5*g**5 + 0*g**4 - 3/5*g + 0*g**2 + p.
-3*g*(g - 1)**2*(g + 1)**2/5
Let b(f) = -8*f**4 - 41*f**3 - 62*f**2 - 12*f. Let r(y) = 3*y**4 + 14*y**3 + 21*y**2 + 4*y. Let c(z) = 6*b(z) + 17*r(z). Find u, given that c(u) = 0.
-1, -1/3, 0, 4
Suppose -21*q**2 - 9/2*q - 49/2*q**3 + 0 = 0. What is q?
-3/7, 0
Let m(a) be the third derivative of a**9/5040 + 3*a**8/2240 - a**6/60 + 7*a**4/24 - 7*a**2. Let b(o) be the second derivative of m(o). Solve b(i) = 0 for i.
-2, 0, 1
Suppose -c - 17 = 2*i, 0 = -0*c - 2*c + 2*i - 46. Let f be 32/14 + 6/c. Factor -6 + 17*a**2 + 27*a**2 + 19*a**3 + 11*a**3 - 9*a - 17*a**f.
3*(a + 1)*(2*a - 1)*(5*a + 2)
Factor -2*i - 3*i - 3*i - 8*i**2 - 1 + i**2.
-(i + 1)*(7*i + 1)
Let c(q) be the second derivative of q**7/3780 + 5*q**4/12 + q. Let l(r) be the third derivative of c(r). Factor l(f).
2*f**2/3
Suppose -13*w + 15 = -8*w. Let a(o) be the third derivative of 0*o + 1/48*o**5 + 7/480*o**6 + 0*o**w - 1/48*o**4 + 4*o**2 + 0. Let a(l) = 0. Calculate l.
-1, 0, 2/7
Let g = -23 + 16. Let x be (5/(-15))/(g/6). Factor 0 - 2/7*t - x*t**3 - 4/7*t**2.
-2*t*(t + 1)**2/7
Let p(f) be the first derivative of f**6/66 - 3*f**4/44 - 2*f**3/33 - 1. Factor p(i).
i**2*(i - 2)*(i + 1)**2/11
Suppose -y - g - 3 = 0, g = 5*y - 4*g - 35. Suppose -2*f - 5*t = -8 - 14, -y*t + 3 = -5*f. Factor 2 + f - 1 + a - a**2.
-(a - 2)*(a + 1)
Factor 0 - 1/8*j**5 - 63/4*j**3 + 343/8*j - 49/2*j**2 - 5/2*j**4.
-j*(j - 1)*(j + 7)**3/8
Let y(z) be the second derivative of -z**4/54 + 2*z**3/27 - z**2/9 - 6*z. Factor y(s).
-2*(s - 1)**2/9
Let j(h) = 34*h**4 + 214*h**3 + 432*h**2 - 2. Let u(r) = -r**5 + 67*r**4 + 427*r**3 + 864*r**2 - 5. Let d(x) = 5*j(x) - 2*u(x). Factor d(f).
2*f**2*(f + 6)**3
Factor 0*r - r**3 - 3*r**2 + 12 + r - 9.
-(r - 1)*(r + 1)*(r + 3)
Factor 3*f**5 + f**4 - 2*f**5 - 4*f**4 + 2*f**3.
f**3*(f - 2)*(f - 1)
Let w(i) be the second derivative of i**7/840 - i**6/480 - i**5/240 + i**4/96 - 3*i**2/2 + 10*i. Let b(x) be the first derivative of w(x). Factor b(v).
v*(v - 1)**2*(v + 1)/4
Let z(b) = 7*b**3 + 8*b**2 - 20*b - 5. Let c(q) = -15*q**3 - 15*q**2 + 39*q + 9. Let y(h) = 5*c(h) + 9*z(h). Suppose y(d) = 0. What is d?
-5/4, 0, 1
Let f be 33/12 - (-2)/8. Let q(t) be the third derivative of 0*t**4 + 0 + 0*t + 0*t**f - 1/420*t**6 - t**2 + 1/210*t**5. Suppose q(z) = 0. What is z?
0, 1
Let a be -3 + 6 - (0 + 1). Let t(f) be the second derivative of 0*f**a - 7/12*f**4 + f + 0 - 1/3*f**3 + 9/20*f**5. Factor t(z).
z*(z - 1)*(9*z + 2)
Let w(z) be the second derivative of -z**7/210 - z**6/150 + 3*z**5/100 + z**4/12 + z**3/15 - 8*z. Factor w(t).
-t*(t - 2)*(t + 1)**3/5
Let z = 85 - 253/3. Factor -z*m**3 + 2/3*m**2 - 2/3 + 2/3*m.
-2*(m - 1)**2*(m + 1)/3
Let a be 16/(-4)*2/(-4). Let f = a - 0. Factor 4 + 1 - p - p**f + p**3 - 4.
(p - 1)**2*(p + 1)
Let k(z) be the third derivative of -1/45*z**3 + 0*z + z**2 + 0 + 1/900*z**6 - 1/150*z**5 + 1/60*z**4. Find l, given that k(l) = 0.
1
Let i be (240/(-200))/(6/(-20)). Factor 1/3 - 1/3*s**i + 0*s**2 - 2/3*s**3 + 2/3*s.
-(s - 1)*(s + 1)**3/3
Let i(o) be the third derivative of 0*o**3 - 1/168*o**8 + 0*o + 2/105*o**7 + 0*o**4 + 2*o**2 - 1/60*o**6 + 0 + 0*o**5. Factor i(u).
-2*u**3*(u - 1)**2
Suppose -4*b = -2*b. Suppose 0 = 3*w - 5*g + 6*g - 12, -3*g = b. Solve 2/5*l**5 + 6/5*l**w + 4/5*l**3 + 0*l**2 + 0 + 0*l = 0.
-2, -1, 0
What is r in 0*r**2 + 6*r**2 - 4*r**2 = 0?
0
Suppose -32 = -4*h - 128. Let p be (h/20)/((-4)/10). Suppose -3*l + 1 + 0*l**2 - l**p + 3*l**2 + 0*l = 0. What is l?
1
Suppose b + 4*n = 1, 6*b + 3*n = b + 22. Solve 0 + 9/2*i**b + 11/2*i**2 - 11/2*i**4 - i - 7/2*i**3 = 0 for i.
-1, 0, 2/9, 1
Let w(u) = -u**3 - 2*u**2 + 8*u. Suppose -2*n + 2 = 10. Let z be w(n). Factor -1/2*h**5 - 1/2*h + z*h**2 + h**3 + 0*h**4 + 0.
-h*(h - 1)**2*(h + 1)**2/2
Let p(x) be the first derivative of -26/45*x**5 - 2 + 0*x**2 + 0*x + 8/9*x**4 - 8/27*x**3 + 1/9*x**6. Factor p(w).
2*w**2*(w - 2)**2*(3*w - 1)/9
Let b = -37/3 + 203/15. Factor 0 + b*n**2 - 42/5*n**3 + 10*n**4 - 18/5*n**5 + 4/5*n.
-2*n*(n - 1)**3*(9*n + 2)/5
Let w(g) = 6*g**4 - 8*g**3 + 4*g**2 + 8*g + 5. Let f(y) = 7*y**4 - 9*y**3 + 5*y**2 + 9*y + 6. Let u(n) = 5*f(n) - 6*w(n). Factor u(o).
-o*(o - 3)*(o - 1)*(o + 1)
Let s(z) be the third derivative of -z**7/35 + 2*z**6/15 - 7*z**5/30 + z**4/6 + 2*z**2. Determine u so that s(u) = 0.
0, 2/3, 1
Suppose 3*k - 76 = -25. Let c = 22 - k. Let 2/9*s + 2/9*s**c - 4/9*s**3 - 2/9 + 4/9*s**2 - 2/9*s**4 = 0. What is s?
-1, 1
Suppose 3*b = 4*o + 13, 0 = -o + 4*o + 3. Let g be b/(-1)*(-4)/6. Factor 0*s - 4*s + 2 + 2*s**3 + 2*s**3 - g*s**4.
-2*(s - 1)**3*(s + 1)
Let m(i) be the second derivative of 1/4*i**2 + 1/48*i**4 + 0 - 1/8*i**3 + i. Factor m(n).
(n - 2)*(n - 1)/4
Let m be (-5)/((-1 - 0)*1). Suppose m*v = 3*v. Factor v + f - 1/2*f**2.
-f*(f - 2)/2
Suppose 0*f = -3*f + 15. Suppose -f*o + 2*o = -3, 4*d - 21 = -o. Factor -8*w**3 + 0*w + 0 - 7*w**4 + 49/3*w**d - 4/3*w**2.
w**2*(w - 1)*(7*w + 2)**2/3
Let l(p) be the first derivative of 0*p + 1/3*p**6 + 2/15*p**3 - 26/25*p**5 + 9/10*p**4 - 1 - 2/5*p**2. Factor l(a).
2*a*(a - 1)**3*(5*a + 2)/5
Suppose 10 - 2 = 4*m. Suppose 8*p**3 + 2*p**2 - m*p + 5*p**4 + 2*p + p**4 = 0. What is p?
-1, -1/3, 0
Let c(m) = 114250*m**4 + 70304*m*