). Suppose 4*l + 0*l = x. Factor 1/2*u**2 + 1/4*u + l + 1/4*u**3.
u*(u + 1)**2/4
Suppose 2*u = 5*f - 10, 0 = 3*f + 3*u - 4 - 2. Determine g, given that -7*g**3 - g**5 - f*g**2 + 3*g**3 - 2 + 4*g**4 + 0 + 5*g = 0.
-1, 1, 2
Let j(v) = -v - 9. Let o be j(-9). Let g = 11 - 11. Factor w**2 + g*w + 45/4*w**4 + o - 6*w**3 - 25/4*w**5.
-w**2*(w - 1)*(5*w - 2)**2/4
Let f(v) be the third derivative of -v**5/120 + v**4/48 - 6*v**2. Factor f(b).
-b*(b - 1)/2
Let q(o) be the third derivative of o**8/1512 + o**7/135 + o**6/30 + 11*o**5/135 + 13*o**4/108 + o**3/9 + 14*o**2. Factor q(n).
2*(n + 1)**4*(n + 3)/9
Find c such that 2/5*c**2 + 16/5*c - 8/5 - 4/5*c**3 = 0.
-2, 1/2, 2
Let a(y) be the first derivative of -y**7/840 + y**5/40 - y**4/12 + y**3/3 - 2. Let n(t) be the third derivative of a(t). Factor n(l).
-(l - 1)**2*(l + 2)
Suppose 0 = -3*m + 13 + 2. Find k, given that -1/2*k**4 + 0 + 0*k**3 + 7/4*k**m + 0*k + 0*k**2 = 0.
0, 2/7
Let p(o) = -o**3 - 8*o**2 - 11*o + 8. Let j be p(-6). Suppose 0*l - 8 = -j*l. Factor -2*u**3 + 0 - 8/3*u - l*u**2 - 1/3*u**4.
-u*(u + 2)**3/3
Let v = 113 + -79. Suppose -2*x + v = 2*r, -22 = -2*x + 5*r - 4*r. Determine c so that -4*c - 5*c**4 + 6*c**5 + 7*c**4 + 9*c**3 - 24*c**4 - 2*c**2 + x*c**3 = 0.
-1/3, 0, 1, 2
Let n be (-18)/6 + (-14)/(-4). Factor n + b**3 - 11/4*b**2 + 5/4*b.
(b - 2)*(b - 1)*(4*b + 1)/4
Let u(z) be the second derivative of 0 - 1/6*z**4 + 1/2*z**3 - 1/10*z**5 - 1/42*z**7 - 1/2*z**2 + 1/10*z**6 - 6*z. Factor u(b).
-(b - 1)**4*(b + 1)
Let u be 96/80*10/14. Factor -2/7 - 2/7*b**3 - u*b**2 - 6/7*b.
-2*(b + 1)**3/7
Let v(x) be the third derivative of x**8/1848 - 2*x**7/1155 - x**6/330 + 4*x**5/165 - 7*x**4/132 + 2*x**3/33 - 4*x**2. Find q, given that v(q) = 0.
-2, 1
Suppose 3*o - 5*o = -8. Factor -m + m**o - m**5 + 3*m - 2*m.
-m**4*(m - 1)
Suppose -7*n - 2 = -16. Let f(w) be the first derivative of 8*w - 1/2*w**4 + 1 + 0*w**n - 2*w**3. What is j in f(j) = 0?
-2, 1
Factor 0 - 5/3*c**3 - 4/3*c + 1/3*c**4 + 8/3*c**2.
c*(c - 2)**2*(c - 1)/3
Find g such that 144*g**5 + 100*g**3 - 336*g**4 + 592 - 8*g**2 - 592 = 0.
0, 1/6, 2
Let a(v) = -v**3 + v. Let o(x) = -x**4 + 6*x**3 - 4*x**2 - 2*x. Let r(u) = -2*a(u) - o(u). Factor r(l).
l**2*(l - 2)**2
Let u(k) be the first derivative of 14*k**3/3 + 9*k**2 + 4*k + 2. Factor u(x).
2*(x + 1)*(7*x + 2)
Let x be 16/(-96) + 2/3. Solve -1/2*z - z**2 + 0 - x*z**3 = 0 for z.
-1, 0
Let i(v) = -6*v**3 - 3*v**2 + 3*v. Let j(u) = 12*u**3 + 5*u**2 - 7*u. Let x(q) = 5*i(q) + 2*j(q). Factor x(h).
-h*(h + 1)*(6*h - 1)
Let g(h) = -3*h**3 + 11*h**2 - 20*h + 8. Let x(n) = 6*n**3 - 21*n**2 + 39*n - 15. Let j(a) = -9*g(a) - 4*x(a). Suppose j(b) = 0. Calculate b.
1, 2
Let o be ((-3531)/22)/((-3)/(-4)). Let q = o + 1076/5. Factor -2/5 + 2/5*y**5 + 4/5*y**3 - q*y - 4/5*y**2 + 6/5*y**4.
2*(y - 1)*(y + 1)**4/5
Let k = 41/28 - 5/7. Suppose -7*j - 2*u = -5*j - 4, -3*j + 6 = 2*u. Factor 1/4*o**3 + 3/4*o**j + k*o + 1/4.
(o + 1)**3/4
Let -15/4*h**3 - 36*h**2 + 75/2 - 315/4*h = 0. What is h?
-5, 2/5
Determine g, given that -1/2*g**4 + 0 - g**2 + 3/2*g**3 + 0*g = 0.
0, 1, 2
Let h(x) be the first derivative of -2*x**3/33 - 6*x**2/11 - 18*x/11 + 11. Solve h(m) = 0 for m.
-3
Let m(f) = -f**2 - 6*f - 6. Let l be m(-4). Suppose -15*u + 189*u**4 - 2 - 1 + 81*u**5 + u**2 + 126*u**3 + 7*u**l - 2*u**2 = 0. Calculate u.
-1, -1/3, 1/3
Let w(c) = -c**2 - 4*c + 2. Let v be w(-6). Let l be -6*v/(-15)*-1. What is f in -1/3*f**l + 0*f**2 - 2/3*f + 2/3*f**3 + 1/3 = 0?
-1, 1
Let w = 62899/165 + -1903/5. Let d = -3/11 + w. Factor -2/3*u**2 + 0 + d*u**3 + 1/3*u.
u*(u - 1)**2/3
Let k be 2 + 9/(-198)*36. Determine a, given that -8/11*a**4 - 2/11*a**5 - 8/11*a**3 + 10/11*a + k*a**2 + 4/11 = 0.
-2, -1, 1
Let o(l) be the second derivative of -l**4/12 + l**3/6 - 3*l. Solve o(v) = 0 for v.
0, 1
Determine q so that 3/4*q - 3/8*q**3 - 3/8*q**2 + 0 = 0.
-2, 0, 1
Let z(b) be the third derivative of 5*b**8/336 - b**7/14 + b**6/12 + b**5/6 - 5*b**4/8 + 5*b**3/6 - 9*b**2. Factor z(q).
5*(q - 1)**4*(q + 1)
What is x in 0 + 0*x + 2/5*x**2 - 2/5*x**3 = 0?
0, 1
Solve 3/4*y**3 - 1/2*y - 1/4*y**2 + 1/4*y**4 + 0 - 1/4*y**5 = 0.
-1, 0, 1, 2
Let h = -259892/5 - -51815. Let v = h + 164. Suppose -1/5 + v*k**4 + 3/5*k - 1/5*k**5 - 2/5*k**3 - 2/5*k**2 = 0. What is k?
-1, 1
Let g be (2/(-6))/(1/(-9)). Let i = g + 0. Factor 0 - 2/11*t**2 + 8/11*t**5 + 0*t + 14/11*t**4 + 4/11*t**i.
2*t**2*(t + 1)**2*(4*t - 1)/11
Let i = -3/8 - -37/56. Suppose 11 = 4*n + 3*d, 3*n - 7 = -2*d + d. Let -i*m**n - 2/7*m**3 + 0 + 0*m = 0. What is m?
-1, 0
Determine k, given that -48/13*k**3 - 4/13*k - 30/13*k**2 - 22/13*k**4 + 0 = 0.
-1, -2/11, 0
Let y(k) = k**2 + k + 1. Suppose 6 = -b - 2*b - 3*i, -i = -1. Let q(u) = u**3 - 7*u**2 + 2*u - 5. Let g = -11 + 10. Let n(o) = b*y(o) + g*q(o). Factor n(s).
-(s - 2)*(s - 1)**2
Factor 1/8*d**5 + 63/8*d**3 + 17/8*d**4 - 81/8*d**2 + 0 + 0*d.
d**2*(d - 1)*(d + 9)**2/8
Let m be 3 - 178/70 - 22/(-55). Factor 1/7*j**3 + 9/7*j + 0 + m*j**2.
j*(j + 3)**2/7
Let r(d) be the first derivative of -5/3*d**2 - 4/3*d + 14/9*d**3 - 2. Factor r(i).
2*(i - 1)*(7*i + 2)/3
Suppose -n = -6*n + 10. Let a be (n/(-4))/(9/(-6)). Solve -a*x**2 - 1/3 + 2/3*x = 0.
1
Let o(d) = 2*d + 2. Let n be o(2). Let c(q) be the third derivative of 0 + 0*q + q**2 - 1/60*q**4 - 1/525*q**7 + 0*q**3 + 1/150*q**5 + 1/300*q**n. Factor c(z).
-2*z*(z - 1)**2*(z + 1)/5
Let t = 341 - 338. Solve 1 - 1/2*g**t - 5/2*g + 2*g**2 = 0 for g.
1, 2
Suppose 0 = -0*h + 3*h. Let u = h + 2. Factor -2/9 + 0*o + 2/9*o**u.
2*(o - 1)*(o + 1)/9
Factor -2/15*g**3 + 0*g + 0 + 2/15*g**2.
-2*g**2*(g - 1)/15
Let y(i) = -i**4 - 3*i**3 - 6*i**2 - i - 3. Let h(q) = 5*q**4 + 12*q**3 + 25*q**2 + 5*q + 13. Let v(k) = -6*h(k) - 26*y(k). Factor v(a).
-2*a*(a - 2)*(a + 1)*(2*a - 1)
Let r(j) be the second derivative of 5*j - 4/21*j**7 + 1/6*j**4 + 0 + 3/5*j**6 - 3/5*j**5 + 0*j**2 + 0*j**3. Factor r(f).
-2*f**2*(f - 1)**2*(4*f - 1)
Suppose d = -3*d. Let y(h) be the third derivative of 0*h + 1/120*h**6 + 0*h**4 - 1/30*h**5 + 1/210*h**7 - 3*h**2 + d*h**3 + 0. Factor y(g).
g**2*(g - 1)*(g + 2)
Let o be (-4)/(-6)*(-6 - -9). Suppose -v = -2 - o. Find z, given that -8*z - 26/3*z**2 - v*z**3 - 8/3 - 2/3*z**4 = 0.
-2, -1
Let o(g) be the first derivative of 2/9*g**3 - 4 + 2/3*g**2 + 0*g - 1/6*g**4. Factor o(d).
-2*d*(d - 2)*(d + 1)/3
Let t = -119 - -1191/10. Let b(y) be the second derivative of 1/6*y**3 + 1/4*y**4 - y + 0 - t*y**6 - 1/20*y**5 + 0*y**2. Factor b(p).
-p*(p - 1)*(p + 1)*(3*p + 1)
Let j(y) = -3*y**3 + 3*y**2 + 3*y + 5. Let r(z) = 4*z**3 - 4*z**2 - 4*z - 6. Let g(u) = 5*j(u) + 4*r(u). Factor g(i).
(i - 1)**2*(i + 1)
Let w(z) = z**3 + 15*z**2 + 14*z + 3. Let c be w(-14). Let s(f) be the first derivative of 1/3*f**2 - 1/9*f**c + 3 + 0*f. Let s(n) = 0. What is n?
0, 2
Suppose 14 = -3*n + 2, 35 = g - 3*n. Let f be 9/(-12) - g/(-4). Factor 25*w + 3*w**f + 48*w**2 + 42*w**3 + 21*w**4 + 6 + w**4 + 2*w - 4*w**4.
3*(w + 1)**4*(w + 2)
Let w be 0/(2 - (-2 + 3)). Let t(f) be the third derivative of 0 - 1/240*f**5 + 0*f**4 - f**2 + 0*f**3 + w*f. Let t(y) = 0. What is y?
0
Let t(u) be the third derivative of 0*u + 1/210*u**5 + 0 + 1/84*u**4 + 3*u**2 + 0*u**3. Factor t(i).
2*i*(i + 1)/7
Suppose 8*m - 3*m = 80. Factor 14*p**4 + 4*p - 4*p - 2*p - m*p**3 + 11*p**2 - 7*p**4.
p*(p - 1)**2*(7*p - 2)
Let f(r) = 0*r**3 + 4*r - 2 - 4*r + 11*r + r**3 - 8*r**2. Let v(c) = -c**3 + 9*c**2 - 12*c + 3. Let g(o) = -3*f(o) - 2*v(o). Find u, given that g(u) = 0.
0, 3
Let m(j) = -j + 4. Let f be m(0). Factor -107*x**2 - 84*x**3 + x**f - 126*x + 11*x**4 + 290*x**2 + 17 + 10.
3*(x - 3)**2*(2*x - 1)**2
Let j = 433/6 + -72. Find t, given that j*t + 0 + 1/6*t**2 = 0.
-1, 0
Let c(y) be the third derivative of -y**8/26880 - y**7/5040 - y**6/2880 - y**4/24 - 3*y**2. Let w(r) be the second derivative of c(r). Factor w(l).
-l*(l + 1)**2/4
Let q(a) be the second derivative of -a**7/1050 + a**6/600 - 3*a**2 - 2*a. Let y(x) be the first derivative of q(x). Suppose y(v) = 0. Calculate v.
0, 1
Let l(q) be the second derivative of q**4/36 + q**3/18 - 3*q. Factor l(f).
f*(f + 1)/3
Let t(s) = 3*s**4 + 3*s**3 - 9*s**2 + s + 6. Let v(i) = -3*i**4 - 3*i**3 + 9*i**2 - 6. Let f(c) = -3*t(c) - 4*v(c). Factor f(l).
3*(l - 1)**2*(l + 1)*(l + 2)
Suppose 5*v = -5, 3*l = 7*l - 2