, 1
Factor 6255/2*r**3 - 108 + 882*r + 375/2*r**5 - 1350*r**4 - 2577*r**2.
3*(r - 3)**2*(5*r - 2)**3/2
Suppose -3*f + 40 = -8*f. Let r(b) = -b. Let o(w) = 2*w**3 + 6*w. Let k(d) = f*r(d) - o(d). Factor k(v).
-2*v*(v - 1)*(v + 1)
Let d = 1 - 1. Suppose 0 = -2*h - 2*k + 6, -2*h - 4*k = -d*h - 8. Suppose 4*s**3 - 2*s**3 + 3*s - s + 4*s**h = 0. Calculate s.
-1, 0
Let a(d) be the first derivative of 5*d**6/6 - 3*d**5 - 5*d**4/4 + 55*d**3/3 - 30*d**2 + 20*d - 4. Factor a(i).
5*(i - 2)*(i - 1)**3*(i + 2)
Let q(a) be the first derivative of -a**4/16 + a**3/6 + 7*a**2/8 + a - 5. Factor q(r).
-(r - 4)*(r + 1)**2/4
Let g(a) be the first derivative of 4/11*a + 4 + 3/11*a**2 + 2/33*a**3. Factor g(i).
2*(i + 1)*(i + 2)/11
Let d be (13 + 2)/3 - 3. Factor -7*v - d*v + 0*v**3 + 7*v + 3*v**4 + 2*v**3 - 3*v**2.
v*(v - 1)*(v + 1)*(3*v + 2)
Let h = -23 - -59. Let y be 56/h*(-12)/(-14). Find x such that y + 1/3*x**2 - 4/3*x = 0.
2
Find y, given that -9*y**2 - 11*y**3 - 8 + 20*y**5 - 4*y - 32*y**4 + 49*y**2 - 5*y**3 = 0.
-1, -2/5, 1
Suppose 3*q - 2*p = -0*q + 8, -5 = -5*q - 5*p. Let z(c) = -2*c**2 + 2*c + 2. Let a(b) = -8*b**2 + 9*b + 8. Let f(d) = q*a(d) - 9*z(d). Factor f(y).
2*(y - 1)*(y + 1)
Let g(z) be the third derivative of -z**6/480 - z**5/120 - z**4/96 + 16*z**2. Suppose g(m) = 0. What is m?
-1, 0
Let h = 5 - 1. Let z = -4 + h. Suppose 3*s - 2*s + 0*s**2 + z*s**3 + 4*s**3 - 5*s**2 = 0. Calculate s.
0, 1/4, 1
Let n(m) be the second derivative of -1/24*m**3 + m + 1/40*m**5 + 0 + 1/24*m**4 - 1/120*m**6 - 1/8*m**2 - 1/168*m**7. Let n(l) = 0. What is l?
-1, 1
Factor -9/4*m**5 + 3/2*m - 9/4*m**2 - 9/4*m**3 + 0 + 21/4*m**4.
-3*m*(m - 1)**3*(3*m + 2)/4
Let f be (22/(-154))/((-2)/4). Let f*l**3 + 2/7*l**2 + 0*l + 0 = 0. What is l?
-1, 0
Let t(k) = -2*k**2 - 2*k + 1. Let w(a) = -a**2. Let z(v) = -t(v) + 3*w(v). Find d such that z(d) = 0.
1
Suppose -4*w + 3 = -7*w + 3*r, 0 = -5*w + r + 15. Factor -p**4 - w*p**4 - p**4 + 2*p**4.
-4*p**4
Let k be (12/(-10))/(3/70). Let j = 310/11 + k. What is s in 2/11 - 4/11*s + j*s**2 = 0?
1
Let 0 + 0*w - w**3 + 0*w**2 + 1/2*w**4 = 0. Calculate w.
0, 2
Let n(x) be the second derivative of x**7/63 - 4*x**6/45 + x**5/6 - x**4/9 + x. Suppose n(w) = 0. What is w?
0, 1, 2
Let j be (-1)/(-4)*2/4. Let v(g) be the first derivative of 2 + 0*g**2 - j*g**4 - 1/6*g**3 + 0*g. Let v(p) = 0. What is p?
-1, 0
Let u(g) = g**2 - 5*g - 2. Let o(a) = 4*a**2 - 26*a - 11. Let v(j) = 2*o(j) - 11*u(j). Factor v(q).
-3*q*(q - 1)
Let 1/6*v + 0 - 1/12*v**3 + 1/12*v**2 = 0. What is v?
-1, 0, 2
Let c(u) be the third derivative of u**9/302400 + u**8/50400 + u**5/10 + 6*u**2. Let b(s) be the third derivative of c(s). Find k, given that b(k) = 0.
-2, 0
Let b(n) be the first derivative of -27*n**4/4 - 7*n**3 + 30*n**2 - 12*n + 32. Factor b(h).
-3*(h - 1)*(h + 2)*(9*h - 2)
Let j(p) = p**2 + 7*p + 7. Let w be j(-6). Suppose -q = w - 3. Factor -1/2*g**3 - 1/2 + 1/2*g + 1/2*g**q.
-(g - 1)**2*(g + 1)/2
Solve 0 - 5*i**2 + i**2 + 5*i**2 - 1 = 0.
-1, 1
Let t be (6*-2)/2*(-1)/2. Let a(d) be the third derivative of 1/12*d**4 - 3*d**2 + 0 + 0*d - 1/30*d**5 + 0*d**t. Solve a(w) = 0 for w.
0, 1
Factor -4*n**3 - 12/5 + 28/5*n**2 + 4/5*n.
-4*(n - 1)**2*(5*n + 3)/5
Factor 0 - 2/5*v**3 + 4/5*v**2 + 6/5*v.
-2*v*(v - 3)*(v + 1)/5
Let h(a) be the second derivative of -a**4/24 - a**3/3 + 5*a**2/4 - 41*a. Factor h(g).
-(g - 1)*(g + 5)/2
Factor 3*g + 1/2*g**2 + 5/2.
(g + 1)*(g + 5)/2
Suppose 399*y + 2 = 400*y. Factor 8/3 + 8/3*n**4 + 40/3*n + 40/3*n**3 + 22*n**y.
2*(n + 2)**2*(2*n + 1)**2/3
Let k(f) be the second derivative of -f**5/90 + 2*f**4/27 - f**3/9 - 8*f. Factor k(j).
-2*j*(j - 3)*(j - 1)/9
Let x be (3/(-9))/(8/(-6)). Let u(h) be the first derivative of -x*h + 0*h**2 + 1/12*h**3 + 1. Let u(m) = 0. What is m?
-1, 1
Let z(k) = k**3 - 9*k**2 + 8*k + 4. Let u be z(8). Factor 4*f**3 - 3*f**2 + 12*f - 13*f**2 + 0*f + u*f.
4*f*(f - 2)**2
Let z = 8 - 8. Let y = 111/215 - 5/43. Determine j so that z*j**2 + y*j + 0 - 2/5*j**3 = 0.
-1, 0, 1
Let b(y) be the first derivative of -y**4 - 2/5*y**5 + 2*y**2 + 0*y**3 + 6 + 2*y. Factor b(x).
-2*(x - 1)*(x + 1)**3
Let t(r) = -3*r**4 - 18*r**3 - 15*r**2 + 18*r + 18. Let z(v) = v**2 - 1. Let u(c) = -t(c) - 3*z(c). Factor u(o).
3*(o - 1)*(o + 1)**2*(o + 5)
Find s, given that 8/7 - 2*s - 1/7*s**3 + s**2 = 0.
1, 2, 4
Let k = 200 - 1798/9. Let l be 12/27 - 0/(-2). Determine u so that l - k*u**2 - 2/9*u = 0.
-2, 1
Let t(q) = 19*q**4 + 46*q**3 + 38*q**2 + 28*q + 3. Let c(s) = 18*s**4 + 45*s**3 + 39*s**2 + 27*s + 3. Let a(z) = 7*c(z) - 6*t(z). Factor a(l).
3*(l + 1)**3*(4*l + 1)
Let t(h) be the first derivative of -h**7/1680 + h**5/80 + h**4/24 - h**3/3 + 1. Let j(r) be the third derivative of t(r). Factor j(c).
-(c - 2)*(c + 1)**2/2
Let c(l) be the first derivative of -l**4 - 4*l**3/3 + 8. Factor c(n).
-4*n**2*(n + 1)
Let u(y) be the third derivative of -1/8*y**4 + 1/7*y**7 + 17/60*y**6 + 1/5*y**5 + 0*y - 1/3*y**3 + 0 + 3/112*y**8 - y**2. Factor u(m).
(m + 1)**3*(3*m - 1)*(3*m + 2)
Let w(p) be the second derivative of -1/9*p**2 + 8/189*p**7 + 4/27*p**3 - 1/54*p**4 + p + 4/135*p**6 + 0 - 1/9*p**5. Factor w(o).
2*(o + 1)**2*(2*o - 1)**3/9
Let l(t) be the third derivative of -t**6/120 - t**5/15 - t**4/12 - t**3 - 2*t**2. Let c be l(-4). Factor 0*i**c - 2/3*i**3 + 0*i + 0.
-2*i**3/3
Let x be (-26)/(-22) - (1 + 0). Find j such that -4/11 + 6/11*j**2 - x*j = 0.
-2/3, 1
Let h(l) = 3*l - 9. Let i be h(4). Let u be i/(-6)*(2 - 2). Suppose 0 + 2/7*p**4 + 2/7*p**3 + 0*p**2 + u*p = 0. What is p?
-1, 0
Let h be (-4)/50*(-38)/9. Let g = 14/25 - h. Determine k, given that 0*k + g*k**2 + 0 = 0.
0
Let g(r) be the first derivative of -3/70*r**5 - 1/21*r**3 - 1/105*r**6 - 1/14*r**4 - 1 + 0*r**2 - 2*r. Let f(y) be the first derivative of g(y). Factor f(j).
-2*j*(j + 1)**3/7
Let s = 11314 + -6528180/577. Let g = s - -2314/1731. Factor g*r + 0*r**2 + 2/3 - 2/3*r**4 - 4/3*r**3.
-2*(r - 1)*(r + 1)**3/3
Let a(g) be the third derivative of -g**6/600 - 7*g**5/300 - 11*g**4/120 - g**3/6 - 59*g**2. Determine d, given that a(d) = 0.
-5, -1
Let a be 8/6 - 4/(-6). Solve -2*v**2 + 4*v + a*v**4 - 4*v = 0 for v.
-1, 0, 1
Determine t, given that -2*t**2 + t + 18*t**3 - 36*t**3 + 19*t**3 = 0.
0, 1
Let u(l) be the third derivative of l**5/210 - l**4/84 - 2*l**3/21 + 2*l**2. Factor u(x).
2*(x - 2)*(x + 1)/7
Let k(j) be the third derivative of -j**8/1512 + j**7/945 + j**6/180 - j**5/54 + j**4/54 - 28*j**2. Factor k(w).
-2*w*(w - 1)**3*(w + 2)/9
Let d = 119/620 + 1/124. What is a in 0*a - d*a**5 + 0*a**2 + 1/5*a**3 + 0*a**4 + 0 = 0?
-1, 0, 1
Let p(v) = -5*v**2 - 3*v - 2. Let a = -117 - -65. Let l be a/14 - 10/35. Let k(u) = -6*u**2 - 4*u - 3. Let z(i) = l*k(i) + 5*p(i). Factor z(d).
-(d - 2)*(d + 1)
Let z(g) be the first derivative of -7*g**6/3 - 32*g**5/5 - 11*g**4/2 - 4*g**3/3 + 6. Suppose z(r) = 0. Calculate r.
-1, -2/7, 0
Let q = 2237/7 - 319. Let m(z) be the first derivative of -5/7*z**2 + q*z - 32/21*z**3 - 9/14*z**4 + 2. Factor m(t).
-2*(t + 1)**2*(9*t - 2)/7
Let w(u) be the first derivative of u**7/350 + 7*u**6/600 - u**5/100 - 7*u**3/3 + 5. Let h(m) be the third derivative of w(m). Factor h(q).
3*q*(q + 2)*(4*q - 1)/5
Let f be (24/16)/(6/8). Factor -4*d**2 - f*d**3 + 0*d**2 + d**4 + 5*d**2.
d**2*(d - 1)**2
Suppose 0 = -7*v + 4*v + 24. Let u be 106/22 - v/(-44). Solve -2/3*t**u + 8/3*t**4 + 8/3*t**2 - 4*t**3 - 2/3*t + 0 = 0.
0, 1
Let d(l) be the third derivative of 3087*l**6/80 - 441*l**5/20 + 21*l**4/4 - 2*l**3/3 + l**2. Solve d(s) = 0.
2/21
Let b(r) be the first derivative of r**8/336 + r**7/42 + 3*r**6/40 + 7*r**5/60 + r**4/12 - r**2 + 6. Let p(u) be the second derivative of b(u). Factor p(j).
j*(j + 1)**3*(j + 2)
Suppose 4*v = -t + 5 + 9, 5*t - 3*v = 1. What is h in -1/2*h**4 + 0*h**3 + 0*h + 0*h**t + 1/2*h**5 + 0 = 0?
0, 1
Let t(u) = u**3 - 2*u**2 - 8*u + 6. Let m be t(5). Find n such that -9*n - 3*n**3 + 17*n**2 + 2 - m*n**2 - 6*n**3 + 4 = 0.
-2, -1, 1/3
Let o(t) be the third derivative of 1/120*t**5 + 0*t - 1/240*t**6 + 0 + 1/24*t**4 - t**2 + 0*t**3. Factor o(a).
-a*(a - 2)*(a + 1)/2
Let b(j) be the first derivative of -3 + 1/8*j**4 + 1/20*j**5 + 1/12*j**3 + 0*j**2 + 0*j. Factor b(i).
i**2*(i + 1)**2/4
Let a = -295 - -297. Determine l, given that -l**a + 3/2*l - 1/2 = 0.
1/2, 1
L