Let k be 68/(-102)*(0 - 3). Factor 0*s + 2/3*s**5 + 2/3*s**2 + 0 + 2*s**4 + k*s**3.
2*s**2*(s + 1)**3/3
Let k = 15742/105 - 747/5. Let a = k + 1/7. Factor -a*y**2 + 0 + 4/9*y.
-2*y*(3*y - 2)/9
Let h = -82/15 - -20/3. Factor -4/5 + 0*v**2 - 2/5*v**3 + h*v.
-2*(v - 1)**2*(v + 2)/5
What is j in -192/5*j - 4/5*j**3 - 256/5 - 48/5*j**2 = 0?
-4
Let b(p) be the third derivative of p**7/945 - p**6/108 + 7*p**5/270 - p**4/36 + 7*p**2. Determine r, given that b(r) = 0.
0, 1, 3
Let x be (-50)/2*(-14)/(-35). Let w be x/(-15) + 256/30. Solve 26/5*s + w*s**3 + 54/5*s**2 + 4/5 + 14/5*s**4 = 0.
-1, -2/7
Suppose 7*c + 110 - 131 = 0. Find o, given that 6/11*o**2 + 2/11*o**c + 6/11*o + 2/11 = 0.
-1
Let x(f) be the second derivative of f + 2/5*f**2 + 1/15*f**3 - 1/3*f**4 + 2/25*f**5 + 8/75*f**6 - 1/21*f**7 + 0. Determine g, given that x(g) = 0.
-1, -2/5, 1
Let u(l) be the second derivative of 0 + 0*l**3 + 5*l + 7/135*l**6 + 4/189*l**7 + 1/45*l**5 - 1/54*l**4 + 0*l**2. Let u(o) = 0. Calculate o.
-1, 0, 1/4
Determine t, given that 0 - 8/5*t + 4/5*t**2 = 0.
0, 2
Let z be 228/350 + (-74)/925. Factor -23/7*u**2 - z - 20/7*u - u**3.
-(u + 1)*(u + 2)*(7*u + 2)/7
Let u be (3/21)/(12/14). Let h(z) be the first derivative of 1/9*z**3 + 0*z + 2 + u*z**2. Find w, given that h(w) = 0.
-1, 0
Let q(a) be the first derivative of a**8/336 - a**7/105 + a**5/30 - a**4/24 + a**2 - 3. Let y(o) be the second derivative of q(o). Factor y(h).
h*(h - 1)**3*(h + 1)
What is i in -18/5*i + 0 - 3/5*i**3 - 21/5*i**2 = 0?
-6, -1, 0
Let g be 0 - ((-6)/(-4) - (-3 + 5)). Let g - 1/2*t**4 + 0*t**2 + t**3 - t = 0. What is t?
-1, 1
Let l(s) be the third derivative of s**9/60480 + s**8/26880 + s**4/24 + 2*s**2. Let g(i) be the second derivative of l(i). Factor g(q).
q**3*(q + 1)/4
Let m be 90/24 + 2/8. Solve -w**4 + 4 - 6 - 4*w - 6*w**2 - m*w**3 + 1 = 0 for w.
-1
Let v(w) = 10*w**4 + 15*w**3 - 7*w**2 - 15*w - 1. Let r(x) = -x**4 + x**2 + 1. Let f(q) = -2*r(q) + v(q). Factor f(u).
3*(u - 1)*(u + 1)**2*(4*u + 1)
Find m, given that -32/5 - 2/5*m**2 - 16/5*m = 0.
-4
Let v(b) = b**2 + b - 2. Let w(a) = -10 - 4 + 9*a + 9*a**2 - 7. Let f(x) = 21*v(x) - 2*w(x). Let f(m) = 0. What is m?
-1, 0
Let s(p) = 3*p + p + 2*p**2 - 5 - p**2. Let q be s(-5). Find m such that -5*m**3 - m**5 - 2/3*m + q + 3*m**2 + 11/3*m**4 = 0.
0, 2/3, 1
Let w = 149/33 + 130/11. Solve -7*t**3 + w*t**4 - 8*t**2 - 4/3*t + 0 = 0 for t.
-2/7, 0, 1
Let l(o) be the third derivative of o**8/672 - o**7/70 + 13*o**6/240 - o**5/10 + o**4/12 - 42*o**2. Find u, given that l(u) = 0.
0, 1, 2
Let k(m) be the third derivative of -m**6/120 - m**5/20 - m**4/12 + 31*m**2. Solve k(f) = 0 for f.
-2, -1, 0
Suppose 5*t - 3*n - 40 = 35, -3*t = -5*n - 61. Let a = t - 12. Solve 2/5*c**2 + a*c - 2/5 = 0 for c.
-1, 1
Let v be (12/(-6) - -8) + -4. Find l, given that 8/3*l - v - 2/3*l**2 = 0.
1, 3
Let y = -47 - -47. Let q(b) be the third derivative of 0 - 1/240*b**5 + 1/24*b**4 - 1/6*b**3 + y*b + b**2. What is t in q(t) = 0?
2
Let r(l) = l**2 + 1. Let s be r(-1). Let x be (-2)/(s/1)*-4. Factor 2*h**5 + 4*h**2 + 2*h**3 - x*h**2 + 4*h**4.
2*h**3*(h + 1)**2
Let r(d) = d + 4. Let q be r(-4). Factor 1/4*m**2 + q*m + 0.
m**2/4
Suppose -20*h + 25*h - 15 = 0. Find t such that -3/2*t**4 - t - 4*t**h + 0 - 7/2*t**2 = 0.
-1, -2/3, 0
Let y(c) be the second derivative of -2/9*c**2 + 1/27*c**3 + 0 + 3*c - 1/90*c**5 + 1/27*c**4. Suppose y(v) = 0. What is v?
-1, 1, 2
Let j(z) = 9*z - 51. Let a be j(6). Let d(p) be the first derivative of 1 - 1/8*p**4 - 1/3*p**a + 0*p**2 + 0*p. Solve d(o) = 0.
-2, 0
Factor 0*g - 2*g**3 - 2/3*g**5 + 0 + 2/3*g**2 + 2*g**4.
-2*g**2*(g - 1)**3/3
Let t(v) be the first derivative of -6*v**5/25 - v**4/5 + 2*v**3/15 - 6. Solve t(x) = 0 for x.
-1, 0, 1/3
Let f(w) be the third derivative of -w**8/84 + 2*w**6/15 - 2*w**5/15 - w**4/2 + 4*w**3/3 + 6*w**2. Factor f(o).
-4*(o - 1)**3*(o + 1)*(o + 2)
Let v(a) be the third derivative of a**10/100800 - a**9/40320 + a**5/15 - 2*a**2. Let z(k) be the third derivative of v(k). Factor z(m).
3*m**3*(m - 1)/2
Let x(g) = 5*g**4 - g**3 - g**2 + g + 4. Let r(j) = j**4 + 1. Let k(f) = -4*r(f) + x(f). Determine z, given that k(z) = 0.
-1, 0, 1
Let x(z) = z**3 - 6*z**2 - 5*z + 8. Let c(u) = -6*u**3 + 42*u**2 + 36*u - 57. Let d(q) = -2*c(q) - 15*x(q). Determine y, given that d(y) = 0.
-1, 1, 2
Suppose 3*c - 705 = -0*c. Let t be 3/(-5) + c/100. Factor 23/4*p**3 - 1/2 - 27/4*p**2 + 13/4*p - t*p**4.
-(p - 1)**3*(7*p - 2)/4
Suppose 3*l = v - 18, -2*l = 2*v - 4*l - 48. Let u = 38 - v. Factor -5*j - 3*j**2 - 2 + u*j**2 + 5*j**3 + 6*j.
(j + 1)**2*(5*j - 2)
Let f(s) = 2*s**2 - 14*s + 3. Let t(v) = 6*v**2 - 42*v + 8. Let z(p) = -8*f(p) + 3*t(p). Suppose z(i) = 0. What is i?
0, 7
Let o(u) be the first derivative of 5*u**4/16 - 5*u**3/3 - 7. Suppose o(t) = 0. Calculate t.
0, 4
Suppose -18 = -26*h + 20*h. Let 0*m**h + 0 + 3/5*m**2 + 0*m - 3/5*m**4 = 0. Calculate m.
-1, 0, 1
Let u(m) be the third derivative of -m**7/630 + m**6/45 - 4*m**5/45 + 64*m**2. Factor u(f).
-f**2*(f - 4)**2/3
Let s(o) be the first derivative of o**6/2160 - o**5/720 - 2*o**3 + 5. Let l(k) be the third derivative of s(k). Determine b so that l(b) = 0.
0, 1
Let d be ((-2)/(-3))/((-105)/(-49) + -2). Factor -8/3 + d*u - u**2.
-(u - 4)*(3*u - 2)/3
Let t = -14 - -15. Let a(y) be the first derivative of -1/2*y**4 - 5*y**2 + 4*y + t + 8/3*y**3. Suppose a(w) = 0. What is w?
1, 2
Let s(y) be the third derivative of -y**2 + 1/30*y**5 - 2/3*y**3 + 0 + 0*y + 1/12*y**4. Let s(z) = 0. What is z?
-2, 1
Let p(q) be the third derivative of q**8/420 - 4*q**7/525 - q**6/600 + 2*q**5/75 - q**4/40 - 5*q**2. Suppose p(b) = 0. What is b?
-1, 0, 1/2, 1, 3/2
Factor -4*t**2 + 8*t**2 - t**3 - t**3 - 2*t**2.
-2*t**2*(t - 1)
Let u be (-242)/(-90) - 567/315. Determine h so that 8/9*h**3 + 0*h + 0 - 2/9*h**4 - u*h**2 = 0.
0, 2
Factor 0*a + 0 + 2/19*a**3 + 4/19*a**2.
2*a**2*(a + 2)/19
Suppose 2*y = 2*c - 6 - 6, 3*c + 4*y = -3. Let 1/2*f**5 + 1/2*f + f**2 - f**c - 1/2*f**4 - 1/2 = 0. What is f?
-1, 1
Suppose -3*x - 5*z + 0 + 3 = 0, 39 = 4*x - 5*z. Factor 3*t**3 + 0 - 1 - 2 - 9*t**2 + x*t + 3*t.
3*(t - 1)**3
Let k(c) be the second derivative of -c**5/80 - c**4/24 + c**3/3 - 23*c. Factor k(d).
-d*(d - 2)*(d + 4)/4
Let q be ((-4)/(-40))/((-3)/(-1914)). Let z = -63 + q. Determine p, given that z - 6/5*p + 2/5*p**2 = 0.
1, 2
Let j be 0 - (2 + -4 + 2). Factor j*v**2 - 15*v - 5*v**2 + 8*v - 2.
-(v + 1)*(5*v + 2)
Let p be ((-60)/(-50))/((-2)/5). Let c(j) = 3*j**2 - 3*j - 7. Let g(a) = -a**2 + a - 1 + 0 + 4. Let m(x) = p*c(x) - 7*g(x). Factor m(f).
-2*f*(f - 1)
Let x be (-3)/(-2*(-1)/(-4)). Let q be (x/(-7))/(2/(-14)). Factor -q*f**2 - 3 + 2*f + 3.
-2*f*(3*f - 1)
Suppose -20*i = -3*i + 6*i. Factor 0 - 2/9*y**3 + 2/9*y**5 + 2/9*y**4 + i*y - 2/9*y**2.
2*y**2*(y - 1)*(y + 1)**2/9
Let q = 1/862 - -2977/34480. Let c(n) be the second derivative of -1/3*n**4 + 0 + 0*n**2 - 1/6*n**3 - q*n**5 + n. Factor c(w).
-w*(w + 2)*(7*w + 2)/4
Let y(v) = -2*v**3 - 7*v**2 + 2*v + 7. Let b(d) = -d**2 + 1. Let q(r) = -6*b(r) + 2*y(r). Suppose q(w) = 0. What is w?
-2, -1, 1
Let v(q) = 5*q**2 + 6*q + 3. Let k(m) = 21*m**2 + 24*m + 12. Let i(y) = -2*k(y) + 9*v(y). Suppose i(r) = 0. What is r?
-1
Let r(w) = -w**2 - 17*w + 3. Let x(j) = -j**2 - 9*j + 1. Let c(z) = 3*r(z) - 5*x(z). Factor c(b).
2*(b - 2)*(b - 1)
Let u be 1*4/2 + 1. Factor -3*d**2 - d**4 + 3*d**u + 3*d**2 - 4*d.
-d*(d - 2)**2*(d + 1)
Let c be (75 + 3)/(6/8). Find m, given that 3*m + c*m**2 + 13*m - 98*m**4 - 25*m**3 + 165*m**3 = 0.
-2/7, 0, 2
Factor 3*f**2 - 2*f**3 + 6*f - 6*f**2 + f**3 - 2*f**3.
-3*f*(f - 1)*(f + 2)
Let k(b) be the first derivative of -3/5*b**2 + 3/10*b**4 - 2/15*b**3 + 3 + 2/5*b. Find d, given that k(d) = 0.
-1, 1/3, 1
Let c(h) be the second derivative of 0*h**2 + 1/27*h**3 + 0 - 1/18*h**4 - 1/135*h**6 + 3*h + 1/30*h**5. Factor c(t).
-2*t*(t - 1)**3/9
Let g(z) be the second derivative of -2/7*z**3 - 3/35*z**5 - 1/70*z**6 + 0 - 3/14*z**2 - 3/14*z**4 - 10*z. Solve g(n) = 0 for n.
-1
Let g(a) be the second derivative of -2*a**6/15 + 3*a**5/5 - a**4 + 2*a**3/3 - 8*a. Solve g(s) = 0.
0, 1
Let i(v) = -v**3 + 10*v**2 + 15*v - 4. Let x(g) = -5*g**3 + 60*g**2 + 90*g - 25. Let a(j) = 25*i(j) - 4*x(j). Find p, given that a(p) = 0.
-1, 0, 3
Let l be (-6 - -2)*((-