t m be ((-4)/(-24))/((-3)/(-9)). Solve m*x**2 + 1/2 + x = 0 for x.
-1
Solve 18*q - 9*q**4 - 15*q**4 + 3*q**2 + 13*q**2 + 3 - 18*q**3 + 5*q**2 = 0 for q.
-1, -1/2, -1/4, 1
Let c = 666/13 - 4142/91. Suppose 62/7*r**2 + 30/7*r**3 + c*r + 8/7 = 0. Calculate r.
-1, -2/3, -2/5
Let r(u) be the first derivative of -u**6/18 + u**5/3 - u**4/2 - 4*u**3/9 + 4*u**2/3 + 11. Factor r(o).
-o*(o - 2)**3*(o + 1)/3
Let r(g) be the first derivative of -7*g**6/720 + g**5/48 + g**4/24 - g**3 - 1. Let z(t) be the third derivative of r(t). Factor z(j).
-(j - 1)*(7*j + 2)/2
Let n(r) be the first derivative of r**5/7 + 3*r**4/28 - 2*r**3/21 - 12. Find j such that n(j) = 0.
-1, 0, 2/5
Factor -2*k - 11*k**2 + 7*k**2 - 2*k.
-4*k*(k + 1)
Suppose 4*z + 3 = -4*c + 35, 4*c = 4*z - 48. Suppose -z*f + 9*f = -1. What is a in 0*a - 3/4*a**2 - 1/4*a**3 + f = 0?
-2, 1
Let w(a) be the third derivative of -a**8/504 - 4*a**7/315 - a**6/45 - 28*a**2. Factor w(s).
-2*s**3*(s + 2)**2/3
Solve 24*d**2 - 44/7*d**3 + 160/7 - 272/7*d + 4/7*d**4 = 0.
2, 5
Suppose -2 = 2*x - 4. Let b be (x/(-4))/((-7)/140). Let 0*w + 0 + 18/5*w**4 + 8/5*w**b + 2/5*w**2 + 12/5*w**3 = 0. What is w?
-1, -1/4, 0
Let g be 25*-1*(-4 - -3). Factor -2*a**4 - 25*a**3 - a**4 + g*a**3 + 3*a**2.
-3*a**2*(a - 1)*(a + 1)
Let r = 25/84 - 1/21. Factor 1/2*a - r*a**2 + 0.
-a*(a - 2)/4
Let a(d) be the third derivative of 0*d**3 + 0 - 1/40*d**4 - 1/100*d**5 + d**2 + 0*d. Determine y, given that a(y) = 0.
-1, 0
Suppose -5*c**2 - c**3 + 4*c - c**2 + 2*c**2 + c**2 = 0. Calculate c.
-4, 0, 1
Let u(p) be the third derivative of p**5/30 + 11*p**4/6 + 121*p**3/3 + 34*p**2. Factor u(n).
2*(n + 11)**2
Let h(z) be the first derivative of z**6/8 - 3*z**5/20 - 3*z**4/8 - 23. Let h(t) = 0. Calculate t.
-1, 0, 2
Let b(t) = 9*t**2 - 8*t - 2. Let d(l) = 5*l**2 - 2*l**2 - 2 + 6*l**2 - 2*l - 5*l. Let j(r) = -4*b(r) + 5*d(r). Factor j(p).
(3*p - 2)*(3*p + 1)
Factor f - f**2 - 2*f**3 - 2 + 2*f + 3*f**2 - f.
-2*(f - 1)**2*(f + 1)
Suppose 0*j + 45 = 3*j. Let v be 3/10*20/j. Factor -4/5*q**2 - v*q - 2/5*q**3 + 0.
-2*q*(q + 1)**2/5
Let x be (4/(-8))/(1/8). Let d = 6 + x. Suppose -d*m + 4/7 - 10/7*m**3 + 2/7*m**4 + 18/7*m**2 = 0. What is m?
1, 2
Suppose 0 = -5*b + 24 - 4. Factor -14*g**b - 7*g**4 + 9*g**5 - 3*g**2 + 15*g**3 - 3 + 3.
3*g**2*(g - 1)**2*(3*g - 1)
Determine y so that -3*y**3 + 6*y**4 - 3*y**2 + 3*y - 3*y**4 + 0*y + 0*y = 0.
-1, 0, 1
Let a(p) be the second derivative of p**7/10080 + p**6/1440 - p**5/160 - p**4/4 - 6*p. Let u(z) be the third derivative of a(z). Factor u(x).
(x - 1)*(x + 3)/4
Suppose 3/2*a**3 + 3 - 3/2*a - 3*a**2 = 0. What is a?
-1, 1, 2
Factor -3*u**5 + 8*u**4 + 4*u + 2*u**5 - 8*u**2 + 0*u - 3*u**5.
-4*u*(u - 1)**3*(u + 1)
Suppose 4*f = -c + 4*c + 42, -2*f = c - 26. Factor 8*q**4 + 8*q**2 - 8*q**3 + 8*q**4 - 4*q**5 - f*q**3.
-4*q**2*(q - 2)*(q - 1)**2
Let k(u) be the first derivative of -u**6/8 - 17*u**5/20 - 17*u**4/8 - 7*u**3/3 - u**2 + 2. What is h in k(h) = 0?
-2, -1, -2/3, 0
Let t(k) be the third derivative of k**9/45360 - k**8/5040 + k**7/1512 - k**6/1080 - k**4/6 - 4*k**2. Let l(f) be the second derivative of t(f). Factor l(o).
o*(o - 2)*(o - 1)**2/3
Let j be (-2 + 9/5)/(2/(-5)). Factor j + 1/2*m - 1/2*m**2 - 1/2*m**3.
-(m - 1)*(m + 1)**2/2
Let j(q) = -q**3 + 2*q**2 + 4*q - 1. Let k = 7 - 4. Let z be j(k). What is a in 4/5 + 2/5*a**z + 6/5*a = 0?
-2, -1
Suppose 4 = 5*p - 11. Factor 3*o**3 - 2*o**p - o - o**5 - 2*o**4 + 2*o**2 + o.
-o**2*(o - 1)*(o + 1)*(o + 2)
Suppose 0 + 1/6*a**5 - 1/6*a**3 - 1/6*a**2 + 0*a + 1/6*a**4 = 0. Calculate a.
-1, 0, 1
Let x(d) = -6*d**2 - 14*d - 6. Let b(l) = 31*l**2 + 71*l + 29. Let g(k) = 2*b(k) + 11*x(k). Factor g(j).
-4*(j + 1)*(j + 2)
Find s, given that 0*s + 1/3*s**5 + 0*s**3 + 0*s**2 + 0*s**4 + 0 = 0.
0
Let s(z) be the second derivative of z**5/50 + 2*z**4/15 + z**3/3 + 2*z**2/5 + 5*z. Determine q, given that s(q) = 0.
-2, -1
Let r be (-396)/(-546) - (-4)/(-26). Let y(a) be the first derivative of -r*a + 2 - 3/7*a**2 + 10/21*a**3. Determine v so that y(v) = 0.
-2/5, 1
Let d(a) = a**2 + a + 1. Let c(h) = 3*h**2 + 4*h - 1. Let y(k) = -c(k) + 2*d(k). Factor y(i).
-(i - 1)*(i + 3)
Let o be ((-267)/(-105) - 1) + (-12)/30. Factor o + 2/7*s**2 + 8/7*s.
2*(s + 2)**2/7
Factor -4/5 + 2*a**3 - 2/5*a**4 - 18/5*a**2 + 14/5*a.
-2*(a - 2)*(a - 1)**3/5
Let r(y) = y**5 + y**4 + y**3 + y**2 + y. Let a(s) = -5*s**5 + 11*s**4 - 21*s**3 + 9*s**2 - 4*s. Let h(x) = -a(x) - 2*r(x). Factor h(n).
n*(n - 2)*(n - 1)**2*(3*n - 1)
Let z(q) be the third derivative of q**5/105 + 4*q**4/21 + 2*q**3/3 + 48*q**2. Factor z(u).
4*(u + 1)*(u + 7)/7
Let c = 185 - 3884/21. Let a(h) be the third derivative of c*h**4 + 0 + 1/210*h**5 + 2*h**2 + 0*h + 4/21*h**3. Factor a(x).
2*(x + 2)**2/7
Let m = 1561/4701 + 2/1567. Determine v, given that -1/3*v**5 + 2/3*v**3 - 1/3*v + 1/3 - 2/3*v**2 + m*v**4 = 0.
-1, 1
Let s = -11 - -11. Let h(n) be the first derivative of 2/15*n**3 - 1 - 1/5*n**2 + s*n. Find v such that h(v) = 0.
0, 1
Let c(f) = -f**3 - 4*f**2. Let o(d) be the second derivative of d**5/20 - 7*d. Suppose 4 + 11 = 5*z + 5*m, -z = -4*m + 7. Let p(h) = z*o(h) - c(h). Factor p(i).
2*i**2*(i + 2)
Let o = -16/7 - -87/35. Find q, given that 2/5 - 3/5*q + o*q**2 = 0.
1, 2
Let v = -29/10 - -17/5. Factor 0 - v*i**3 - i**2 + 3/2*i.
-i*(i - 1)*(i + 3)/2
Let j(n) = -33*n - 198. Let o be j(-6). Factor 24*q**3 + o*q + 14/3*q**5 + 0 - 16/3*q**2 - 20*q**4.
2*q**2*(q - 2)**2*(7*q - 2)/3
Let w(y) be the first derivative of -4*y**5/5 - 4*y**4 + 32*y**2 + 64*y - 1. Factor w(k).
-4*(k - 2)*(k + 2)**3
Let y be 9/(243/6)*(24 + -3). Let t(v) be the first derivative of 2*v**2 + 0*v - 4 - y*v**3. Let t(o) = 0. What is o?
0, 2/7
Let m(u) = -u**4 + u**3 + u + 1. Let h(p) = -14*p**4 - 11*p**3 + 9*p + 4. Let v(o) = h(o) - 4*m(o). Factor v(j).
-5*j*(j + 1)**2*(2*j - 1)
Let y be -7 + (3 - 3) + 2. Let z = y - -7. Factor l - 2*l + 0*l**2 + l**z + 0*l.
l*(l - 1)
Find t such that -58 + 119 - 3*t**2 - 79 + 21*t = 0.
1, 6
Let u(w) be the third derivative of 0*w**3 + w**2 - 1/240*w**6 + 0*w + 0 + 1/40*w**5 - 1/24*w**4. Determine q, given that u(q) = 0.
0, 1, 2
Suppose p + 8 = -5*z, -5*z - 1 = 4*p - 2*p. Let f(h) = -3*h**2 + 5*h - 12. Let q(t) = -t**2 + 2*t - 4. Let x(i) = p*q(i) - 2*f(i). Factor x(a).
-(a - 2)**2
Factor 13 - i**3 - i**2 - 13.
-i**2*(i + 1)
Let x(a) = 8*a**2 + 0*a - a + 4*a**3 + 10 - 5*a**3. Let d be x(8). What is z in -1 + 2*z**3 + 1 + 8*z**d + 8*z = 0?
-2, 0
Let r(y) be the second derivative of y**7/2520 - y**5/120 + y**4/12 + 3*y. Let h(t) be the third derivative of r(t). What is w in h(w) = 0?
-1, 1
Let u(y) be the second derivative of 2/15*y**5 - 1/3*y**4 + 0 + 0*y**3 - 1/60*y**6 + 3/2*y**2 + 3*y. Let n(c) be the first derivative of u(c). Factor n(k).
-2*k*(k - 2)**2
Let r(p) be the first derivative of -p**6/180 - p**5/20 - p**4/6 + 5*p**3/3 + 3. Let h(q) be the third derivative of r(q). Factor h(f).
-2*(f + 1)*(f + 2)
Let j(i) = i**3 + 3*i. Let z(x) = -7 - 6*x**3 - 16*x + 7. Let m(p) = -11*j(p) - 2*z(p). Find v such that m(v) = 0.
-1, 0, 1
Let q be (1/(-2))/((-7 - -2)/15). Suppose q*y**2 + 0*y + 0 = 0. What is y?
0
Let c(r) = 2*r + 14. Let f be c(-5). Let y(b) be the second derivative of 1/90*b**6 + 0*b**3 + 0 + 0*b**2 - 2*b + 0*b**5 - 1/36*b**f. Factor y(h).
h**2*(h - 1)*(h + 1)/3
Let o(l) = -l**2 - l + 7. Let f be o(0). Suppose f + 7 - 12 + y - y**2 = 0. Calculate y.
-1, 2
Let 21/4 + 111/8*b + 15/8*b**2 = 0. What is b?
-7, -2/5
Suppose -3*v = 2*m - 32, 4*m + 3*v - 46 - 6 = 0. Let r = -5 + m. Find c, given that -1/3*c**4 + 0*c**3 + 0 + 0*c + 1/3*c**r + 0*c**2 = 0.
0, 1
Let o be 12/40 - 3/(-15). Factor -1/2 - o*k**2 + k.
-(k - 1)**2/2
Let u(q) = -8*q**5 - 6*q**4 - 8*q**2 - 6*q. Let s(w) = 7*w**2 + 2 + 7*w**5 + 5*w + 3*w**4 - 2 + 3*w**4 + w**3. Let r(y) = -6*s(y) - 5*u(y). Factor r(n).
-2*n**2*(n + 1)**3
Let i be (1*(-16)/(-108))/((-5)/(-30)). Solve 10/9*f - i*f**2 - 2/9 = 0.
1/4, 1
Suppose 18 = h - 3*h. Let s = -7 - h. Factor -s*y**5 - 9*y**4 + y**5 + y**2 - 4*y**2 - 9*y**3 - 2*y**5.
-3*y**2*(y + 1)**3
Suppose -4*a + 10*a = 0. Let h(j) be the first derivative of a*j + 1/3*j**3 - 1 + 1/2*j**2. What is g in h(g) = 0?
-1, 0
Let s(h) be the third derivative of 0*h + 1/20*h**5 + 0 - h**2 + 1/8*h**4 - h**3. Suppose s(z) = 0. Calculate z.
-2, 1