se 5*y = 2*y + 6. Let s be (-56)/42 + 5/(5/2). Factor s*n**y + 0 + 2/3*n.
2*n*(n + 1)/3
Let i(x) = -x**5 - x**4 + x**3 - 1. Let h(p) = -3*p**5 - 4*p**4 + 2*p**2 + 3*p - 6. Let m(s) = 3*h(s) - 12*i(s). Factor m(w).
3*(w - 1)**3*(w + 1)*(w + 2)
Let g(y) be the first derivative of -4*y**5/35 + 4*y**3/21 - 22. Let g(u) = 0. What is u?
-1, 0, 1
Let a = 61/18 + -26/9. Solve -a*b**2 + 1 - 1/2*b = 0 for b.
-2, 1
Let h be 132/(-32) + 4 - (-20)/32. Determine p so that -p - h - 1/2*p**2 = 0.
-1
Factor 0 + 8/5*w**2 - 4*w**3 + 0*w - 28/5*w**4.
-4*w**2*(w + 1)*(7*w - 2)/5
Let t(v) be the third derivative of v**5/300 + v**4/120 + 29*v**2. Determine w, given that t(w) = 0.
-1, 0
Let f(c) be the second derivative of 0 + 1/4*c**4 - 3/140*c**5 + 0*c**3 + 1/98*c**7 - 6/7*c**2 - 3/70*c**6 + 8*c. Let f(t) = 0. Calculate t.
-1, 1, 2
Suppose 0 = -k + 2*k - 2. Let z be k/(-6)*(-4 + -5). Factor -21*i + 18*i + 9*i**2 + 1 - 1 - 9*i**4 + 3*i**z.
-3*i*(i - 1)*(i + 1)*(3*i - 1)
Let w be (1/(-2)*4)/2. Let q = 3 + w. Solve -q*h**2 - 5/2*h - 1/2 = 0.
-1, -1/4
Let y(c) = c**2 - 10*c + 2. Let d be y(10). Factor t**4 + d*t**3 + 2*t**2 + t**5 - 8 - 4*t**4 - 3*t + 9.
(t - 1)**4*(t + 1)
Suppose 0 = -d - 4 - 0, -5*w + 2*d = 142. Let t = -27 - w. Factor -2/3*v + 2/3*v**t + 2/3 - 2/3*v**2.
2*(v - 1)**2*(v + 1)/3
Let t be 1/(40 - 4)*2. Let q(a) be the first derivative of 0*a**3 - t*a**4 - 1 + 0*a + 0*a**2 - 2/45*a**5. Suppose q(c) = 0. What is c?
-1, 0
Suppose -4/5 + 2/5*j**2 + 2/5*j = 0. What is j?
-2, 1
Let f = 107 + -213/2. Let w(x) be the first derivative of -1/2*x**2 + 1 + f*x**3 + 0*x. Find b such that w(b) = 0.
0, 2/3
Let w be ((-4)/5)/(2/(-5)). Find f, given that -f**3 - w - 4 + f**3 + 3*f**3 - 9*f = 0.
-1, 2
Let h(u) be the second derivative of -u**5/40 - u**4/12 + u**3/4 + 30*u - 1. Determine c, given that h(c) = 0.
-3, 0, 1
Let z(w) be the third derivative of w**8/1344 + w**7/420 - w**6/160 - 4*w**2. Suppose z(x) = 0. What is x?
-3, 0, 1
Let a(b) = -17*b**2 - 8*b + 45. Let v(s) = 4*s**2 + 2*s - 11. Let w(p) = 6*a(p) + 26*v(p). Find i such that w(i) = 0.
-4, 2
Suppose 4 = -2*o - 8. Let y be ((-9)/(-6))/(o/(-8)). Solve 1/2*f + y*f**2 + 0 = 0.
-1/4, 0
Let x(t) be the second derivative of -t**7/28 - t**6/20 + 3*t**5/40 + t**4/8 + 2*t. Let x(c) = 0. Calculate c.
-1, 0, 1
Let j be -3 + (-3 - -2)*-3. Factor 11 - 2 + m**2 + j*m**2 - 6*m.
(m - 3)**2
Factor 51*b**3 - 19*b**4 - 18*b**2 - 6*b**2 - 11*b**4 + 3*b**5.
3*b**2*(b - 8)*(b - 1)**2
Suppose -4*q + 6 = -q. Let g(a) be the second derivative of 1/6*a**4 + a + 0 - 8/15*a**3 - 4/5*a**q. Suppose g(i) = 0. What is i?
-2/5, 2
Suppose 2/3*v**2 - 2/3*v**4 + 2*v**3 - 2*v + 0 = 0. What is v?
-1, 0, 1, 3
Let v(q) be the second derivative of -q**5/30 + q**3/9 - 3*q. Factor v(x).
-2*x*(x - 1)*(x + 1)/3
Let s(d) be the second derivative of -d**7/14 - 7*d. Factor s(t).
-3*t**5
Let t = -34 - -103/3. Suppose 0 - 1/3*j - 2/3*j**2 - t*j**3 = 0. Calculate j.
-1, 0
Let b(j) be the second derivative of -j**5/5 - j**4/3 + 5*j. Suppose b(t) = 0. What is t?
-1, 0
Find t, given that 3*t**4 - 3*t**2 - 3*t**5 + 3*t**2 + 2*t**2 - 5*t**2 - 18*t + 21*t**3 = 0.
-2, -1, 0, 1, 3
Let p(z) = 1 - z - 3 - 3 + 4*z**2. Let t(u) = 3*u**2 - u - 4. Let j(w) = -4*p(w) + 5*t(w). Factor j(a).
-a*(a + 1)
What is t in -2*t**2 - 54 + 22 + 10*t + 24 = 0?
1, 4
Let v(b) = -b**3 - b**2 + 40*b + 12. Let y be v(6). Suppose y + 1/2*g**3 + 1/2*g**2 - g = 0. What is g?
-2, 0, 1
Let x(a) be the first derivative of -16/9*a**3 + 1/3*a**2 + 0*a - 2 + 11/3*a**4 + a**6 - 16/5*a**5. Factor x(s).
2*s*(s - 1)**2*(3*s - 1)**2/3
Let b(t) be the third derivative of -t**6/1440 - t**5/480 + t**4/48 - t**3/6 + 4*t**2. Let q(m) be the first derivative of b(m). Solve q(a) = 0.
-2, 1
Let m(r) = -8*r**3 + 12*r**2 - 12*r + 8. Let h(k) = k**3 - k. Let q(g) = -6*h(g) - m(g). Factor q(w).
2*(w - 4)*(w - 1)**2
Let g(v) be the second derivative of -v**9/45360 + v**7/7560 + v**4/6 - 3*v. Let i(j) be the third derivative of g(j). Factor i(u).
-u**2*(u - 1)*(u + 1)/3
Let f = 16 + -16. Let p(z) be the third derivative of -2*z**2 + 0 + 0*z + 0*z**5 + f*z**3 + 1/60*z**6 - 1/336*z**8 - 1/24*z**4 + 0*z**7. Factor p(n).
-n*(n - 1)**2*(n + 1)**2
Let p(b) = -2*b**2 - b - 1. Let f be p(-1). Let i = f - -7. Let u(h) = -h + 1. Let j(w) = 98*w**2 - 51*w + 3. Let g(r) = i*u(r) + j(r). Factor g(x).
2*(7*x - 2)**2
Factor -8*n**3 + 5*n**5 - n**5 - 133*n**4 + 68*n**4 + 61*n**4.
4*n**3*(n - 2)*(n + 1)
Let s = -10 + 16. Let j(b) be the third derivative of 0*b + 1/42*b**4 - b**2 + 0*b**3 + 0 + 1/140*b**s + 1/42*b**5. Factor j(p).
2*p*(p + 1)*(3*p + 2)/7
Let i(v) be the first derivative of v**6/2 - 9*v**5/5 + 3*v**4/2 - 3. Factor i(k).
3*k**3*(k - 2)*(k - 1)
Solve -1/5*q**4 - 2/5*q + 0 + 2/5*q**3 + 1/5*q**2 = 0 for q.
-1, 0, 1, 2
Let k = 6135 - 18601/3. Let u = k + 66. Find q, given that -4/3*q**3 + 4/3*q**2 + 2*q - 2*q**4 - 2/3*q**5 + u = 0.
-1, 1
Factor 2 + 1/2*j**2 - 2*j.
(j - 2)**2/2
Let s(m) be the second derivative of m**6/90 - m**5/10 + m**4/4 + 2*m**3/9 - 2*m**2 - 49*m. Factor s(p).
(p - 3)*(p - 2)**2*(p + 1)/3
Let b = 8 + -18. Let s be ((-9)/b)/((-33)/(-44)). Factor -2/5*j**3 - 2/5 - 6/5*j - s*j**2.
-2*(j + 1)**3/5
Let r(d) be the third derivative of 5/12*d**4 - 2/3*d**3 - 2/15*d**5 + d**2 + 0 + 0*d + 1/60*d**6. Suppose r(n) = 0. Calculate n.
1, 2
Suppose a + 3 = -4*a - z, 15 = -5*a - 5*z. Suppose a = v + 3*d, -d = -2*v - 3*d. Factor v*n - 3/2*n**2 + 3/2.
-3*(n - 1)*(n + 1)/2
Let d(k) be the second derivative of -k**6/120 + k**5/80 + k**4/48 - k**3/24 + 4*k. Find y, given that d(y) = 0.
-1, 0, 1
Let j(q) be the first derivative of 1/3*q**6 + 3/5*q**5 + 0*q**3 + 1/4*q**4 - 2 + 0*q + 0*q**2. Factor j(g).
g**3*(g + 1)*(2*g + 1)
Factor 2/7*c**2 + 0*c - 2/7*c**3 + 2/7*c**5 + 0 - 2/7*c**4.
2*c**2*(c - 1)**2*(c + 1)/7
Let b(x) be the first derivative of x**5/15 + x**4/6 - x**3 - x**2/3 + 8*x/3 - 53. Solve b(f) = 0 for f.
-4, -1, 1, 2
Let v be ((-98)/(-6))/7 - 1. Suppose -2/3 - 2/3*w**4 + 2/3*w + 2/3*w**5 - v*w**3 + 4/3*w**2 = 0. Calculate w.
-1, 1
Factor 2*s**4 + s**3 + 3*s**5 + 4*s**4 + 10*s**3 - 8*s**3.
3*s**3*(s + 1)**2
Let o(z) = 8*z**4 + 5*z**3 + z**2 + 7*z - 7. Let d(l) = -7*l**4 - 4*l**3 - l**2 - 6*l + 6. Let g(r) = -7*d(r) - 6*o(r). Factor g(c).
c**2*(c - 1)**2
Let w(u) be the third derivative of u**11/83160 + u**10/37800 - u**5/60 - 7*u**2. Let a(c) be the third derivative of w(c). Factor a(p).
4*p**4*(p + 1)
Let u = -6777 + 27253/4. Let n = u + -36. Factor 1/2*g - 1/4*g**2 - n.
-(g - 1)**2/4
Suppose -16*d = 25*d - 3*d. Determine i, given that -1/4*i**3 + 1/4*i**2 + 0 + d*i = 0.
0, 1
Let o(g) be the third derivative of 0*g**5 - 5*g**2 + 0*g + 0 + 0*g**4 - 1/120*g**6 + 0*g**3. Factor o(k).
-k**3
Suppose 2*v + 2*f - 12 = 0, -f + 4*f = v + 6. Let d be (2/(-4))/(v/(-18)). Factor 0*m**2 - 2*m**5 - 4*m**d + 0 + 16/3*m**4 + 2/3*m.
-2*m*(m - 1)**3*(3*m + 1)/3
Factor -8/5*k**2 + 0 - 4/5*k**3 + 0*k.
-4*k**2*(k + 2)/5
Let a(d) be the first derivative of d**4/4 + 8*d**3/3 - d**2/2 - 8*d + 1. Let w be a(-8). Factor -1 - 2*n**2 - 3 + n**2 + 4*n + w.
-(n - 2)**2
Factor 8 + 7*h**4 - 9*h**2 + 5*h**4 + 2*h**4 - 13*h**4 + 7*h - 7*h**3.
(h - 8)*(h - 1)*(h + 1)**2
Let a = -361 - -723/2. Suppose 0 - 2*u**2 - 2*u - a*u**3 = 0. What is u?
-2, 0
Let n(d) be the second derivative of -d**7/126 + 2*d**6/45 - d**5/15 - d**4/18 + 5*d**3/18 - d**2/3 - 9*d. Factor n(g).
-(g - 2)*(g - 1)**3*(g + 1)/3
Let r(u) = -u**3 - 3*u**2 + 3*u + 3. Let a be r(-4). Let s = 7 - a. Suppose 1/5*g**3 + 0*g**2 + s - 1/5*g = 0. What is g?
-1, 0, 1
Let c be -3 + 1 - (-2 + -3). Let m(i) be the third derivative of -1/90*i**5 + 0*i + 1/9*i**c + 0*i**4 + 0 - 3*i**2. Factor m(z).
-2*(z - 1)*(z + 1)/3
Let p = 11 + 4. Let h = p + -29/2. Factor -7/2*b**2 + b + 2*b**3 + h.
(b - 1)**2*(4*b + 1)/2
Let y = -12 + 14. Factor -4*o**y + 2*o**3 - 3*o**2 + 3*o**2.
2*o**2*(o - 2)
Find a, given that 3/2*a**5 + 0*a - 15/2*a**4 + 0 - 3/2*a**3 + 15/2*a**2 = 0.
-1, 0, 1, 5
Let c(b) be the first derivative of b**3/3 + 2*b**2 + 4*b + 51. Find g, given that c(g) = 0.
-2
Suppose 3 - 1 = q. Suppose 0 = q*p - 4*a, 0*a = 4*p - 5*a. Factor 0*w + p - 2/3*w**2.
-2*w**2/3
Let y(f) be the second derivative of f**4/48 - 7*f**3/24 + 3*f**2/4 - 30*f. Let y(m) = 0. Calculate m.
1, 6
Let x(d) be the second deriva