r t(w).
3*(w - 2)*(w - 1)**3*(7*w - 2)
Suppose 15*g = 236 - 236. Factor g*t**2 + 0*t + 0 - 1/5*t**3.
-t**3/5
Let k(t) = -t**3 - 7*t**2 - 6*t + 3. Let u be (1 + 5/(-2))*4. Let y be k(u). Factor 4*i**4 - 5*i**4 + 3*i**4 + 2*i**y.
2*i**3*(i + 1)
Let a = 34 - 22. Let d be (a/(-54))/(2/(-3)). Factor 0 - 1/3*q - d*q**2.
-q*(q + 1)/3
Let o(g) = -22*g**2 + 24*g - 2. Let r(w) = 44*w**2 - 47*w + 3. Let j(b) = 11*o(b) + 6*r(b). Find f, given that j(f) = 0.
-2/11, 1
Let r = 115 - 115. Let l(j) be the second derivative of r + 0*j**2 + 0*j**3 + 4*j - 1/12*j**4. Suppose l(s) = 0. What is s?
0
Let v(f) be the third derivative of f**8/84 - 2*f**7/105 - f**6/5 + 4*f**5/15 + 4*f**4/3 - f**2 - 4. Factor v(x).
4*x*(x - 2)**2*(x + 1)*(x + 2)
Let t(f) = f + 12. Let w be t(-10). Suppose w*p - 2 = 4. What is n in -4/5*n**p + 2/5*n + 2/5*n**5 + 0*n**2 + 0*n**4 + 0 = 0?
-1, 0, 1
Solve -41/2*k**2 + 3 - 7/2*k - 14*k**3 = 0.
-1, -3/4, 2/7
Let i = 5 - 5. Suppose i = 3*s - 12 + 3. Determine b so that 1/4*b**s + 1/4*b**2 + 0 + 0*b = 0.
-1, 0
Let 2/7*j**4 - 8/7*j**3 + 4/7*j**2 - 6/7 + 8/7*j = 0. What is j?
-1, 1, 3
Suppose -j = 2*s + 4, -5*s + 8*s + 6 = j. Let j - 1/6*r + 1/6*r**2 = 0. What is r?
0, 1
Let h(l) be the second derivative of l**4/78 - l**3/13 - 4*l**2/13 - 32*l. Factor h(r).
2*(r - 4)*(r + 1)/13
Let f(g) = g**3 + 16*g**2 + 14*g - 14. Let u be f(-15). Let c(z) be the first derivative of 8/9*z**3 - u - 5/3*z**2 + 2/3*z. Let c(b) = 0. What is b?
1/4, 1
Let f be 16/72 - 4/18. Factor 0*g**2 + 2/7*g**5 + 8/7*g**3 + 8/7*g**4 + f*g + 0.
2*g**3*(g + 2)**2/7
Let c(o) be the second derivative of -o**4/16 - o**3/8 - 7*o. Factor c(h).
-3*h*(h + 1)/4
Let b(f) = f**4 - f**3 - f**2 + f - 1. Let t(l) = -l**4 + l**3 + l**2 - l + 2. Let j(d) = 6*b(d) + 3*t(d). Find k, given that j(k) = 0.
-1, 0, 1
Let b = 163/3 + -54. What is r in 1/3*r - b*r**2 + 0 = 0?
0, 1
Let b(j) be the third derivative of -j**6/480 + j**5/60 - 5*j**4/96 + j**3/12 - 6*j**2. Factor b(f).
-(f - 2)*(f - 1)**2/4
Let o(q) be the second derivative of -q**7/84 - q**6/40 - q**5/60 - 2*q**3/3 - 2*q. Let a(x) be the second derivative of o(x). Factor a(h).
-h*(2*h + 1)*(5*h + 2)
Let u be (1 - (-4 + 0))/(-1). Let t = 5 + u. Find x, given that 0*x + 1/6*x**3 + t + 1/3*x**2 = 0.
-2, 0
Factor -6*p**3 + 5*p**2 - p - p**2 + 13*p**5 + 4*p**4 - 3*p**5 - 11*p**5.
-p*(p - 1)**4
Let g(o) be the first derivative of o**4/6 - 2*o**3/3 + 54. Factor g(d).
2*d**2*(d - 3)/3
Let o(d) be the second derivative of 5*d**4/8 + d**3 - 3*d**2/4 + 7*d. Determine s so that o(s) = 0.
-1, 1/5
Let z be 7/(-2)*8/(-2). Suppose -z = 2*d - 5*d - 4*n, -d = -4*n + 6. Determine x, given that x - 2*x - x**2 + 1 + d*x - x**3 = 0.
-1, 1
Suppose 13*m - 6 = 15*m - 5*a, 3*m + 3*a - 12 = 0. Factor 2/13*b**m + 4/13*b - 6/13.
2*(b - 1)*(b + 3)/13
Let i = -682 - -6130/9. Let d = -2/9 - i. Factor 2/3*u**2 + d - 4/3*u.
2*(u - 1)**2/3
Let o be 36/(-48) - 33/(-12). Let 0*k**o - 4/7 + 8/7*k + 4/7*k**4 - 8/7*k**3 = 0. Calculate k.
-1, 1
Suppose 9 - 2 = -j + 2*u, -3*u = -12. Let s be 6/(-9)*(-2 - j). Suppose -2*c**3 - 3*c**4 - c**s - 3*c + 3*c**2 + 4*c**3 + 1 + c**5 = 0. What is c?
-1, 1
Let r(h) be the second derivative of 0*h**6 + 0*h**2 + 1/189*h**7 + 0*h**4 - 1/90*h**5 + 0 + 4*h + 0*h**3. Factor r(u).
2*u**3*(u - 1)*(u + 1)/9
Factor -2/3 - 1/3*n**4 - 7/3*n - 3*n**2 - 5/3*n**3.
-(n + 1)**3*(n + 2)/3
Let w(q) = -q**2 + 1. Let h(m) = -15*m**2 + 3*m + 18. Let g(i) = h(i) - 18*w(i). Factor g(t).
3*t*(t + 1)
Let f = -478/5 - -96. Let 0 - 4/5*w + f*w**2 = 0. Calculate w.
0, 2
Let h(m) be the third derivative of 0*m**3 + 1/20*m**5 + 0 - 1/8*m**4 + 3*m**2 + 0*m. Factor h(w).
3*w*(w - 1)
Let n(m) = m**2 - 5*m - 1. Let y be n(6). Factor y*a**2 + 2*a - 3*a**2 - 4*a + 0*a.
2*a*(a - 1)
Suppose 0 + 0*w**2 - 2/13*w**3 + 0*w**4 + 2/13*w**5 + 0*w = 0. What is w?
-1, 0, 1
Let o(m) be the second derivative of 1/360*m**6 + 0 + 0*m**3 + 1/180*m**5 - 1/2*m**2 - 1/36*m**4 - 2*m. Let s(i) be the first derivative of o(i). Factor s(c).
c*(c - 1)*(c + 2)/3
Let u(o) = -12*o**5 + 7*o**4 + 87*o**3 - 177*o**2 + 128*o - 30. Let f(g) = -g**5 + g**4 + g**3 - g**2 - g. Let y(r) = 3*f(r) + u(r). What is l in y(l) = 0?
-3, 2/3, 1
Let j(i) be the second derivative of -1/2*i**5 - 2/3*i**3 + 0*i**2 - i + 0 + 7/6*i**4. Factor j(r).
-2*r*(r - 1)*(5*r - 2)
Let n(z) be the first derivative of z**6/15 - 2*z**5/25 - z**4/10 + 2*z**3/15 - 53. Factor n(w).
2*w**2*(w - 1)**2*(w + 1)/5
Let w(j) = 2*j**2 - 4*j + 4. Let h be w(2). Suppose -h*i = -i. Factor -4/5*n**3 + 0 + i*n + 6/5*n**4 - 2/5*n**2.
2*n**2*(n - 1)*(3*n + 1)/5
Suppose 1/3*b**5 + 2/3*b**4 + 0*b**3 + 0 - 1/3*b - 2/3*b**2 = 0. Calculate b.
-1, 0, 1
Let d(r) be the third derivative of r**6/1020 - r**5/510 - r**4/204 + r**3/51 - 8*r**2. Find l such that d(l) = 0.
-1, 1
Suppose 0 = 4*f - 7*f. Suppose -4*m - 4*w - 3 + 11 = f, 5*w = -3*m + 2. Find c, given that -4/3*c**3 - 2/3*c**2 + c**5 + 2/3*c**m + 0 + 1/3*c = 0.
-1, 0, 1/3, 1
Let o = -719 + 752. Determine u so that o*u**3 - 6*u + 35/2*u**4 + 23/2*u**2 - 2 = 0.
-1, -2/7, 2/5
Let b(c) be the second derivative of -c**5/70 - c**4/21 - c**3/21 + 6*c. Factor b(j).
-2*j*(j + 1)**2/7
Let m(i) be the first derivative of -i**5/90 - i**4/18 + 4*i**2/9 - 4*i + 1. Let w(r) be the first derivative of m(r). Factor w(a).
-2*(a - 1)*(a + 2)**2/9
Let u(w) be the second derivative of w**6/2 - 5*w**5/2 + 5*w**4/4 + 24*w + 2. Find v, given that u(v) = 0.
0, 1/3, 3
Let t = 22 + -14. Let w be 22/t - 2/(-8). Let n(b) = b**2 + b + 7. Let v(r) = -r + 1. Let d(f) = w*v(f) - n(f). Suppose d(m) = 0. Calculate m.
-2
Factor -2/5*q**3 + 8/5*q**2 - 2*q + 4/5.
-2*(q - 2)*(q - 1)**2/5
Suppose -3*v + 0 = -6. Factor v*d**3 + 2*d**2 + 2 + 6*d + 7*d**2 - 3*d**2.
2*(d + 1)**3
Suppose -2*j = -3*j - 3*r - 7, -2*j + 1 = r. Factor 2*i + 18/7*i**j + 4/7 + 10/7*i**3 + 2/7*i**4.
2*(i + 1)**3*(i + 2)/7
Determine g so that -1/9*g + 1/9*g**2 - 1/9*g**4 + 1/9*g**3 + 0 = 0.
-1, 0, 1
Let k(t) be the third derivative of 1/3*t**3 + 0*t + 1/42*t**7 - 3*t**2 - 1/8*t**4 + 1/40*t**6 - 7/60*t**5 + 0. Factor k(c).
(c - 1)*(c + 1)**2*(5*c - 2)
Solve -4/9*r**3 + 0 + 0*r**4 + 2/9*r + 0*r**2 + 2/9*r**5 = 0 for r.
-1, 0, 1
Suppose 0 = 3*k - 7 + 1. Suppose -3*c = 5*q - 20 + 1, -25 = -5*q - 5*c. Factor 1/2*a**k + 2*a + q.
(a + 2)**2/2
Let n(b) = -b**4 + b**2 - b. Let r(y) be the first derivative of -7*y**5/5 + 9*y**4/4 - y**3 - y**2 + 2. Let u(m) = 3*n(m) - r(m). Factor u(t).
t*(t - 1)**2*(4*t - 1)
Let i(j) be the second derivative of -2/25*j**5 - 1/5*j**2 - 2/15*j**3 + 9*j + 0 + 7/30*j**4. Suppose i(z) = 0. Calculate z.
-1/4, 1
Let o(k) be the third derivative of -7*k**8/24 + 13*k**7/15 - 17*k**6/20 + 3*k**5/10 - 15*k**2. Factor o(u).
-2*u**2*(u - 1)*(7*u - 3)**2
Let u(d) be the second derivative of d**6/60 + 2*d**5/45 - d**4/36 - 2*d**3/9 - 3*d**2/2 - d. Let r(o) be the first derivative of u(o). Factor r(g).
2*(g + 1)**2*(3*g - 2)/3
Let m be (8 - 0)/(-3 + 5). Let h - 3*h**4 + 0*h**m - h = 0. Calculate h.
0
Find j such that -1/4*j**2 + j - 3/4 = 0.
1, 3
Let r be 4/(-14) + (-4 - 132/(-21)). Let 6/5*j + 9/5*j**r + 0 = 0. What is j?
-2/3, 0
Factor 4/7*t**3 - 4/7*t + 8/7*t**2 - 8/7.
4*(t - 1)*(t + 1)*(t + 2)/7
Let q(w) = w**3 - 3*w**2 + 3*w + 8. Let b(v) = v**2 - v - 2. Let p(x) = 9*b(x) + 2*q(x). Factor p(a).
(a - 1)*(a + 2)*(2*a + 1)
Suppose -3*y + 0 = -j + 2, 5*y - 15 = -2*j. Let w be 1/(j/(-15)) + 5. Solve 1/3*b**4 - 1/3*b**w + 0*b + 0 - b**3 + b**5 = 0.
-1, -1/3, 0, 1
Suppose u**4 + 0*u + 1/2*u**3 + 0*u**2 + 0 = 0. Calculate u.
-1/2, 0
Let t(l) be the first derivative of -1 - 1/2*l**3 + 3/10*l**5 + 3/4*l**2 - 3/8*l**4 + 0*l. Factor t(d).
3*d*(d - 1)**2*(d + 1)/2
Let y(b) be the first derivative of 0*b + b**2 + 1/2*b**4 + 4/3*b**3 - 2. Let y(n) = 0. What is n?
-1, 0
Let h = -4 + 8. Factor -11*z**3 - z**2 - 4*z**4 - z**2 - 4*z**h + z**3.
-2*z**2*(z + 1)*(4*z + 1)
Let y(n) be the second derivative of 0 + 1/40*n**5 - n + 1/24*n**4 + 0*n**2 - 1/60*n**6 - 1/12*n**3. Factor y(g).
-g*(g - 1)**2*(g + 1)/2
Suppose -2*b - 5*n + 67 = 0, 4*n - 55 = -4*b + 49. Factor 4/3*o + b*o**3 + 0 - 32/3*o**2.
o*(7*o - 2)*(9*o - 2)/3
Factor 24/17 - 104/17*q + 14/17*q**3 + 66/17*q**2.
2*(q - 1)*(q + 6)*(7*q - 2)/17
Let h be 75/18 + 6/(-36). Let k = h - 2. Factor -4/7 + k*o**2 - 10/7*o.
2*(o - 1)*(7*