 0.
2/5, 1, 2
Let o(b) be the first derivative of b**6/15 - 2*b**4/5 + 4*b**3/15 + 3*b**2/5 - 4*b/5 - 1. Factor o(r).
2*(r - 1)**3*(r + 1)*(r + 2)/5
Suppose -3*r = -g - 0*g - 32, 5*g + 40 = 5*r. Let o be ((-3)/2)/(r/(-16)). Factor 8*w - w**4 - w**o - 2*w**3 - 8*w.
-w**2*(w + 1)**2
Let k(j) = j**3 + 6*j**2 - 6*j + 7. Let g be k(-7). Suppose z - 2*a + 5*a + 3 = g, -3*z + 4*a = -17. What is u in 2*u - u + 1 - 5 - u**2 + z*u = 0?
2
Let u(a) = 16*a**2 - 11*a - 20. Let o(l) = 3*l**2 - 2*l - 4. Let v(n) = -22*o(n) + 4*u(n). What is r in v(r) = 0?
-2, 2
Let c(s) = 2*s - 7. Let h be c(5). Factor 6*i**5 - 4*i**2 + i**3 - 24*i**4 + 17*i**h + 4*i**5.
2*i**2*(i - 1)**2*(5*i - 2)
Let d be (-6)/216*-8 - 4/18. Let j(m) be the third derivative of 0*m**6 + 0*m**4 + 1/210*m**7 - 2*m**2 + 0 + 0*m + d*m**3 - 1/60*m**5. Factor j(z).
z**2*(z - 1)*(z + 1)
Let x(h) be the first derivative of 2*h**5/35 - 3*h**4/14 + 2*h**3/21 + 3*h**2/7 - 4*h/7 + 9. Suppose x(a) = 0. What is a?
-1, 1, 2
Suppose q = -0*q + 5. Factor 0*b + 6*b**q + 0*b - 7*b**3 + 3*b**3 - 2*b**4.
2*b**3*(b - 1)*(3*b + 2)
Let h = -59 - -355/6. Let r(v) be the first derivative of -3/4*v**2 - 1 + v + h*v**3. Determine c, given that r(c) = 0.
1, 2
Let p(r) be the second derivative of -3*r**5/80 + 5*r**4/16 - 3*r**3/8 - 27*r**2/8 + 18*r. Factor p(m).
-3*(m - 3)**2*(m + 1)/4
Let g be 16/(-4)*(-2)/8. Let f(r) = -r**2 + r + 1. Let k(p) = 18*p**2 - 33*p + 12. Suppose v + 3*v - 60 = 0. Let n(s) = g*k(s) + v*f(s). Factor n(h).
3*(h - 3)**2
Let m = 7 - 1. Let h = -1 + m. Solve -6*t**3 - 8*t**4 + t**5 - 3*t**h + t - t**5 = 0.
-1, 0, 1/3
Let j(z) be the first derivative of 2/3*z**3 + 0*z**2 - 8*z - 2. Factor j(l).
2*(l - 2)*(l + 2)
Let t(n) be the third derivative of n**5/20 + n**4/8 - n**3 - 23*n**2. Factor t(o).
3*(o - 1)*(o + 2)
Let g(s) be the first derivative of s**3/2 - 6*s**2 + 24*s + 6. Factor g(v).
3*(v - 4)**2/2
Find v such that 3/2*v + 3/2*v**2 + 0 = 0.
-1, 0
Suppose x + x + 8 = 0. Let a be 1/(0 - 1/x). Factor -2*p**2 + p**a + 2*p**3 + 2*p**2.
p**3*(p + 2)
Let n = -26 - -37. Let f = -7 + n. Factor -r**4 - 3*r**f + 5*r**4.
r**4
Let k be (-2 - (-12)/7)*-7. Factor 6*b + 2*b**3 + 0*b**2 - 2 + 0*b**2 - 6*b**k.
2*(b - 1)**3
Let s(i) be the second derivative of 11/90*i**5 + 1/27*i**7 + 1/27*i**4 + 0*i**2 + 0 - 5*i + 16/135*i**6 + 0*i**3. Factor s(x).
2*x**2*(x + 1)**2*(7*x + 2)/9
Factor -2/9*z**3 + 0*z + 0 - 2/9*z**2 + 4/9*z**4.
2*z**2*(z - 1)*(2*z + 1)/9
Let w(q) be the second derivative of 0 - 2/7*q**2 + 3/70*q**5 + 1/21*q**4 - 1/7*q**3 + 4*q. What is v in w(v) = 0?
-1, -2/3, 1
Let w(p) = -p**3 + p**2 - p - 1. Let c(j) = 3*j**4 - 3*j**3 + 3*j**2 - 3*j - 3. Let m(r) = -c(r) + 3*w(r). Determine u, given that m(u) = 0.
0
Let a = 28340715/44 - 644154. Let i = a - -191/4. Let -2/11*v**4 - i*v + 4/11 + 6/11*v**2 + 2/11*v**3 = 0. What is v?
-2, 1
Let x = 19 - 2/3. Let b = 19 - x. Factor -2*q**3 - 2/3*q + 0 + 2*q**2 + b*q**4.
2*q*(q - 1)**3/3
Let d(m) be the second derivative of 0 + 1/24*m**4 - 1/60*m**5 + 1/3*m**3 + 1/2*m**2 - 2*m. Let o(f) be the first derivative of d(f). Solve o(v) = 0.
-1, 2
Suppose -91 + 91 = -11*r. Find s, given that -4/9*s + r + 2/9*s**2 = 0.
0, 2
Suppose 3*c = c - 4*m + 20, -5*m = 3*c - 26. Factor 0 - 2/3*l**c - 2/3*l.
-2*l*(l + 1)/3
Let r be (-9)/(-24)*28/21. Let o(f) be the first derivative of r*f - 1/2*f**2 + 4 + 1/6*f**3. Factor o(g).
(g - 1)**2/2
Let o(w) = w**2 - 5*w + 3. Let j be o(6). Solve -3*s**3 + 6*s**3 - 22*s**2 + j*s**4 + 16*s**2 = 0.
-1, 0, 2/3
Let q(y) = -29*y - 10 - 13*y**2 + 10 + 18*y**3. Let t(r) = -3*r**3 + 2*r**2 + 5*r. Let z(b) = 6*q(b) + 34*t(b). Factor z(x).
2*x*(x - 2)*(3*x + 1)
Let m(z) = 3*z**3 - 2*z**2 - z - 2. Let y be m(2). Suppose 3*t - y = -0*t. Factor -3*i**4 - i - 3*i**2 + 8*i**3 + t*i**4 - 7*i**3 + 2.
(i - 1)**2*(i + 1)*(i + 2)
Suppose -5*y = -0*s - s - 18, -3*y + 6 = s. Suppose -r + y = 1. Factor 5*z**2 - 3*z**2 + 2*z**2 - 2*z**r.
2*z**2
Let n be 2/(-6) - (-3)/9. Suppose d + 0*t = -3*t + 17, n = -4*t + 20. Find c such that 0*c**5 + 0*c**2 - 2*c**5 - d*c**2 + 0*c**2 - 6*c**3 - 6*c**4 = 0.
-1, 0
Let t = -17 + 19. Let m(j) be the third derivative of 0*j**4 + 1/240*j**5 + 0 - 1/24*j**3 + 0*j + 3*j**t. Factor m(l).
(l - 1)*(l + 1)/4
Let f(r) be the first derivative of r**6/2340 + r**5/390 + r**4/156 + 8*r**3/3 - 6. Let m(y) be the third derivative of f(y). Determine g so that m(g) = 0.
-1
Factor 3/2*s**4 + 0 - 3/2*s**2 + 9/4*s**3 + 0*s.
3*s**2*(s + 2)*(2*s - 1)/4
Factor 4/11*l + 0 - 2/11*l**2.
-2*l*(l - 2)/11
Suppose -v**5 - 2/7*v**2 + 0 + v**3 + 2/7*v**4 + 0*v = 0. Calculate v.
-1, 0, 2/7, 1
Let o = -1 + 4. Let u be 3 - -1*(o - 3). Factor 1/5*r + 1/5 - 1/5*r**u - 1/5*r**2.
-(r - 1)*(r + 1)**2/5
Determine u, given that -6*u**2 - 1/3*u**4 - 20/3*u - 7/3*u**3 - 8/3 = 0.
-2, -1
Let v(n) be the second derivative of -3*n**4/22 + n**3/3 - 2*n**2/11 + 6*n. Solve v(m) = 0 for m.
2/9, 1
Factor -4/3 + 8/3*h + 1/3*h**3 - 5/3*h**2.
(h - 2)**2*(h - 1)/3
Factor h + 1/8*h**3 - 5/8*h**2 - 1/2.
(h - 2)**2*(h - 1)/8
Let n = -48 - -50. Factor -2/3 - n*k - 2/3*k**3 - 2*k**2.
-2*(k + 1)**3/3
Suppose -q + 7 = -1. Factor -q*o**4 - 7*o**5 - 4*o**3 - 2*o**2 + 10*o**5 + 11*o**3.
o**2*(o - 1)**2*(3*o - 2)
Let b(n) be the third derivative of n**7/8820 - n**6/1260 - n**5/140 + n**4/24 - 3*n**2. Let y(r) be the second derivative of b(r). Factor y(c).
2*(c - 3)*(c + 1)/7
Let j(m) be the third derivative of -m**8/6720 + m**7/1680 + m**6/360 - m**5/60 + 2*m**3/3 - 3*m**2. Let u(v) be the first derivative of j(v). Factor u(y).
-y*(y - 2)**2*(y + 2)/4
Let x(c) = 2*c**2 - 71*c + 37. Let v be x(35). Let -1/4*a**v + 0 + 1/4*a = 0. What is a?
0, 1
Suppose 0 = -3*y - 0*y - 2*t + 32, 3*y - 17 = -5*t. Suppose -c - 12 = -y. Find b, given that 2/5*b**3 + 0 + 0*b**c - 9/5*b**4 + 0*b = 0.
0, 2/9
Let l = 13/4 - 3. Suppose 5/4*i - 1/4*i**3 - l*i**4 + 3/4*i**2 + 1/2 = 0. What is i?
-1, 2
Suppose 4*q - 3 = 4*h - 19, 0 = 5*h - 4*q - 16. Suppose h = -3*o + 6*o - 6. Factor -2/7*p**3 + 0*p + 2/7*p**4 + 0 + 0*p**o.
2*p**3*(p - 1)/7
Let m be (-15)/1*(14 - 12). Let w = m + 30. Find x, given that 1/2*x**2 - 1/4*x**3 + w*x + 0 = 0.
0, 2
Let r be ((-1542)/(-4) + -1)/220. Let h = 1/440 + r. Determine m so that -h*m - 5/4*m**2 - 1/2 = 0.
-1, -2/5
Let u(g) = -17*g**3 - 37*g**2 - 7*g + 40. Let t(i) = -8*i**3 - 18*i**2 - 3*i + 20. Let k(h) = -7*t(h) + 3*u(h). Suppose k(f) = 0. Calculate f.
-2, 1
Let p = 3 + 12. Suppose p = 7*n - 2*n - q, n = 4*q + 3. Solve 14*d**2 - 12*d**2 + n*d - 4 - d = 0 for d.
-2, 1
Factor 0 - 1/2*y**2 - 5/2*y.
-y*(y + 5)/2
Let z(q) = -5*q. Suppose a + a - 5 = d, -5*a + 13 = -3*d. Let l be z(d). Find j, given that l*j**3 - 18*j**2 + 8*j - 8*j - 2 + 12*j + 3*j**3 = 0.
1/4, 1
Let h(n) be the third derivative of 2/9*n**3 + 0 + 2*n**2 + 1/90*n**6 + 4/45*n**5 - 2/315*n**7 + 7/36*n**4 - 1/504*n**8 + 0*n. Factor h(u).
-2*(u - 2)*(u + 1)**4/3
Suppose -10/13*m**3 - 32/13*m - 8/13 + 38/13*m**2 = 0. What is m?
-1/5, 2
Let r(o) = -7*o**4 + 23*o**3 - 35*o**2 + 16*o - 3. Let s(t) = -34*t**4 + 114*t**3 - 174*t**2 + 80*t - 14. Let h(p) = 14*r(p) - 3*s(p). Factor h(x).
4*x*(x - 2)**2*(x - 1)
Suppose 3/2 + 3/8*x**2 + 15/8*x = 0. What is x?
-4, -1
Suppose -3*p = 80 - 80. Let h be (4/10)/((-2)/(-2)). Factor p*u + 0 - h*u**2 + 2/5*u**3.
2*u**2*(u - 1)/5
Let l(v) be the third derivative of 0*v - 1/90*v**5 + 0*v**3 - 1/180*v**6 + 0*v**4 + v**2 + 0. Factor l(g).
-2*g**2*(g + 1)/3
Let n(p) be the second derivative of p**7/63 + 13*p**6/135 + 11*p**5/45 + p**4/3 + 7*p**3/27 + p**2/9 - 4*p. Factor n(a).
2*(a + 1)**4*(3*a + 1)/9
Let o(j) = 4*j**2 - 6*j + 5. Let r(y) = -5*y + 6 + 5*y**2 + 0*y + 3*y - 5*y. Let a(t) = -4*o(t) + 3*r(t). Let a(l) = 0. Calculate l.
1, 2
Let x(h) be the second derivative of -h**4/4 + 3*h**3/2 - 3*h**2 + h. Factor x(o).
-3*(o - 2)*(o - 1)
Let k(y) = 5*y**5 - 14*y**3 + 8*y**2 + 9*y - 8. Let i(s) = 6*s**5 - 15*s**3 + 9*s**2 + 9*s - 9. Let h(m) = -2*i(m) + 3*k(m). Factor h(q).
3*(q - 1)**3*(q + 1)*(q + 2)
Let f(x) = x**3 - x - 2. Let w be f(2). Determine i, given that -5*i**3 - i**5 + w*i**3 - 2*i**4 + 0*i**3 = 0.
-1, 0
Let p = -1 - -4. Let w be (12/18)/(1/p). Suppose -4*b - 2*b**2 + 4*b**w - 4*b**2 + 0*b = 0. What is b?
-2, 0
Let r be (-18)/(-12) - 2/4. Suppose 3*h - 35 = -i - 4*i, i = h - r. Determine m, g