pose 0*h + 2 = -h. Let r be h*2/20*-2. Factor 0 + 2/5*c - r*c**2.
-2*c*(c - 1)/5
Let g be (-7 + 2)*(-12)/15. Suppose -9 = p - g*p. Find n such that 7*n**2 + 0*n - 2*n**2 + 2*n - p*n**2 = 0.
-1, 0
Let l = 15/2 - 43/6. Solve 0 - 2/3*s**2 + l*s + 1/3*s**3 = 0 for s.
0, 1
Let k(b) = b + 9. Let j be k(-5). Suppose 3 = j*o - a, 0*o = 3*o - 5*a + 19. Determine r, given that 7*r**3 - 3*r**2 - 3*r**2 - o*r + r**2 = 0.
-2/7, 0, 1
Let d(g) be the third derivative of g**6/1440 + g**5/160 - g**3/2 - 5*g**2. Let z(n) be the first derivative of d(n). Factor z(v).
v*(v + 3)/4
Factor -2*k**3 - 10*k**2 - 11*k**2 + 0*k**3 + 17*k**2.
-2*k**2*(k + 2)
Factor 33/4*w**2 - 9/2*w**3 + 0 + 3/4*w**4 - 9/2*w.
3*w*(w - 3)*(w - 2)*(w - 1)/4
Let j(x) = -6*x**5 - 38*x**4 - 104*x**3 - 124*x**2 - 70*x - 16. Let u(r) = r**4 - r**3 + r. Let s(f) = j(f) - 2*u(f). Suppose s(o) = 0. Calculate o.
-2, -1, -2/3
Let q be 5/180 - 4/(-18). Let a be ((-51)/(-12) - 4)/1. Factor 0 + q*m + a*m**2.
m*(m + 1)/4
Suppose -3/7 + 2/7*z + 5/7*z**2 = 0. Calculate z.
-1, 3/5
Let k(a) be the first derivative of -a**3/12 + 3*a**2/8 - a/2 - 6. Factor k(r).
-(r - 2)*(r - 1)/4
Let h(d) be the second derivative of -3*d**4/4 + d**3/3 + 8*d. Factor h(k).
-k*(9*k - 2)
Let g be (-2)/(2 + 16/(-6)). Let -3*t + 3*t**3 - t**g + 4*t**2 + 5*t = 0. What is t?
-1, 0
Let w(f) = f**2 - 6*f + 5. Let u be w(5). Let j(n) be the third derivative of u*n + 0 - 1/6*n**3 + 1/120*n**6 - 1/24*n**4 - n**2 + 1/60*n**5. Factor j(i).
(i - 1)*(i + 1)**2
Let n = 2 + -2. Let b(o) be the first derivative of -2/3*o**3 + n*o + 1/3*o**4 - 2/3*o**2 + 2. Factor b(q).
2*q*(q - 2)*(2*q + 1)/3
Let y(t) be the second derivative of t**5/5 - t**4/6 - 2*t**3/3 + t**2 + 18*t. Factor y(i).
2*(i - 1)*(i + 1)*(2*i - 1)
Find h, given that -2*h**2 + 2*h**4 + 18644 - 4*h - 18644 + 6*h**3 - 2*h**5 = 0.
-1, 0, 1, 2
Solve -9*g**5 + 4*g**2 + 2*g**5 - 4*g**4 + 5*g**5 + 2*g**3 = 0.
-2, -1, 0, 1
Let k(r) be the third derivative of 1/6*r**4 + 0*r - 1/10*r**5 + 0 + 0*r**3 - 1/12*r**6 - 11*r**2. Factor k(l).
-2*l*(l + 1)*(5*l - 2)
Let n(u) = -u + 10. Let t be n(6). Let x be (t/(-5))/((-10)/25). Determine z, given that 1/3*z**4 - 1/3*z - 2/3*z**x + 2/3*z**3 - 1/3*z**5 + 1/3 = 0.
-1, 1
Let h(n) be the first derivative of -n**5 - 5*n**4 + 40*n**2 + 80*n - 8. Factor h(z).
-5*(z - 2)*(z + 2)**3
Let w(d) be the second derivative of -d**4/42 - 2*d**3/7 - 9*d**2/7 + 11*d. Factor w(a).
-2*(a + 3)**2/7
Let l be (6 - 7) + (-8)/(-3)*1. Factor 3 - l*c**2 - 1/3*c**3 - c.
-(c - 1)*(c + 3)**2/3
Suppose i = -2 - 4. Let d = i - -8. Factor -1/2 - 1/2*b**d - b.
-(b + 1)**2/2
Suppose -15 = -2*c - 3*k - 3, 2*k + 18 = 3*c. Factor -3*n**2 - 6 + 4*n - c*n + 11*n.
-3*(n - 2)*(n - 1)
Let u = 13 + -13. Suppose -4*c = -u*c. Determine n so that c - 2/3*n**2 + 2/3*n = 0.
0, 1
Let d = 24 - 22. Let q(r) be the first derivative of -d + 1/6*r**3 - 1/4*r**2 + 0*r. What is g in q(g) = 0?
0, 1
Let n(q) be the first derivative of -2/55*q**5 + 3 - 4/11*q**3 - 2/11*q + 4/11*q**2 + 2/11*q**4. Let n(s) = 0. What is s?
1
Let a(u) be the first derivative of -5 - 3/25*u**5 + 0*u + 0*u**2 + 0*u**4 + 1/5*u**3. Factor a(x).
-3*x**2*(x - 1)*(x + 1)/5
Let c(p) = -13*p**4 + 66*p**3 - 90*p**2 + 54*p - 17. Let i(h) = 6*h**4 - 33*h**3 + 45*h**2 - 27*h + 9. Let o(z) = 3*c(z) + 5*i(z). Factor o(q).
-3*(q - 1)**3*(3*q - 2)
Let w be ((-438)/(-327))/((-2)/(-2)). Let p = -2/327 + w. Factor 2/9*d**3 - 16/9 + 8/3*d - p*d**2.
2*(d - 2)**3/9
Suppose -h - 42 = -15*h. Factor 0*l**2 + 2/7 - 2/7*l**4 + 4/7*l**h - 4/7*l.
-2*(l - 1)**3*(l + 1)/7
Let o = 10 + -5. Let w(u) = -u**5 + 4*u**4 - 9*u**3 + u**2 + 5*u. Let h(n) = 2*n**4 - 4*n**3 + 2*n. Let g(z) = o*h(z) - 2*w(z). Solve g(m) = 0 for m.
-1, 0, 1
Let r(y) be the first derivative of y**4/42 - 2*y**3/21 + y**2/7 + 2*y + 2. Let z(b) be the first derivative of r(b). Solve z(w) = 0 for w.
1
Let v(l) = -l**3 + 5*l**2 - l + 7. Let t be v(5). Suppose 4*b - 15 = -i, -t*b + 3*i = 3*b - 6. Factor -2*p + b*p**3 - 2*p**3 + p.
p*(p - 1)*(p + 1)
Let b(r) = -2*r**5 + 3*r**3 - r**2 + 1. Let q(n) = -n**5 + n**3 - n**2 + n + 1. Let x(j) = b(j) - q(j). Factor x(m).
-m*(m - 1)**2*(m + 1)**2
Let b = 25/207 - 2/207. Let q(x) be the first derivative of 0*x**2 - 3 + 1/12*x**4 + b*x**3 + 0*x. Factor q(y).
y**2*(y + 1)/3
Let k(m) be the second derivative of m**8/6720 + m**7/3360 - m**6/1440 - m**5/480 - m**3/2 + 3*m. Let p(q) be the second derivative of k(q). Factor p(u).
u*(u - 1)*(u + 1)**2/4
Suppose -3 - 5 = 2*o. Let r be 13/20 - o/(-10). Factor -1/2*j**2 + r*j + 0 + 1/4*j**3.
j*(j - 1)**2/4
Let p = -38 - -275/7. Find v such that 1/7*v**2 + 6/7*v + p = 0.
-3
Let x(q) be the third derivative of q**6/720 - 13*q**5/360 + 23*q**4/144 - 11*q**3/36 - 22*q**2. Factor x(w).
(w - 11)*(w - 1)**2/6
Suppose 8/11*f**3 + 0*f - 2/11*f**4 + 0 + 0*f**2 = 0. Calculate f.
0, 4
Let c be 18/(-45) + 32/30. Determine v so that -c*v**2 + 1/3 + 2/3*v**3 - 1/3*v**5 + 1/3*v**4 - 1/3*v = 0.
-1, 1
Let c(m) = m**2 - 8*m + 8. Let d be c(8). Suppose 6*o + 4 = d*o. Suppose 0 + 5/4*w**4 - 5/4*w**o - 1/2*w + 1/2*w**3 = 0. What is w?
-1, -2/5, 0, 1
Let z(g) = g + 10. Let l be z(-7). Determine r, given that 3*r**3 + 7*r**l - 5*r**2 - 4 - 10*r + 6*r**4 + 3*r**2 = 0.
-1, -2/3, 1
Let f(a) be the third derivative of a**8/80640 + a**7/6720 + a**6/1440 - a**5/60 - 2*a**2. Let q(n) be the third derivative of f(n). Factor q(z).
(z + 1)*(z + 2)/4
Determine s so that 2/3*s**4 + 0 + 2/3*s**3 + 0*s**2 + 0*s = 0.
-1, 0
Let m(t) = 5*t**4 + 10*t**3 + 16*t**2 + 14*t + 5. Let o = -15 + 4. Let j(u) = 26*u**4 + 49*u**3 + 79*u**2 + 71*u + 26. Let d(c) = o*m(c) + 2*j(c). Factor d(y).
-3*(y + 1)**4
Let p = 30 + -24. Suppose -3 = -3*a - 6, -5*f - 4*a = -p. Factor 0 - 2/5*x**f + 1/5*x**3 + 1/5*x.
x*(x - 1)**2/5
Let k(n) be the first derivative of 0*n - 6 - 9/2*n**4 - 4*n**2 + 8*n**3. Factor k(t).
-2*t*(3*t - 2)**2
Let h(x) = -9*x**2 - x. Let r be h(-1). Let l = -5 - r. Factor v**3 - 3*v**3 + v**3 - v**l.
-2*v**3
Let l(f) be the second derivative of -3*f**5/80 + 3*f**4/16 - 3*f**3/8 + 3*f**2/8 + 6*f. Solve l(s) = 0.
1
Solve -2/9*s**2 - 8/9*s - 8/9 = 0.
-2
Let j(q) = -4*q**5 - 3*q**4 - 6*q**3 - 2*q**2 + 5*q. Let o(i) = -i**5 - i**4 - i**3 + i. Let v(n) = -2*j(n) + 10*o(n). Suppose v(f) = 0. Calculate f.
-2, -1, 0, 1
Determine i so that -9/4*i**2 + 3*i**4 + 0*i + i**3 + 1/4 = 0.
-1, -1/3, 1/2
Let g(i) = -i**2 + 5*i + 5. Let r be g(5). Find f, given that -f - r*f**3 - 2*f**2 + 19*f**3 + 25*f**4 - f**3 + 12*f**5 + f**2 = 0.
-1, -1/3, 0, 1/4
Suppose 3*h - 4*y - 15 = -1, h - y - 4 = 0. Let a be ((-6)/(-75))/((-2)/(-20)). Determine q, given that 4/5*q + 1/5*q**h + a = 0.
-2
Determine b so that 2*b - 2*b**3 - 44 + 44 - 2*b**2 + 2*b**4 = 0.
-1, 0, 1
Suppose -6*p + 2*p = 360. Let z be (p/(-3 + 0))/7. Factor -z*t**2 + 4/7 - 2*t**4 - 38/7*t**3 - 2/7*t.
-2*(t + 1)**3*(7*t - 2)/7
Let p be 4/14 + ((-8)/14)/2. Factor -2/9*a - 4/9*a**2 - 2/9*a**3 + p.
-2*a*(a + 1)**2/9
Let k(v) be the third derivative of v**8/336 + v**7/105 + v**6/120 + 10*v**2. Factor k(z).
z**3*(z + 1)**2
Let f = -5 - -11. Factor -9*a - 15*a**2 - f + 6*a**2 + 6*a**2.
-3*(a + 1)*(a + 2)
Let b(m) = m**3 - 7*m**2 - 9*m + 8. Suppose 0 = -3*n + 5*n - 16. Let a be b(n). Find s such that -4*s - 1 + a*s + 4*s + s**2 = 0.
-1, 1
Factor -40*m**4 - 8*m**2 + 83*m**4 + 4*m**3 - 39*m**4.
4*m**2*(m - 1)*(m + 2)
Let a(d) be the second derivative of 0 - 7/45*d**6 - 1/3*d**2 + 4/9*d**4 + d - 4/63*d**7 + 2/9*d**3 + 1/15*d**5. Solve a(g) = 0.
-1, 1/4, 1
Let m = 125/11 + -123/11. Solve 0 - m*f**3 - 2/11*f**2 + 0*f = 0 for f.
-1, 0
Suppose 3*r - 50 = -20. Let o(x) = 6*x**5 + 4*x**4 + 6*x**3 - x**2 + 6*x - 5. Let c(f) = -f**5 + f**2 - f + 1. Let w(l) = r*c(l) + 2*o(l). Factor w(n).
2*n*(n + 1)**4
What is v in 14*v**3 - 3*v**2 - 7*v**2 - 6*v**3 + 2*v**4 = 0?
-5, 0, 1
Let l(f) be the second derivative of 1/10*f**5 + 0*f**2 - f + 0*f**3 - 1/15*f**6 + 0 + 1/3*f**4. Suppose l(r) = 0. Calculate r.
-1, 0, 2
Let y be (3*(-28)/(-12))/1. Let l be y/3 + 7/(-21). Factor 3/4*n + 3*n**l + 0.
3*n*(4*n + 1)/4
Suppose 5*y - 13 = -v, 4*y - 5*v = 2 - 9. Let j(m) be the first derivative of 0*m**3 + y + 0*m**2 + 1/2*m**4 + 0*m - 2/5*m**5. Factor j(c).
-2*c**3*(c - 1)
Suppose z = -5*p - 3, 4*p = -p + z + 3. Determine w so that p - 6/5*w**4 - 2/5*w**5 + 0