+ 4*b**2 - 2*b + 5. Find c, given that o(c) = 0.
1/2, 1
Let m(b) be the first derivative of 1/30*b**4 - 2/5*b**2 - 1 + 1/15*b**3 - 2*b. Let h(t) be the first derivative of m(t). Factor h(y).
2*(y - 1)*(y + 2)/5
Suppose 3 - 9 = -3*w. Let j = -35 + 106/3. Factor j + 1/3*b**w + 2/3*b.
(b + 1)**2/3
Let t = 228 - 43091/189. Let v(n) be the second derivative of 0 + 1/90*n**5 - 1/135*n**6 - 4*n + 0*n**3 + 1/54*n**4 - t*n**7 + 0*n**2. Factor v(m).
-2*m**2*(m - 1)*(m + 1)**2/9
Let i(h) be the first derivative of -h**6/6 + 2*h**5/5 + 6. Find m such that i(m) = 0.
0, 2
Factor 8/5 + 8/5*l + 2/5*l**2.
2*(l + 2)**2/5
Let j(l) be the first derivative of -5*l**6/36 + l**5/2 - 5*l**4/12 + 1. Factor j(k).
-5*k**3*(k - 2)*(k - 1)/6
Let s be 45/10 - (-2)/4. Let m(x) be the first derivative of -1/4*x**4 + 0*x**2 + 1 + 0*x**3 - 1/10*x**s + 1/4*x**6 + 0*x. Let m(h) = 0. What is h?
-2/3, 0, 1
Suppose d - 30*o - 12 = -26*o, 3*d + 3*o = -9. Let u = -18 - -37/2. Factor d - 1/4*r**2 + u*r.
-r*(r - 2)/4
Let p(z) = -z**3 + 7*z**2 + 10*z - 10. Let a be p(8). Suppose 4 = -4*u + a*u. Solve 6/7*f**3 + 0 + 2/7*f + 6/7*f**u + 2/7*f**4 = 0.
-1, 0
Let q(a) be the third derivative of a**8/840 - 13*a**7/1575 + 17*a**6/900 - a**5/150 - 2*a**4/45 + 4*a**3/45 - 14*a**2. What is z in q(z) = 0?
-2/3, 1, 2
Suppose -v + 20 = -4*r, 3*v - 2*v - 2*r - 10 = 0. Let t(m) be the first derivative of 1 + v*m**2 + 2*m - 2/3*m**3. Factor t(k).
-2*(k - 1)*(k + 1)
Let b(g) be the first derivative of g**6/6 - g**5/5 - g**4/4 + g**3/3 + 20. Factor b(l).
l**2*(l - 1)**2*(l + 1)
Let p(t) = -1. Let z(l) = -l**2 - 2*l + 6. Let i(c) = -3*p(c) - z(c). Determine u, given that i(u) = 0.
-3, 1
Let m(h) = h. Let w(x) = x**2 + 2. Suppose -3*q + f - 8 = 0, -3 = f + 2*f. Let r(t) = q*m(t) - w(t). What is d in r(d) = 0?
-2, -1
Suppose -15 = -3*x - 3*h, -5*x + 11 + 4 = 3*h. Solve x - 2/11*p**2 + 4/11*p = 0.
0, 2
Let g(c) be the second derivative of -2/7*c**7 - 1/5*c**5 - 2/3*c**6 + 0*c**2 + 0*c**3 + 1/3*c**4 + 0 + 3*c. Determine d so that g(d) = 0.
-1, 0, 1/3
Let h(u) be the first derivative of u**4/2 + 2*u**3 + 2*u**2 + 4. Factor h(t).
2*t*(t + 1)*(t + 2)
Suppose 0 = -12*b + 11*b + 6. Suppose -3*q**5 - 3 - 3*q + q**2 + b*q**3 + 5*q**2 - 3*q**4 + 0*q**3 = 0. Calculate q.
-1, 1
Let -4593 - 12*g + 2*g**2 + 4607 - 4*g**2 = 0. Calculate g.
-7, 1
Let v(u) = u**5 + u**4 - u. Let t(p) = 14*p**5 + 12*p**4 - 2*p**3 - 7*p. Let m(s) = 2*t(s) - 14*v(s). What is r in m(r) = 0?
-1, 0, 2/7
Let o(a) be the second derivative of 0 - a**2 + 1/20*a**5 + 1/3*a**3 - 5/24*a**4 - 2*a. Let s(x) be the first derivative of o(x). Factor s(p).
(p - 1)*(3*p - 2)
Let s(v) = -3*v**2 + 9*v + 3. Let b be (-20)/(-50) + (-47)/5. Let n(a) = -a. Let q(k) = b*n(k) - s(k). Factor q(l).
3*(l - 1)*(l + 1)
Let y be 0/(1 + 1) + 0/27. Factor y*a + 2*a**2 + 0 + 2/3*a**3.
2*a**2*(a + 3)/3
Let m(r) be the second derivative of -1/2*r**2 - 1/6*r**6 - r - 5/6*r**4 - 1/42*r**7 + 0 - 5/6*r**3 - 1/2*r**5. Suppose m(o) = 0. Calculate o.
-1
Let p(b) be the second derivative of -b**4/4 + 3*b**3 - 27*b**2/2 + 5*b. Let p(y) = 0. Calculate y.
3
Let w(f) be the second derivative of f**7/63 - f**6/15 + f**5/15 + f**4/9 - f**3/3 + f**2/3 + 5*f. Determine m so that w(m) = 0.
-1, 1
Let s = 19 + -56/3. Determine g, given that 4/3*g**4 + 0 - 1/2*g**5 + s*g**2 - 7/6*g**3 + 0*g = 0.
0, 2/3, 1
Let q(t) be the third derivative of -t**5/60 + t**4/24 + t**3/3 + 13*t**2. Let q(o) = 0. Calculate o.
-1, 2
Let r = -76271/1020 + 1276/17. Let t = r - -1/20. Factor 0*s - t*s**2 + 1/3.
-(s - 1)*(s + 1)/3
Suppose 0*a + a = 0. Suppose 0 = y + b - 3, 8*y - 10 = 5*y - 2*b. Determine p so that 1/5*p**3 + 1/5*p**2 - 1/5*p**5 + a*p + 0 - 1/5*p**y = 0.
-1, 0, 1
Let s be -26 - 3/((-6)/4). Let w = -14 - s. Factor 0 + 3 - 24*n + 5 + w*n**2.
2*(n - 2)*(5*n - 2)
Let k(b) = -b**3 - 3*b**2 + 16*b + 48. Let m be k(-3). Suppose m - 6/5*g - 2/5*g**2 = 0. What is g?
-3, 0
Let w(r) be the first derivative of r**7/3780 - r**6/1620 - r**5/540 + r**4/108 + 7*r**3/3 + 8. Let j(c) be the third derivative of w(c). Factor j(z).
2*(z - 1)**2*(z + 1)/9
Let y(q) = 2*q**4 - q**2 - 1. Let z(r) = -r**4 + r**3 - r + 1. Let s(d) = -d + 2. Let t be s(3). Let x(o) = t*z(o) - y(o). Factor x(g).
-g*(g - 1)*(g + 1)**2
Suppose 0 = -y + 5*m - 10, -5*y + 10*m - 5*m = 10. Suppose j - 3*l + 15 = 0, y*j + 2*j - 2*l + 10 = 0. Factor 0 + j*x**2 + 0*x**3 - 2/3*x**5 + 0*x**4 + 0*x.
-2*x**5/3
Let l(d) = 6*d**4 - 5*d**3 - 6*d**2 - 8*d + 2. Let u(t) = t**4 - t**3 + 1. Let o be 10/(-5)*(1 - 0). Let v(f) = o*l(f) + 10*u(f). Solve v(g) = 0 for g.
-1, 3
Let t be 50/24 + 0 - (-18)/(-9). Let j(v) be the third derivative of 3*v**2 + 0 + t*v**4 + 0*v**3 - 1/30*v**5 + 0*v. Factor j(q).
-2*q*(q - 1)
Suppose -2*s - 2*s + 16 = 0. Let w(f) be the first derivative of -2 - 4*f - 2*f**3 + 4*f**2 + 2*f - s*f**2 - 4*f**2. Determine n so that w(n) = 0.
-1, -1/3
Let z(j) be the second derivative of -j**5/60 - j**4/12 - j**2/2 - 3*j. Let l(n) be the first derivative of z(n). Factor l(i).
-i*(i + 2)
Let p(k) be the third derivative of -1/105*k**5 + 1/420*k**6 + 1/84*k**4 - 2*k**2 + 0*k**3 + 0*k + 0. Determine u so that p(u) = 0.
0, 1
Let a(t) be the second derivative of -t**6/216 - 7*t**5/360 - t**4/36 - t**3/2 - t. Let j(v) be the second derivative of a(v). Factor j(i).
-(i + 1)*(5*i + 2)/3
Let q = -13 - -5. Let p be (q*(-4)/8)/2. Determine l so that -1/2*l**p + 1 + 1/2*l = 0.
-1, 2
Let u be (48/(-36))/(4/(-6)). Factor 0 - 6/5*s**u + 0*s + 0*s**4 + 3/5*s**5 - 9/5*s**3.
3*s**2*(s - 2)*(s + 1)**2/5
Let z(v) = -8*v - 1. Suppose -5*d - 6*n = -3*n + 20, -5*d - 5*n - 30 = 0. Let p be z(d). Factor -q + p*q - 2*q - 2*q**2.
-2*q*(q - 2)
Let y(x) be the third derivative of -x**6/60 - 7*x**5/150 - x**4/30 - 3*x**2. Factor y(a).
-2*a*(a + 1)*(5*a + 2)/5
Let u(b) = 9*b**2 + 5*b - 7. Let q(o) = 19*o**2 + 11*o - 13. Let c(l) = 3*q(l) - 5*u(l). Find d such that c(d) = 0.
-1, 1/3
Suppose -3*t - 3*a = 15, 0*a + 3*a = -15. Let k(w) be the first derivative of 0*w + t*w**2 - 2 + 0*w**4 + 2/5*w**5 - 2/3*w**3. Determine h so that k(h) = 0.
-1, 0, 1
Let o(y) be the first derivative of y**4/12 + 5*y**3/9 + y**2/2 - 3*y + 5. Factor o(d).
(d - 1)*(d + 3)**2/3
Suppose 0 = 2*v + 4*a - 4, -5*v - 4*a + a = -17. Let k(d) be the first derivative of 0*d**3 + 1/4*d**6 + 2 + 0*d + 0*d**2 - 1/4*d**v + 1/10*d**5. Factor k(n).
n**3*(n + 1)*(3*n - 2)/2
Suppose -5*m = 5, k + m = -4*k + 199. Factor 1 + b**2 + k*b + 7 + 45*b**2 + 14*b**3.
2*(b + 1)*(b + 2)*(7*b + 2)
Suppose 17 = h + 5*o, 11 = 5*o + 1. Let p = h - 27/4. What is b in -1/4*b**3 + p*b**2 + 1/4*b + 0 - 1/4*b**4 = 0?
-1, 0, 1
Factor 2/11*k**2 + 0 - 2/11*k**3 + 4/11*k.
-2*k*(k - 2)*(k + 1)/11
Let f(c) be the first derivative of 1/24*c**4 + 1/2*c**2 + 2 + 2*c + 1/4*c**3. Let d(i) be the first derivative of f(i). Factor d(w).
(w + 1)*(w + 2)/2
Let r(f) be the second derivative of -f**5/240 + f**4/96 + f**3/12 + 3*f**2/2 + f. Let z(l) be the first derivative of r(l). Factor z(c).
-(c - 2)*(c + 1)/4
Factor -2 + 176/9*k**3 - 194/9*k**2 - 44/3*k - 32/9*k**4.
-2*(k - 3)**2*(4*k + 1)**2/9
Factor 0*y**3 - 3/2*y**5 + 0 + 0*y - 3*y**4 + 0*y**2.
-3*y**4*(y + 2)/2
Suppose 2*d + 2*v = -2*v + 16, 0 = 3*d + 4*v - 30. Let z be 2*(d/4 + -2). Factor -2*a - 9*a**3 - 7*a**4 + 28*a**3 + z*a + 2 - 15*a**2.
-(a - 1)**3*(7*a + 2)
Let u(z) be the first derivative of 2*z**3/39 - 2*z**2/13 - 1. Solve u(l) = 0 for l.
0, 2
Let m(i) = 1. Let k(j) = -9*j**3 + 11*j**2 - 2*j - 2. Let w(g) = -2*k(g) - 4*m(g). Factor w(x).
2*x*(x - 1)*(9*x - 2)
Let d(w) be the first derivative of -21*w**5/40 - 5*w**4/8 + w**3/2 - 2*w - 1. Let k(v) be the first derivative of d(v). Factor k(m).
-3*m*(m + 1)*(7*m - 2)/2
Let w(v) be the third derivative of -v**5/12 + 5*v**3/6 - 4*v**2. Factor w(s).
-5*(s - 1)*(s + 1)
Factor -2*v**2 + 4*v - 8*v + 5*v**4 + 19*v - 3*v**2 - 15*v**3.
5*v*(v - 3)*(v - 1)*(v + 1)
Let b be 2/(-1)*(-5)/((-50)/(-15)). What is s in 4/5*s**b + 8/5*s**4 - 8/5*s**2 - 6/5*s**5 + 2/5*s + 0 = 0?
-1, 0, 1/3, 1
Let u = 16/15 - 11/15. Factor 4/3 + 0*q - u*q**2.
-(q - 2)*(q + 2)/3
Let -3 - 14*a**3 + 3 + a + 15*a**3 - 2*a**2 = 0. Calculate a.
0, 1
Suppose 4*r + 13 = 5*v, -4*v + 14 = -4*r + 2*r. Factor 2*g**3 + 7*g - 4*g - 2*g**r - 3*g**3.
-3*g*(g - 1)*(g + 1)
Let k(z) be the second derivative