o*f**5 + 4. Factor h(k).
3*k*(k + 1)**2*(2*k + 1)
Let r(g) be the second derivative of 0 - 1/195*g**6 - 1/13*g**2 + 0*g**5 + 0*g**3 + 1/39*g**4 - 3*g. Factor r(n).
-2*(n - 1)**2*(n + 1)**2/13
Let r(o) = -o**2 + 7*o**2 - 12 - 1 + 7*o**3. Let a = 35 - 40. Let c(p) = 6*p**3 + 6*p**2 - 12. Let g(n) = a*c(n) + 4*r(n). Suppose g(s) = 0. Calculate s.
-2, 1
Let x(k) be the third derivative of k**6/240 - k**5/30 + 37*k**2. What is w in x(w) = 0?
0, 4
Factor -2/7 + 2/7*r**2 + 0*r.
2*(r - 1)*(r + 1)/7
Factor 0 - 3*u - 1/3*u**2.
-u*(u + 9)/3
Let p(j) be the third derivative of j**6/60 - 7*j**5/30 + 11*j**4/12 - 5*j**3/3 - 8*j**2. Factor p(h).
2*(h - 5)*(h - 1)**2
Let s be 2 + (2 - 1 - 1). Factor r**4 + 6*r**5 + r**3 + r**s - 7*r**5 - 2*r**4.
-r**2*(r - 1)*(r + 1)**2
Let c(l) = -4*l**5 + 11*l**4 - 8*l**3 + 8*l**2. Let r(j) = 4*j**5 - 12*j**4 + 9*j**3 - 7*j**2. Let y(p) = 4*c(p) + 5*r(p). Solve y(n) = 0.
0, 1/2, 3
Let r = 7 + -20. Let y(t) = -t**3 - 14*t**2 - 15*t - 26. Let a be y(r). Factor a + 2/9*i**2 + 2/9*i.
2*i*(i + 1)/9
Let t(s) be the third derivative of -5*s**8/112 - 23*s**7/70 - s**6/4 + 2*s**5/5 + 18*s**2. Solve t(q) = 0.
-4, -1, 0, 2/5
Determine t so that -2/7*t + 0*t**2 + 0 + 2/7*t**3 = 0.
-1, 0, 1
Let i(f) be the second derivative of -f**5/10 - f**4/3 + 7*f**3/3 - 4*f**2 - 11*f. Suppose i(r) = 0. Calculate r.
-4, 1
Suppose -2*y + 4*y - 4*r = 12, 0 = -3*y + 5*r + 14. Let w(s) = 4*s**3 + 4*s**2 + 2. Let k(l) = -17*l**3 - 17*l**2 - 9. Let a(g) = y*k(g) - 9*w(g). Factor a(v).
-2*v**2*(v + 1)
Factor -2/11*j**4 - 4/11*j + 2/11 + 0*j**2 + 4/11*j**3.
-2*(j - 1)**3*(j + 1)/11
Factor -1/2*s**2 - 1 - 3/2*s.
-(s + 1)*(s + 2)/2
Let o(m) be the second derivative of m**6/75 - m**5/50 - m**4/30 + m**3/15 - 10*m. Suppose o(a) = 0. What is a?
-1, 0, 1
Suppose 3*p + 0*p = 12. Factor x**5 + x**2 + 3*x**3 - 4*x**4 + 3*x**4 + p*x**4.
x**2*(x + 1)**3
Let x be (-82)/(-210) - (-3)/(-9). Let l = x + 27/140. Factor l*t**2 - 1/2*t + 1/4.
(t - 1)**2/4
Let i(h) be the first derivative of h**2 + 0*h - 1/3*h**3 - 2. Determine t so that i(t) = 0.
0, 2
Let o(r) be the first derivative of 8 + 0*r - 1/9*r**3 - 1/3*r**2 + 1/12*r**4. Factor o(i).
i*(i - 2)*(i + 1)/3
Factor 7*u**4 - 3*u**2 - u**5 - 7*u**3 - 4*u - 12*u**4 + 4*u.
-u**2*(u + 1)**2*(u + 3)
Let z be 5*((-20)/6 - -3)*-3. Factor 0*o + 3/4*o**2 + 3/4*o**3 + 0 - 3/4*o**4 - 3/4*o**z.
-3*o**2*(o - 1)*(o + 1)**2/4
Let u(v) be the first derivative of v**5/40 + v**4/2 + 4*v**3 + 16*v**2 - 7*v + 3. Let x(q) be the first derivative of u(q). Let x(c) = 0. What is c?
-4
Let s(j) be the first derivative of 3 - 1/5*j**5 + 0*j**3 + 0*j**2 - 1/8*j**4 - 1/12*j**6 + 0*j. Factor s(q).
-q**3*(q + 1)**2/2
Determine t, given that 0 + 0*t - 3/7*t**2 + 3/7*t**3 = 0.
0, 1
Let a(w) be the third derivative of 3*w**6/140 + 4*w**5/35 + w**4/7 + 19*w**2. Factor a(k).
6*k*(k + 2)*(3*k + 2)/7
Let r(b) = b**2 - 2*b + 1. Let c(f) = -f**3 - f**2 - f + 1. Let j be c(0). Let v be r(j). Solve 1/2*d**2 - 1/2*d**3 + 0*d + v = 0.
0, 1
Let c(h) be the third derivative of h**5/15 + 7*h**4/6 + 4*h**3 - 15*h**2. Find m, given that c(m) = 0.
-6, -1
Suppose 0 = 5*x - 5*j + 45, 2*x - 4*j = 3*x - 11. Let q be 2 - (x - 1)/2. Factor 0*m + 3/5*m**q + 6/5*m**2 + 0*m**4 + 0 - 9/5*m**3.
3*m**2*(m - 1)**2*(m + 2)/5
Let s(c) be the second derivative of c**7/63 + 4*c**6/45 + c**5/5 + 2*c**4/9 + c**3/9 + 12*c. Solve s(g) = 0 for g.
-1, 0
Suppose -11 = -2*v - 5. Determine j, given that -3*j**4 - j + 3 - 5*j**3 + 11*j**v - 4*j - j = 0.
-1, 1
Let b(o) be the second derivative of 1/6*o**4 - o**2 + 5*o + 0 + 0*o**3. Factor b(z).
2*(z - 1)*(z + 1)
Factor -338*c + 158*c - 20*c**2 - 4*c**3 + 156*c.
-4*c*(c + 2)*(c + 3)
Let v(n) = 7*n**2 + 4*n + 7. Let w(y) = -20*y**2 - 11*y - 20. Let j(g) = -17*v(g) - 6*w(g). Factor j(s).
(s - 1)**2
Let z(y) be the first derivative of -y**5/3 + 25*y**4/12 - 35*y**3/9 + 5*y**2/2 + 26. Factor z(b).
-5*b*(b - 3)*(b - 1)**2/3
Let n = -12/4387 + -739963/526440. Let o = -3/40 - n. Find k such that -4/3 - o*k + 19*k**2 + 28/3*k**4 + 85/3*k**3 = 0.
-2, -1, -2/7, 1/4
Let b be (-2)/3*3/(-1). Let j(k) be the first derivative of 1/14*k**4 - 3 + 0*k + 1/7*k**b - 4/21*k**3. Suppose j(x) = 0. Calculate x.
0, 1
Let k(t) = -5*t**2 + t - 2. Let v(z) = -5*z**2 - 6*z**2 - 1 - 3 + z + 0. Let l(s) = 7*k(s) - 3*v(s). Suppose l(a) = 0. Calculate a.
1
Let w(y) = y**3 - 4*y**2 - 5*y**3 - 2*y**2. Let x(v) = 2*v**2 - 4*v**3 - 4*v**2 + v**3 + 2*v**3. Let z(o) = -3*w(o) + 10*x(o). Factor z(b).
2*b**2*(b - 1)
Suppose -3*j - 28 = 3*p - 7*p, 4*p = -3*j + 4. Let c(q) be the second derivative of -1/3*q**3 + 0*q**2 - 1/6*q**p + 0 + 3*q. Factor c(w).
-2*w*(w + 1)
Let a(o) be the third derivative of 0*o + 1/350*o**7 - 1/20*o**5 + 3/40*o**4 - 2*o**2 + 0 + 0*o**3 + 1/200*o**6. Factor a(i).
3*i*(i - 1)**2*(i + 3)/5
Let d(t) be the third derivative of t**5/40 - t**4/16 - t**3/2 - 4*t**2. Factor d(z).
3*(z - 2)*(z + 1)/2
Let h(u) = u**4 + u**2 - u + 1. Let v(r) = -18*r**4 - 2*r**3 + 18*r**2 + 33*r - 5. Let t(i) = -18*h(i) - 2*v(i). Let t(d) = 0. What is d?
-1, -2/9, 2
Let r be (-2)/4 - ((-30)/8 + 3). Factor r*b**2 - b + 1.
(b - 2)**2/4
Factor -4/5 + 8/5*b**3 + 2/5*b**5 - 2*b + 8/5*b**4 - 4/5*b**2.
2*(b - 1)*(b + 1)**3*(b + 2)/5
Suppose 2*u - 8 = -3*v + 12, 0 = 5*u - v - 33. Suppose -4*f = -u*f. Factor -1/2*x**5 + 3/2*x**4 + 0*x + 1/2*x**2 + f - 3/2*x**3.
-x**2*(x - 1)**3/2
Let m be (-3 + 6 - -4)*2/7. Let u(q) be the third derivative of -49/300*q**5 + 0 - 2/15*q**3 + 7/30*q**4 + m*q**2 + 0*q. Factor u(g).
-(7*g - 2)**2/5
Let a be -4*-1*(3 + -2). Determine r, given that -3*r - a - 3*r**2 + 3*r + 4*r + 2*r**2 = 0.
2
Let o(l) be the second derivative of -1/8*l**4 + 5*l - 1/18*l**3 + 0 - 7/120*l**5 + 0*l**2. Factor o(d).
-d*(d + 1)*(7*d + 2)/6
Let y(b) be the second derivative of -3*b + 1/2*b**4 + 3/10*b**5 + 1/3*b**3 + 1/15*b**6 + 0 + 0*b**2. Find n such that y(n) = 0.
-1, 0
Let w(y) be the first derivative of -2*y**3/45 + 2*y**2/15 - 2*y/15 + 3. Suppose w(j) = 0. What is j?
1
Suppose 2*x = 5*x. Suppose x = w + 3 - 5. Solve -2*s - 8 - w*s**4 + 2*s**2 + 8 + 2*s**3 = 0 for s.
-1, 0, 1
Suppose -4*f + 2*l + 13 = 5*l, 2*l = -f + 2. Let b(q) be the first derivative of 0*q - 2*q**3 - 2/5*q**5 + 3/2*q**f + q**2 + 2. What is d in b(d) = 0?
0, 1
Suppose 1 - 13/3*a**2 - 13/6*a - 7/6*a**3 = 0. What is a?
-3, -1, 2/7
Solve -6/5*u - 2/5*u**2 - 4/5 = 0 for u.
-2, -1
Suppose z - 8 = 3*v - 5, 0 = 5*z - 3*v - 15. Let h = -852/7 - -122. Suppose 2/7*k**4 + 0 - h*k**2 + 0*k**z + 0*k = 0. Calculate k.
-1, 0, 1
Let r(m) = -8*m**2 + 8*m. Let z(w) = 7*w**2 - 7*w. Let f(t) = 2*r(t) + 3*z(t). Determine n, given that f(n) = 0.
0, 1
Let o(v) = v**2 + v. Let w(f) = -6*f**2 - 14*f + 4. Let a(b) = 8*o(b) + w(b). Suppose a(m) = 0. Calculate m.
1, 2
Let t(b) be the second derivative of -1/6*b**4 - 2*b**2 - 10*b - b**3 + 0. What is l in t(l) = 0?
-2, -1
Let m(v) = -2*v**4 + 10*v**2 - 6*v - 5. Let i(k) = -3*k**4 - k**3 + 21*k**2 - 13*k - 11. Let z(o) = 6*i(o) - 14*m(o). Suppose z(w) = 0. Calculate w.
-1, -2/5, 1
Let 1/5*n**4 - 1/5*n - 3/5*n**3 + 0 + 3/5*n**2 = 0. Calculate n.
0, 1
Let z = -2 + 5. Suppose 0 = z*y + d + 1 - 8, -1 = -y + d. Factor -2*s**2 - 3*s**3 - 3*s**2 + 3*s + y*s**2 + 3*s**4.
3*s*(s - 1)**2*(s + 1)
Let a(d) be the third derivative of d**5/390 + d**4/52 + 2*d**3/39 + 9*d**2. Factor a(w).
2*(w + 1)*(w + 2)/13
Let c(l) be the first derivative of -l**7/840 + l**6/360 + l**5/120 - l**4/24 + l**3 + 1. Let v(m) be the third derivative of c(m). What is n in v(n) = 0?
-1, 1
Let k(l) = -3*l**3 - l**3 + 1 - 7*l**2 + 3*l**3 - 8*l. Let b(h) = h**2 + h - 1. Let j(n) = -6*b(n) - 2*k(n). Solve j(s) = 0.
-2, -1
Let m be -1*(-10)/2 - 0. Let d(u) = u**3 + 2*u**2 + u + 2. Let i = -2 + 0. Let g(t) = 2*t**3 + 5*t**2 + 3*t + 5. Let x(c) = i*g(c) + m*d(c). Factor x(a).
a*(a - 1)*(a + 1)
Let f be (-88)/(-18) - ((-3 - -7) + 0). Suppose 4/9 - 32/9*t**4 - 22/9*t + 14/9*t**5 + f*t**3 + 28/9*t**2 = 0. What is t?
-1, 2/7, 1
Let j(b) be the first derivative of -4*b**3/7 + 13*b**2/7 - 12*b/7 - 3. Suppose j(y) = 0. Calculate y.
2/3, 3/2
Let q be ((-24)/(-4))/(-3 - -6). Suppose 0 = q*x - 4*p - 16, 4*x - 2*x - 2 = -3*p. Solve 2*t**3 - 2*t**2 - 1/5 + 1/5*t**5 + t - t**x = 0 for t.
1
Let a(h) be the second derivative of h**5/5 + 2*h**4 + 6*h**3 - 2