**2 - 1. Factor f(v).
2*(v - 1)**2*(v + 1)*(v + 5)/5
Let s be (-20)/(8/(-4)) + 3. Let n = s - 11. Find p, given that -7/2*p + 5/2*p**n + 1 = 0.
2/5, 1
Factor 6*v - 9 - 3/4*v**3 + 3/4*v**2.
-3*(v - 2)**2*(v + 3)/4
Let l = -23/39 - -12/13. Let u = -311 + 313. Factor -2/3*m**3 + 2/3*m - 1/3*m**u + l.
-(m - 1)*(m + 1)*(2*m + 1)/3
Let k(t) = 0 + 17*t**2 - 2*t**2 - 3*t**3 + 4 + 2 - 21*t. Let v(c) = 3*c**3 - 15*c**2 + 21*c - 5. Let z(a) = 4*k(a) + 3*v(a). Factor z(u).
-3*(u - 3)*(u - 1)**2
Let i(c) be the third derivative of 2*c**3 + 0*c - 2*c**2 + 23/12*c**4 + 0 + 1/12*c**6 + 11/15*c**5. Determine o, given that i(o) = 0.
-3, -1, -2/5
Let i(z) = 2*z**2 - z - 2. Let r be i(2). Let l be (r/14)/((-7)/(-49)). Suppose 1/4*b**l + 1/2*b + 1/4 = 0. Calculate b.
-1
Let i(z) = -2*z**5 - 11*z**3 - 5*z**2 + 8*z. Let s(o) = -o**5 - 10*o**3 - 4*o**2 + 7*o. Let y(g) = 4*i(g) - 5*s(g). Factor y(a).
-3*a*(a - 1)**2*(a + 1)**2
Let z be (-1 - -1)/(0 + 3). Suppose -4 = 2*t - 8. Find k such that 1/2*k**t + k + z = 0.
-2, 0
Factor k**5 + 2*k + 8*k**2 - 13*k**2 + 9*k**3 - 5*k**4 - 2*k**2.
k*(k - 2)*(k - 1)**3
Factor 4*p + 5*p**2 + p**3 + 11*p**2 - 11*p**2.
p*(p + 1)*(p + 4)
Suppose 0*n + 5*n = 10. Let r = -1099/3 - -367. Find i such that 0*i + r - 2/3*i**n = 0.
-1, 1
Suppose 0 = 5*f + 5 - 0, -5*f + 4 = 3*d. Factor 3*b - 2*b**3 - 3*b**3 + 2*b**d + 0*b**3.
-3*b*(b - 1)*(b + 1)
Let l(n) be the third derivative of 0*n + 1/48*n**4 + 0*n**3 + 0 - 1/120*n**5 - 4*n**2. What is p in l(p) = 0?
0, 1
Suppose g = 3*g - 12. Let x(q) = -g - q**2 - q + 7*q + 0*q - 3*q. Let h(v) = -2*v**2 + 6*v - 11. Let l(s) = 4*h(s) - 7*x(s). Factor l(a).
-(a - 2)*(a - 1)
Let d(q) be the first derivative of q**4/30 + 4*q**3/15 + 3*q**2/5 + 1. Solve d(l) = 0.
-3, 0
Let x(r) = 2*r - 12. Let w be x(7). Find l, given that 2*l**4 - 6*l**4 + 3*l**4 + w*l**4 = 0.
0
Let g(l) be the third derivative of 1/10*l**5 - 2*l**2 - 1/6*l**4 + 0*l**3 + 0 + 0*l. What is w in g(w) = 0?
0, 2/3
Let g(d) = 45*d**4 + 165*d**3 + 177*d**2 - 57*d - 105. Let w(t) = 11*t**4 + 41*t**3 + 44*t**2 - 14*t - 26. Let c(l) = 2*g(l) - 9*w(l). What is h in c(h) = 0?
-2, -1, 2/3
Suppose 0 = 9*m + 3*m. Solve 1/6*o**4 - 1/3*o**3 + m + 1/6*o**2 + 0*o = 0 for o.
0, 1
Let v be 3/(-12) + 7/14. Factor -v*d**2 + 0*d + 1/4.
-(d - 1)*(d + 1)/4
Let o(f) be the first derivative of -f**6/2 - 3*f**5/25 + 3*f**4/4 + f**3/5 + 7. Let o(t) = 0. Calculate t.
-1, -1/5, 0, 1
Let r be -2 + 5 - (-368)/(-144). Factor r*b - 2/3 + 2/9*b**2.
2*(b - 1)*(b + 3)/9
Let j(v) be the first derivative of 3 + 1/3*v**6 + 0*v**3 + 0*v**4 + 0*v + 0*v**2 + 0*v**5. Factor j(n).
2*n**5
Factor 0*t + 0 + 1/6*t**2 + 1/6*t**3.
t**2*(t + 1)/6
Suppose 2*g - x - 4 = -0*g, -16 = 3*g + 4*x. Find d such that -8/7*d**3 - 4/7*d + g + 10/7*d**2 + 2/7*d**4 = 0.
0, 1, 2
Suppose 3*t - 7 = 8. Let y be 12/t + (-12)/30. Suppose 0 + 4/9*u**y + 2/9*u**4 - 2/3*u**3 + 0*u = 0. Calculate u.
0, 1, 2
Let l be 1 - 6 - -2 - -6. Suppose 3*j**3 + l*j**3 + 2*j**2 - 5*j**3 = 0. What is j?
-2, 0
Let w(l) be the first derivative of -l**6/40 + 3*l**5/20 - l**4/4 - 2*l**2 + 1. Let x(a) be the second derivative of w(a). Factor x(k).
-3*k*(k - 2)*(k - 1)
Find b such that 3/7*b**4 - 6/7*b**2 + 0*b + 0*b**3 + 3/7 = 0.
-1, 1
Let p(f) be the second derivative of -f**6/70 + 3*f**5/28 - 2*f**4/7 + 2*f**3/7 - 9*f. Solve p(o) = 0 for o.
0, 1, 2
Let l be (-6 + 3)/(3/6 - 2). Suppose -3/4*g**3 - 1/4*g**4 - 3/4*g**l + 0 - 1/4*g = 0. Calculate g.
-1, 0
Factor -5 - 7/2*u - 1/2*u**2.
-(u + 2)*(u + 5)/2
Suppose -19 = -4*w + 1. Suppose w*z - z - 20 = 0. Suppose -3*l**5 + 3*l**z + l**5 + l**4 = 0. What is l?
-1, 0
Let q(t) = -t**3 + 6*t**2 - 8*t + 2. Let i be q(4). What is c in -2/7*c - 2/7*c**3 + 0 + 4/7*c**i = 0?
0, 1
Let y(k) be the first derivative of -k**6/600 - k**5/150 - k**2/2 - 8. Let p(o) be the second derivative of y(o). Let p(r) = 0. What is r?
-2, 0
Let o(u) = u - 2. Let l be o(4). Suppose l*p - 2 - 3*p - 2*p**2 + 0 - 3*p = 0. Calculate p.
-1
Factor n + 5 - 4 - n**2 + 1.
-(n - 2)*(n + 1)
Let q(m) = -m**2 - 7*m - 15. Let a be q(7). Let w = a - -797/7. Let -w*j**2 + 0 - 8/7*j**3 + 2/7*j = 0. Calculate j.
-1, 0, 1/4
Let a(u) be the third derivative of -1/72*u**4 + 1/315*u**7 - 1/90*u**5 + 0*u**3 + 1/1008*u**8 + 0*u + 4*u**2 + 0*u**6 + 0. Factor a(o).
o*(o - 1)*(o + 1)**3/3
Suppose 4*z - 2*q + 254 = -0*z, 112 = -2*z - 4*q. Let n = -432/7 - z. Factor -2/7*f - n*f**2 + 0.
-2*f*(f + 1)/7
Let n(b) be the first derivative of b**4/42 + b**3/21 + 7*b + 5. Let o(q) be the first derivative of n(q). Solve o(w) = 0.
-1, 0
Let o = -34 + 36. Let w(y) be the third derivative of y**o + 0 + 1/60*y**6 + 0*y + 1/4*y**4 - 1/3*y**3 - 1/10*y**5. Let w(v) = 0. Calculate v.
1
Let d(f) be the second derivative of 0*f**6 + 1/60*f**5 + 0*f**4 - 1/252*f**7 - 2*f + 0 + 0*f**2 - 1/36*f**3. Factor d(k).
-k*(k - 1)**2*(k + 1)**2/6
Let q(w) be the second derivative of w**5/4 - 5*w**4/6 - 5*w**3/6 + 5*w**2 - 9*w. Factor q(d).
5*(d - 2)*(d - 1)*(d + 1)
Let w(k) = -k**3 - 6*k**2 + 9*k + 5. Let r be w(-7). Let o be 2*((-19)/r - 2). Find j such that 0 - 4/9*j**2 - o*j - 2/9*j**3 = 0.
-1, 0
Factor -5*u**2 + 5*u**3 - 5*u + 5*u**4 + 8 + 0*u - 8.
5*u*(u - 1)*(u + 1)**2
Let a be 6/3 - -1 - (5 - 2). Factor -4/11*v**2 + 4/11*v**4 + a + 0*v**3 - 2/11*v + 2/11*v**5.
2*v*(v - 1)*(v + 1)**3/11
Let w(t) = 3*t - 3. Let n be w(2). Let q = -5 + 9. Factor 0*d**3 - 2*d**q + 0*d**4 + 0*d**3 + 2*d**n.
-2*d**3*(d - 1)
Let n(b) be the third derivative of -1/15*b**5 - 2*b**2 - 1/3*b**3 - 1/30*b**6 + 0*b + 7/24*b**4 + 0. Solve n(k) = 0 for k.
-2, 1/2
Let v(i) be the second derivative of -3/2*i**2 - 1/4*i**3 + 0 + 1/8*i**4 - 3*i. Find x such that v(x) = 0.
-1, 2
Let j(r) = r**2 + r - 4. Let y be j(-3). Factor 3 + 3 + 2*l + 7*l - 12*l**3 + 3*l**5 + 0*l**5 - 6*l**y.
3*(l - 2)*(l - 1)*(l + 1)**3
Let z(x) = -x**5 + 24*x**4 - 19*x**3 + 5*x**2. Let i(r) = -2*r**5 + 36*r**4 - 29*r**3 + 7*r**2. Let n(u) = 5*i(u) - 7*z(u). Factor n(l).
-3*l**3*(l - 2)**2
Let b(l) be the first derivative of l**7/84 - l**5/40 - 3*l - 3. Let k(o) be the first derivative of b(o). Solve k(p) = 0.
-1, 0, 1
Let d(i) be the third derivative of i**6/15 - i**5/10 - i**4/3 + i**3 - 4*i**2. Factor d(v).
2*(v - 1)*(v + 1)*(4*v - 3)
Suppose 0 = -p + 2*p - 12. Suppose -3*a = -0*a - p. Let -3 - a*g**2 + 4 + 3*g**2 = 0. Calculate g.
-1, 1
Let a(p) be the first derivative of p**4/2 - 2*p**3 - 1. Factor a(k).
2*k**2*(k - 3)
Let m = -2 + 5. Suppose r = -4*r. Factor r*c**5 - 2*c**5 - 2*c**3 + 0*c**5 + 4*c**m.
-2*c**3*(c - 1)*(c + 1)
Let w(g) be the third derivative of -g**8/16800 - g**7/12600 + g**5/30 - g**2. Let t(r) be the third derivative of w(r). Suppose t(a) = 0. What is a?
-1/3, 0
Let o(w) be the second derivative of -w**4/3 + 2*w**3/3 + 16*w. Let o(i) = 0. What is i?
0, 1
Let q(m) be the first derivative of 1/11*m**2 + 2 - 3/22*m**4 + 4/11*m - 8/33*m**3. Factor q(k).
-2*(k + 1)**2*(3*k - 2)/11
Let -10/3*b**3 + 2*b**2 - 8/3 + 10/3*b + 2/3*b**4 = 0. Calculate b.
-1, 1, 4
Suppose 5*r**2 - 7*r**4 + 0*r**3 - 4*r**2 + 2*r - 12*r**5 - 6*r**3 + 10*r**5 = 0. What is r?
-2, -1, 0, 1/2
Let g(w) be the second derivative of -w**4/6 - 2*w**3/3 - w**2 + 16*w. Factor g(r).
-2*(r + 1)**2
Let z(k) be the second derivative of -8*k**4/3 + 2*k**3/3 - 13*k. Suppose z(q) = 0. Calculate q.
0, 1/8
Let i(w) = -w**5 - 13*w**4 - 5*w**2 - 5*w. Let b(d) = 4*d**5 + 64*d**4 + 24*d**2 + 24*d. Let r(y) = -5*b(y) - 24*i(y). Solve r(f) = 0.
0, 2
Let g = -11 - -13. Let o(q) be the third derivative of -1/30*q**3 + 0 - 1/60*q**4 + 0*q - 1/300*q**5 - g*q**2. Solve o(x) = 0.
-1
Let c(o) be the third derivative of -o**6/480 + o**5/60 - o**4/24 - 27*o**2. Factor c(b).
-b*(b - 2)**2/4
Let j be (4/10)/(2/10). Let a(n) be the first derivative of -4/15*n**3 + 0*n**4 + 2/5*n + 0*n**2 - j + 2/25*n**5. Determine f, given that a(f) = 0.
-1, 1
Let f(d) = -11*d**2 - d + 10. Let w(u) = 10*u**2 - 10. Let a(v) = 5*f(v) + 6*w(v). Factor a(b).
5*(b - 2)*(b + 1)
Suppose 0 = -10*o + 72 - 22. Let i(u) be the third derivative of 16/3*u**3 + 4/5*u**o + 2/15*u**6 + 1/105*u**7 + 8/3*u**4 + 0 + 2*u**2 + 0*u. Factor i(d).
2*(d + 2)**4
Let 1/4*r**2 + 9/4 + 3/2*r = 0. Calculate r.
-3
Suppose 4*n + 2*d + d + 3 = 0, -2*n + 4*d = -4. Suppose 2*x - f = -0*f - 4, 0 = -x + 3*f - 12. Let 0 + n*h**2 