-3. Factor k*t**3 - 2*t**4 + t**4 + t**2 + 2*t - 4*t.
-t*(t - 2)*(t - 1)*(t + 1)
Let y = 32 - 30. Let f be (y - 2)/(-10 + 12). Factor 4/5*v**5 + 0 + f*v**3 + 6/5*v**4 - 2/5*v**2 + 0*v.
2*v**2*(v + 1)**2*(2*v - 1)/5
Let -2/17 - 2/17*w**3 - 6/17*w**2 - 6/17*w = 0. Calculate w.
-1
Determine x so that -3/2 - 3/2*x**4 + 3/2*x - 3*x**3 + 3*x**2 + 3/2*x**5 = 0.
-1, 1
Let w(j) = 3*j**4 - 6*j**3 + 6*j**2 - 6*j + 6. Let p be 3/15 + 58/10. Let g(i) = 4*i**4 - 7*i**3 + 7*i**2 - 7*i + 7. Let f(a) = p*g(a) - 7*w(a). Factor f(n).
3*n**4
Factor -2 + 1504*l**2 - 3*l**3 + l**3 + 2*l - 1502*l**2.
-2*(l - 1)**2*(l + 1)
Factor 1/4*i**4 - 1/4*i**2 - 1/2*i**3 + 1/2*i + 0.
i*(i - 2)*(i - 1)*(i + 1)/4
Factor -4*r**2 + 5*r**2 + 105*r - 102*r + 2.
(r + 1)*(r + 2)
Let j(i) be the second derivative of -2*i**7/63 - 4*i**6/45 + 2*i**4/9 + 2*i**3/9 + 14*i. Find g, given that j(g) = 0.
-1, 0, 1
Determine p, given that 4/7*p + 0 - 2/7*p**2 = 0.
0, 2
Let l = -7 + 6. Let q be (-1)/(l - (-2)/3). Suppose c**4 - 5*c**4 + 3*c**4 + 6*c**3 - q*c**3 - 2*c**2 = 0. What is c?
0, 1, 2
Let v(c) be the second derivative of -c**7/70 - c**6/50 - 14*c. Factor v(f).
-3*f**4*(f + 1)/5
Let v(s) = s**2 - s + 2. Suppose 5*z - 29 = -9. Let p(a) = 1. Let n(y) = z*p(y) - v(y). Factor n(b).
-(b - 2)*(b + 1)
Let a(u) = -u + 2. Let j be a(0). Let s be 5/j - (-4)/8. Solve 2*d**s + 0*d**3 - 4*d**5 - 2*d**5 + 4*d**4 = 0.
-1/3, 0, 1
Solve 2/3*v**2 - 4/3*v + 0 = 0 for v.
0, 2
Suppose 3*v = 2*v + 3. Let u(d) be the first derivative of 3 + 2/7*d**2 - 2/7*d - 2/21*d**v. Let u(r) = 0. Calculate r.
1
Let v be (0/3 + 0)/(5 + -4). Let m(h) be the third derivative of 0*h**5 - 1/168*h**8 + 0*h**6 - 1/105*h**7 + 0*h**3 + h**2 + 0*h + 0 + v*h**4. Factor m(i).
-2*i**4*(i + 1)
Let g(p) be the first derivative of -p**3/15 + p/5 - 5. What is u in g(u) = 0?
-1, 1
Suppose 2*p = 2*j + 2*j - 6, 4*j + 15 = -5*p. Find h, given that -6*h**3 - 15/2*h**2 - 3/2*h + j = 0.
-1, -1/4, 0
Let u be 0/(3/3 - 3). Let n(z) be the second derivative of 0 - 1/24*z**4 - 2*z + 0*z**3 - 1/40*z**5 + u*z**2. Factor n(l).
-l**2*(l + 1)/2
Let t(a) = 5*a**2 + 5*a**4 - 1 - a**3 - 3*a**3 + 8. Let l(f) = 2*f**4 - 2*f**3 + 2*f**2 + 3. Let s(p) = -7*l(p) + 3*t(p). Factor s(z).
z**2*(z + 1)**2
Let p be 2/(-7)*14/(-6). Let x = 54 + -51. Determine b, given that 2/3*b**2 - 2/3*b + p*b**x - 2/3 = 0.
-1, 1
Let s(h) be the first derivative of -h**9/15120 + h**8/8400 + h**7/4200 - h**6/1800 - 5*h**3/3 - 1. Let t(n) be the third derivative of s(n). Factor t(x).
-x**2*(x - 1)**2*(x + 1)/5
Let p(n) be the first derivative of 1/24*n**4 + 5/12*n**2 - 1/3*n - 2/9*n**3 - 5. Determine f, given that p(f) = 0.
1, 2
Let t(k) be the first derivative of 2/27*k**3 + 3 - 1/18*k**4 + 0*k**2 + 0*k. Factor t(x).
-2*x**2*(x - 1)/9
Let w(b) be the second derivative of b**6/45 - b**4/6 - 2*b**3/9 + b. Factor w(h).
2*h*(h - 2)*(h + 1)**2/3
Suppose 3*q - 21 = 3*h, -h - 6 = q - 3. Determine s, given that 2*s**2 + 3 + 4*s**2 - q*s**2 + 13 - 16*s = 0.
2
Factor 2/17*y**2 - 4/17 + 2/17*y.
2*(y - 1)*(y + 2)/17
Let o be (1 - 6/3)*-2. Suppose 3*n = -o*n + 20. Factor 0*z**3 - 2*z**n + 0*z - 2*z + 2*z**3 + 2*z**2.
-2*z*(z - 1)**2*(z + 1)
Factor -2/3*g**3 - 1/3*g + 5/3*g**2 - 2/3.
-(g - 2)*(g - 1)*(2*g + 1)/3
Determine g so that 4*g**2 - 20*g - 4*g + 23 + 13 = 0.
3
Solve -2/9*g**2 + 16/9*g + 2 = 0.
-1, 9
Let q(a) be the second derivative of a**6/90 - a**5/60 + 2*a. Solve q(m) = 0 for m.
0, 1
Let d(k) = -4*k**2 - 16*k - 13. Let r(j) = j**2 + 4*j + 3. Let t(z) = -6*d(z) - 26*r(z). Solve t(n) = 0 for n.
-4, 0
Let l be ((-8)/6)/(70/26376). Let d = 504 + l. Find t such that 24/5*t + 6*t**2 - d + 8/5*t**3 = 0.
-2, 1/4
Let y(h) be the first derivative of -2*h**6/3 + 13*h**5/5 - 15*h**4/4 + 7*h**3/3 - h**2/2 + 2. Determine o, given that y(o) = 0.
0, 1/4, 1
Let z(x) = -9*x**3 - x**2 + 10*x. Let c(l) = 3*l**3 - 3*l. Let i(d) = 8*c(d) + 3*z(d). Factor i(w).
-3*w*(w - 1)*(w + 2)
Let u = -4 + 1. Let f be (-4 + (u - -2))*-1. Find g such that -4/7 + 622/7*g**3 + 54/7*g - 624/7*g**4 + 32*g**f - 272/7*g**2 = 0.
1/4, 2/7, 1
Let h(a) be the second derivative of a**6/480 - a**5/240 - a**4/96 + a**3/24 - a**2 + a. Let w(j) be the first derivative of h(j). Factor w(b).
(b - 1)**2*(b + 1)/4
Let y(q) be the first derivative of -4*q**3/15 - 2*q**2 - 16*q/5 - 2. Suppose y(a) = 0. What is a?
-4, -1
Let h be 0/(-2 - (-3)/1). Let l be h + 2 + 10/(-5). Factor -1/4*i - 1/4*i**2 + l.
-i*(i + 1)/4
Let h(b) be the first derivative of 2*b**6/15 + 26*b**5/75 + b**4/10 - 22*b**3/45 - 3*b**2/5 - 4*b/15 - 18. Let h(r) = 0. Calculate r.
-1, -2/3, -1/2, 1
Let y(a) be the third derivative of -a**8/80640 - a**7/20160 + a**6/1440 - a**5/10 + 6*a**2. Let t(j) be the third derivative of y(j). What is p in t(p) = 0?
-2, 1
Let i(h) = -41*h**2 - 115*h - 24. Let f(y) = 81*y**2 + 230*y + 49. Let p(r) = -6*f(r) - 11*i(r). Factor p(m).
-5*(m + 3)*(7*m + 2)
Let t = -32 + 36. Let a(r) = r**3 + r**2. Let g be a(1). Factor 1 - t*x - g*x + 1 - 6*x**2 + 2*x.
-2*(x + 1)*(3*x - 1)
Suppose -4 - 2 = -3*d. Factor -2*n**2 + n**3 + 6*n**d + n**3 + 0*n**3.
2*n**2*(n + 2)
Suppose -9 = -5*l + 5*h + 11, 5*l - 4*h - 16 = 0. Factor 1/2*t**4 + 1/4*t**3 + l*t + 0 + 1/4*t**5 + 0*t**2.
t**3*(t + 1)**2/4
Let t(d) = -8*d**3 + 6*d - 3. Let o(u) = 9*u**3 - u**3 - 3*u - 2 + 4 - 3*u. Let k(r) = -5*o(r) - 4*t(r). Factor k(l).
-2*(l - 1)*(2*l + 1)**2
Let p(v) be the third derivative of -v**7/70 - v**6/10 + v**5/10 + 3*v**4/2 - 9*v**3/2 - 10*v**2. Solve p(j) = 0.
-3, 1
Let w be (-12)/(-20)*(-80)/(-108). Factor -2*m + 32/9*m**2 + w - 2/9*m**5 - 28/9*m**3 + 4/3*m**4.
-2*(m - 2)*(m - 1)**4/9
Let h(z) be the third derivative of -z**7/2520 - z**6/720 - z**4/24 + 4*z**2. Let q(a) be the second derivative of h(a). Factor q(x).
-x*(x + 1)
Let i(v) = 0 + v**2 + 3 - 4*v**2 + 7*v. Let r(p) be the first derivative of -p**3/3 + p**2 + p + 1. Let q(z) = 2*i(z) - 7*r(z). Let q(s) = 0. What is s?
-1, 1
Let j(l) = -9*l**4 + 9*l**3 + 2*l**2 - 9*l + 7. Let w(b) = 5*b**2 - 2*b**4 - 16*b**4 + 19*b**3 - 19*b - 4 + 7 + 10. Let c(r) = 5*j(r) - 3*w(r). Factor c(h).
(h - 1)*(h + 1)*(3*h - 2)**2
Let h = -338/3 - -113. Let l(k) be the third derivative of 0*k - h*k**3 - 1/240*k**6 - 1/24*k**5 - 1/6*k**4 + 0 + 3*k**2. Factor l(a).
-(a + 1)*(a + 2)**2/2
Let j be (4 + (-55)/15)/(3/2). Factor 2/9*w - j*w**3 + 2/9*w**2 - 2/9.
-2*(w - 1)**2*(w + 1)/9
Suppose -y - 3*c + 15 = 0, 2*y - 3*c - c + 10 = 0. Determine j so that -1/2*j**4 + 0*j**y + j**2 + 0*j - 1/2 = 0.
-1, 1
Let q(g) = 2*g**4 - 24*g**3 + 40*g**2 + 168*g + 98. Let n(m) = 2*m**4 - 24*m**3 + 39*m**2 + 168*m + 98. Let u(y) = -4*n(y) + 5*q(y). Factor u(t).
2*(t - 7)**2*(t + 1)**2
Let p(d) be the third derivative of 1/96*d**4 + 0*d - 3*d**2 - 1/480*d**6 + 0 - 1/12*d**3 + 1/120*d**5. Factor p(y).
-(y - 2)*(y - 1)*(y + 1)/4
Let r(c) = c**5 - c**3 + c**2 - c - 1. Let p(n) = n**5 - 2*n**4 + 6*n**2 - 3*n - 4. Let f(b) = p(b) - 2*r(b). Factor f(x).
-(x - 1)**2*(x + 1)**2*(x + 2)
Let f be 0 + (-33)/(-9) - 3. Let l = 4 + -10/3. Factor 0 - f*q**2 - 4/3*q**3 - l*q**4 + 0*q.
-2*q**2*(q + 1)**2/3
Suppose 0 + 1/6*r**2 + 0*r - 1/6*r**4 + 0*r**3 = 0. Calculate r.
-1, 0, 1
Let p(m) = -3*m - 4 + 3 + m + 3 - 2*m**4. Let k(d) = d**5 - d**4 + d**3 - 3*d + 3. Let w(s) = -2*k(s) + 3*p(s). Suppose w(c) = 0. Calculate c.
-1, 0
Let g(i) be the second derivative of -1/3*i**3 - 1/12*i**4 - 1/2*i**2 + 0 - 6*i. Find w, given that g(w) = 0.
-1
Let d(n) be the second derivative of -n**4/6 - 2*n**3/3 - n**2 + 3*n. Factor d(f).
-2*(f + 1)**2
Let g be (-10)/6*(15/(-9))/5. Let w(k) be the first derivative of -g*k**3 - 2/3*k + 3 - 7/6*k**2. Find m such that w(m) = 0.
-1, -2/5
Let o(g) be the second derivative of 2*g**6/15 + 4*g**5/5 + 4*g**4/3 + 11*g. What is b in o(b) = 0?
-2, 0
Factor 58/17*p**3 + 4/17 + 30/17*p + 66/17*p**2 + 18/17*p**4.
2*(p + 1)**3*(9*p + 2)/17
Solve -26/3*w**4 - 22/3*w**2 + 0 + 0*w + 2/3*w**5 + 46/3*w**3 = 0.
0, 1, 11
Let q(a) = 17*a**4 + 28*a**3 - 18*a**2 - 25*a - 8. Let d(v) = -v**4 + v**3 - v**2 - 1. Let x(w) = -3*d(w) + q(w). Factor x(z).
5*(z - 1)*(z + 1)**2*(4*z + 1)
Let a = -22 - -26. Let b(d) be the second derivative of -4/7*d**2 + d + 12/7*d**3 - 27/14*d**a + 0. Factor b(u).
-2*(9*u - 2)**2/7
Let z be (0 - (-4)/(-1)) + 51 + -47. Factor 1/5*b**5 + 0*b**2 + 0*b + 