3 - 39*f**2 + f. Factor t(w).
-3*(w - 2)*(w + 2)*(7*w + 2)/4
Let x(v) be the second derivative of 0 + 1/10*v**6 + 0*v**3 - v + 0*v**2 + v**4 - 3/5*v**5. Factor x(q).
3*q**2*(q - 2)**2
Let d(g) be the second derivative of -g**9/98280 + g**8/14560 + g**7/4095 + g**4/12 - 3*g. Let t(m) be the third derivative of d(m). Factor t(q).
-2*q**2*(q - 4)*(q + 1)/13
Solve 1/4*f**5 - 11/2*f**2 + 8 - 8*f + 2*f**4 + 13/4*f**3 = 0 for f.
-4, -2, 1
Let o(n) = n**3 + n**2 + n. Let m(w) = 5*w**3 - 72*w**2 + 108*w + 64. Let v(z) = -m(z) - 4*o(z). Suppose v(l) = 0. Calculate l.
-4/9, 4
Let c be 320/100 - (-4)/30. Let a be (-6)/2 - (-78)/18. Factor a*y**3 - c*y + 2/3*y**2 + 4/3.
2*(y - 1)*(y + 2)*(2*y - 1)/3
Let j = 50876/3 + -16958. Factor -1/3*o**4 + 5/3*o**3 + 7/3*o - j - 3*o**2.
-(o - 2)*(o - 1)**3/3
Let a be (-1 + 5)/(5 + 5 + -8). Factor -5/2*r + 7/2*r**4 + 1 + 5/2*r**3 - 9/2*r**a.
(r - 1)*(r + 1)**2*(7*r - 2)/2
Let o(r) be the third derivative of r**10/22680 + r**9/5670 + 13*r**4/24 + 15*r**2. Let d(j) be the second derivative of o(j). Suppose d(t) = 0. What is t?
-2, 0
Let p(f) = -2*f**2 - 24*f - 22. Let g(c) = 2*c**2 + 23*c + 23. Let x(y) = 6*g(y) + 5*p(y). Factor x(m).
2*(m + 2)*(m + 7)
Let k(a) be the second derivative of 1/30*a**4 + 5*a**2 + 13*a + 2/3*a**3 + 0. Find z such that k(z) = 0.
-5
Let z = -6 - -9. Suppose -4*b - 1 = 5*s, 0 = -0*b + z*b + 2*s - 1. Factor x**2 + 3 + 0 + b - 5.
(x - 1)*(x + 1)
Let a(z) = 5*z**2. Suppose 6 - 4 = 2*h. Let f be a(h). Factor r**4 + 2*r**f - r**4 - 8*r**3 + 6*r**3.
2*r**3*(r - 1)*(r + 1)
Let q be ((-4)/(-18))/(515/927). Let -2/5*z**5 + 24/5*z + q*z**3 + 16/15 + 76/15*z**2 - 4/3*z**4 = 0. What is z?
-2, -1, -1/3, 2
Factor -2/7*f**2 - 1152/7 - 96/7*f.
-2*(f + 24)**2/7
Let l = -50 - -38. Let g(f) = f**3. Let w(t) = 8*t**2 + 4*t. Let y(p) = l*g(p) + w(p). Let y(m) = 0. Calculate m.
-1/3, 0, 1
Let v(z) = -z**2 - 40*z - 64. Let w be v(-38). Let r be 4/(-6)*(-54)/w. Let -48*t**3 - 39/2*t - 9/2*t**5 - 45*t**2 - r - 24*t**4 = 0. What is t?
-2, -1, -1/3
Let d = 112 - 58. Let q be d/(-12)*4*-1. Let -3*v**2 - 22*v**3 - q*v**3 - 19*v**3 + 56*v**3 = 0. What is v?
-1, 0
Factor 1365*g - 1701 + 4*g**3 - 96*g**2 - 2*g**3 + 171*g - 6491.
2*(g - 16)**3
Suppose 27*v + 45 = 68 + 85. Find f such that -15/7*f**5 + 30/7*f**3 + 6/7 + 6/7*f**v - 12/7*f**2 - 15/7*f = 0.
-1, 2/5, 1
Let o(l) be the third derivative of 2*l**7/315 - 4*l**6/45 + 7*l**5/15 - l**4 + 85*l**2. Factor o(r).
4*r*(r - 3)**2*(r - 2)/3
Let x(o) = -5*o - 27. Let r be x(-6). Factor 175*w - 180*w + w**2 + w**r + 0 + 3.
(w - 1)**2*(w + 3)
Suppose -15 = -5*c + 2*f + 24, -5*c + 43 = -4*f. Determine v, given that 2*v**5 - 12*v**4 + 0*v**5 - 29*v**2 - 4 + 18*v + 28*v**3 + c*v**2 - 10*v**2 = 0.
1, 2
Find f, given that -24*f**3 + 234*f**2 + 3/4*f**4 + 588 - 672*f = 0.
2, 14
Let l = 1483858 + -1060956729/715. Let g = l + -5/143. Determine c, given that 3/5*c**3 - 9/5*c**2 + g + 0*c = 0.
-1, 2
Let p(b) be the first derivative of -b**6/1260 + b**5/42 + b**3/3 + 45. Let c(t) be the third derivative of p(t). Factor c(x).
-2*x*(x - 10)/7
Suppose 0 = -f + 4*q + 21, -q - 10 = -2*f + 11. Let -g**3 - 4*g + 11*g**2 + 2*g**2 - f*g**2 = 0. Calculate g.
0, 2
Let u(d) = d**3 + 6*d**2 + 4*d - 3. Suppose -10*b + 6*b - 20 = 0. Let v be u(b). Factor -3/2*s**v + 0*s + 0 + 0*s**3 + 3/2*s**4.
3*s**2*(s - 1)*(s + 1)/2
Let i(h) = -h**4 - h**3 - h**2 - 2*h. Let k(y) = 10*y**4 + 100*y**3 - 130*y**2 - 55*y + 150. Let x(m) = -15*i(m) - k(m). Determine c so that x(c) = 0.
-1, 1, 2, 15
Let j(k) be the third derivative of -7/120*k**6 + 0*k**4 - 18*k**2 + 0*k**3 - 1/15*k**5 + 1/336*k**8 + 0 + 0*k - 1/105*k**7. Factor j(d).
d**2*(d - 4)*(d + 1)**2
Let u be (-7)/2*40/(-70). Let v be ((-4)/(-24))/(2/8). What is r in 2/3*r**u + r - v = 0?
-2, 1/2
Let d = 6000 - 6000. What is o in d + 3/8*o**2 - 3/4*o = 0?
0, 2
Suppose -2/7*a**3 - 88/7*a - 8 - 34/7*a**2 = 0. Calculate a.
-14, -2, -1
Let p(a) = 8*a - 8. Let v be p(4). Suppose -4*g = -0*g - v. Factor -l**2 - 2*l**2 + 6*l**2 - g*l.
3*l*(l - 2)
Factor 25/7*d**4 - 8/7*d**5 - 27/7*d**3 + 11/7*d**2 - 1/7*d + 0.
-d*(d - 1)**3*(8*d - 1)/7
Let q be (28/(-35))/((-44)/80). Factor -q - 2/11*f**2 - 12/11*f.
-2*(f + 2)*(f + 4)/11
Suppose 1584 = -19*k + 30*k. Solve 4*p - 12*p**3 - 4*p + 2*p + 4*p**5 - p**4 - k*p**2 + 139*p**2 = 0.
-1, 0, 1/4, 2
Let w = -9 + 11. Suppose 0 = -5*x - 3*f - 0 - 3, -2 = w*f. Factor -t + t**2 - 1/4*t**3 + x.
-t*(t - 2)**2/4
Let i(b) be the second derivative of -5*b**4/7 + 13*b**3/21 - b**2/7 + 75*b. Let i(n) = 0. What is n?
1/10, 1/3
Let i = -1/9217 + 36871/27651. Suppose i*v**3 - 4*v**2 + 0 + 8/3*v = 0. What is v?
0, 1, 2
Let z(y) be the second derivative of -y**5/50 + 4*y**4/5 - 11*y**3 + 242*y**2/5 - 176*y. Find k such that z(k) = 0.
2, 11
Let g(q) = q - 20 + 40 - 14 - 2*q. Let l be g(4). Factor 7/6*p**l + 8/3*p + 2/3.
(p + 2)*(7*p + 2)/6
Factor 1/2*t**3 - 5*t - 3 - 7/4*t**2 + 1/4*t**4.
(t - 3)*(t + 1)*(t + 2)**2/4
Let t(z) be the third derivative of -5*z**8/672 - 11*z**7/84 - 35*z**6/48 - 25*z**5/24 - 29*z**2. Factor t(r).
-5*r**2*(r + 1)*(r + 5)**2/2
Let d be 1/7 - (-5)/((-140)/(-1116)). Factor -3208*g - 40*g**3 + 144*g**2 - 39*g**2 + 3098*g + d + 5*g**4.
5*(g - 4)*(g - 2)*(g - 1)**2
Let k(m) be the third derivative of 1/4*m**5 + 0*m - 1/42*m**7 + 1/24*m**6 - 5/24*m**4 - 5/3*m**3 + 0 + 6*m**2. Factor k(a).
-5*(a - 2)*(a - 1)*(a + 1)**2
Let b = -11 + -4. Let r = b + 20. Determine x so that -r*x + 3*x - 3*x**2 + x - 3*x**3 - x**4 = 0.
-1, 0
Let j(l) = -l**3 + 8*l**2 - 6*l - 6. Let x be j(6). Suppose -p + 3*h = 10, -5*p + x = -0*p + 5*h. Let 4*g + 2 + 5/2*g**p + 1/2*g**3 = 0. What is g?
-2, -1
Let q(a) be the first derivative of -a**5/90 - a**4/18 - 2*a**3/27 + 36*a - 32. Let o(i) be the first derivative of q(i). Factor o(k).
-2*k*(k + 1)*(k + 2)/9
Let n = 883/108 + -33/4. Let b = n + 20/27. Factor b*k - k**2 + 0 + 1/3*k**3.
k*(k - 2)*(k - 1)/3
Factor -6*x**4 - 36*x**5 - 2*x**2 + 17*x**5 + 6*x**3 + 21*x**5.
2*x**2*(x - 1)**3
Suppose q = -3*s - 2*q + 12, -2*s = 3*q - 5. Let 22*l**2 - 2*l**2 + 30*l**3 + 20*l**4 + 5*l**5 + 0*l**4 - s*l + 12*l = 0. Calculate l.
-1, 0
Suppose -4*m - 30 = -2*k, 0 = -0*k + k - 5*m - 27. Let g be (10/(-40))/(k/(-8)). Find n, given that -g*n**2 + 2/7*n**4 - 2/7*n + 0 + 2/7*n**3 = 0.
-1, 0, 1
Let c(f) be the third derivative of f**5/15 - 43*f**4/3 + 3698*f**3/3 + 49*f**2 - f. Factor c(t).
4*(t - 43)**2
Let y be (6/81 - 207/243)/(7/(-6)). Determine v, given that 2/3*v**3 - y - 2*v**2 + 2*v = 0.
1
Let p = -61 + 245/4. Let t = -8740 + 8745. What is f in -1/4 - 1/4*f**4 + 1/4*f + 1/2*f**2 + p*f**t - 1/2*f**3 = 0?
-1, 1
Let h be (-1 - 1) + 4 - 1. Suppose -9 = -3*o + 3*b, 0 = -o - 5*b - 2 - h. Let -4 + 15*y + 12*y**o - 14*y**3 + 27*y + 28*y**4 - 36*y**3 - 28*y = 0. What is y?
-1/2, 2/7, 1
Let v(z) be the second derivative of -z**8/1680 + z**7/126 - 2*z**6/45 + 2*z**5/15 + 53*z**4/12 + 46*z. Let m(r) be the third derivative of v(r). Factor m(p).
-4*(p - 2)**2*(p - 1)
Let t = -17320/3 + 5775. Solve t*u**2 - 5/3*u**3 + 0 + 10/3*u = 0.
-1, 0, 2
Let b(j) be the second derivative of -j**5/30 - 5*j**4/12 - 3*j**2 + 7*j. Let f(w) be the first derivative of b(w). Solve f(u) = 0 for u.
-5, 0
Let y(b) be the first derivative of 8*b - 15 - 2*b**3 - 1/2*b**4 + 0*b**2. Factor y(a).
-2*(a - 1)*(a + 2)**2
Let j(l) = -3*l**2 - 9*l - 6. Let p(i) = 3*i**2 + 9*i + 6. Let r be (2/(-2) - -1) + 6. Suppose -29*q + 27*q = -10. Let k(x) = q*p(x) + r*j(x). Factor k(v).
-3*(v + 1)*(v + 2)
Let y = -153 + 155. Let u(b) be the second derivative of 0 + 0*b**3 - 1/18*b**4 + 0*b**y - 5*b. Suppose u(z) = 0. Calculate z.
0
Let r = 87 - 82. Let a(x) = 5*x**3 + 7*x**2 - 8*x - 4. Let h(q) = -9*q**3 - 13*q**2 + 14*q + 8. Let c(i) = r*a(i) + 3*h(i). Factor c(w).
-2*(w - 1)*(w + 1)*(w + 2)
Let x(c) be the second derivative of 5*c**4/12 + 200*c**3/3 + 4000*c**2 - 22*c - 3. Solve x(n) = 0 for n.
-40
Suppose 0*v + 10*v = -180. Let x be (6*-1)/(9/v). Factor 6*z**2 - x*z - 3/2*z**4 + 3*z**3 + 0.
-3*z*(z - 2)**2*(z + 2)/2
Let x(j) be the third derivative of -j**6/30 + 13*j**5/15 + 2*j**4/3 + 28*j**2. Let p(t) = t**3 - 17*t**2 - 5*t. Let g(c) = 16*p(c) + 5*x(c). Factor g(w).
-4*w**2*(w + 3)
Factor 2/3*w**3 - 22/3*w**2 + 24 + 16*w.
2*(w - 6)**2*(w + 1)/3
Let x(a) be the third derivativ