. Factor 2/3*l - 4/3*l**3 - g*l**4 - 2/3 + 2/3*l**5 + 4/3*l**2.
2*(l - 1)**3*(l + 1)**2/3
Suppose 0 = -5*n, 0 = -97*y + 98*y + 3*n. Factor -2/3*t**3 + 2/3*t**2 + y*t + 0.
-2*t**2*(t - 1)/3
Let u(m) be the third derivative of -m**7/35 + 133*m**6/240 + 193*m**5/180 + 119*m**4/144 + m**3/3 + 102*m**2. Solve u(q) = 0 for q.
-1/3, -1/4, 12
Let k = -89043/7 + 12721. Factor k - 2/7*u - 2/7*u**2.
-2*(u - 1)*(u + 2)/7
Let w(s) = 21*s**3 + 144*s**2 - 354*s + 18. Let p(v) = 6*v**3 + 41*v**2 - 101*v + 5. Let y(x) = -18*p(x) + 5*w(x). Solve y(o) = 0 for o.
-8, 0, 2
Let o = -25 - -29. Suppose o*x - 6*k + k = 21, -4*k - 24 = -5*x. Find j such that 24*j - 5 - 3 + 3*j**3 - x + 0 - 15*j**2 = 0.
1, 2
Suppose 0*u = 2*u - 48. Suppose 4*x - 4*p - u = 0, -p = -2*x - 2*x + 21. What is y in 1/5*y**x - 2/5 + 0*y**4 - 4/5*y**3 + 3/5*y + 2/5*y**2 = 0?
-2, -1, 1
Let u(k) be the third derivative of k**8/168 - k**6/12 + k**4/3 + 54*k**2. Suppose u(g) = 0. What is g?
-2, -1, 0, 1, 2
Let p(u) be the second derivative of 1/120*u**6 + 5/24*u**4 + 4*u + 1/2*u**2 + 1/3*u**3 + 1/15*u**5 + 0. Let b(n) be the first derivative of p(n). Factor b(q).
(q + 1)**2*(q + 2)
Let w be (-12)/(-18)*15 - 5. Suppose -4*k + 27 = 3*j, -3*k + 40 = 2*k + w*j. What is s in 2/3*s + 0 + 2/3*s**k - 4/3*s**2 = 0?
0, 1
Suppose 4 = 2*g - 20. Let y(x) = -x + 14. Let m be y(g). Factor t**2 + 12*t**2 + 13*t**3 - 23*t**3 + 2*t**4 - 6*t + t**m.
2*t*(t - 3)*(t - 1)**2
Let k(o) be the second derivative of o**7/35 + o**6/15 - 49*o**5/50 - 97*o**4/30 + 22*o**3/5 + 72*o**2/5 + 49*o - 1. Solve k(n) = 0 for n.
-3, -2/3, 1, 4
Let n be 4*(4 + 7/(-2)). Let a be (-28)/(-6) - n/3. Find y such that 0*y - 18/5*y**a - 2/5*y**2 + 0 + 12/5*y**3 + 8/5*y**5 = 0.
0, 1/4, 1
Let w(l) = l**3 + 6*l**2 - 7*l + 1. Let b be w(-7). Let v(x) = 5*x + 2. Let j be v(b). Factor -11*h**3 - 2*h - 1 - 6*h**2 + j*h**3 - h**4 - 2*h.
-(h + 1)**4
Suppose 5*m - 5*p - 15 = -3*p, -m + 3*p - 10 = 0. Suppose -4*t + 13 = z, -t + m*z + 27 = 2*t. Factor 3*h**2 - 8*h**3 - 7*h**4 + 3*h**t - 7*h**2.
-4*h**2*(h + 1)**2
Let i(w) be the second derivative of -1/4*w**2 - 7/16*w**5 - 11/120*w**6 + 0 - 17/24*w**3 - 13/16*w**4 - 3*w. Factor i(r).
-(r + 1)**3*(11*r + 2)/4
Let s(z) = z**3 + 30*z**2 + 113*z + 234. Let a be s(-26). Factor 0*d - 2/3*d**2 - 2/3*d**3 + a.
-2*d**2*(d + 1)/3
Let y(r) be the first derivative of 3*r**4/16 - 3*r**3/2 + 15*r**2/8 + 9*r + 158. Solve y(u) = 0 for u.
-1, 3, 4
Let v = 68623/4 + -17155. Suppose -3/4*k + 3/2 - v*k**2 = 0. Calculate k.
-2, 1
Let f be (-2 - -14)/((-4)/(-2)). Solve 4*p - 25*p**3 - 18*p + 47*p**2 + 18*p**2 - 20 - f*p = 0 for p.
-2/5, 1, 2
Let u(x) be the first derivative of -2 - 8/13*x - 2/39*x**3 + 4/13*x**2. Suppose u(i) = 0. Calculate i.
2
Let p(n) be the second derivative of n**5/20 + n**4/4 + 3*n**2/2 + 19*n. Let h(x) be the first derivative of p(x). Determine m so that h(m) = 0.
-2, 0
Let p(f) be the first derivative of -2*f**3/3 + 360*f**2 - 64800*f + 514. Suppose p(o) = 0. Calculate o.
180
Let v(r) be the second derivative of 1/6*r**6 + 13/20*r**5 + 7/16*r**4 - 1/3*r**3 - 9*r + 0 - 1/2*r**2. Determine l so that v(l) = 0.
-2, -1/2, 2/5
Let g(i) be the third derivative of -i**8/280 + 2*i**7/525 + 7*i**6/100 + 2*i**5/75 - i**4/5 + 21*i**2 - 3*i. Find r such that g(r) = 0.
-2, -1, 0, 2/3, 3
Let u = -410 + 413. Let b(v) be the first derivative of 3/2*v**4 + 8*v + 22/3*v**3 - u + 12*v**2. Factor b(o).
2*(o + 1)*(o + 2)*(3*o + 2)
Let d(w) be the second derivative of 2/7*w**2 - 1/140*w**5 - 1/28*w**4 + 0*w**3 - 22*w + 0. Factor d(q).
-(q - 1)*(q + 2)**2/7
Let v = 1740 + -34797/20. Let a(g) be the second derivative of -v*g**5 - g**4 - 6*g - 5/2*g**3 + 0 - 3*g**2. Determine j, given that a(j) = 0.
-2, -1
Let b(v) be the first derivative of -2*v**3/21 + 2*v**2 - 90*v/7 + 333. Suppose b(x) = 0. Calculate x.
5, 9
Let j = 22 - 37. Let w = j + 15. What is p in -2*p**2 - 2*p**3 - p**5 + 2*p**4 + 3*p**5 + w*p**5 = 0?
-1, 0, 1
Find c, given that 1424*c**2 - 17*c**4 - 10900*c - 1402*c**2 + 1876*c + 4774*c**2 - 192*c**3 + 19*c**4 + 4418 = 0.
1, 47
Let j(y) be the third derivative of 1/84*y**8 + 0*y**5 - 2*y**2 + 0*y**4 + 1/30*y**6 + 0 + 0*y + 0*y**3 - 4/105*y**7. Let j(p) = 0. What is p?
0, 1
Let w(z) = -z**3 - 5*z**2 + 7*z + 11. Let n be w(-6). Determine a so that 67*a + n*a**2 + 69*a - 126*a = 0.
-2, 0
Let l(a) = a**3 + 6*a**2 - 8*a - 5. Let m be l(-7). Suppose -m*j + 42 - 134 = -5*i, 2*i - j = 37. What is g in -4 + 2 - 3*g**2 - 25 + 0*g**2 - i*g = 0?
-3
Let s be (9/(-2))/(57/(-38)). Let g(o) be the third derivative of -2*o**2 + 4/3*o**s + 0 + 1/15*o**5 + 0*o - 1/2*o**4. Let g(y) = 0. What is y?
1, 2
Let i(k) be the third derivative of k**6/60 + 2*k**5/3 + 37*k**4/12 + 6*k**3 + 9*k**2. Find d, given that i(d) = 0.
-18, -1
Suppose 0 = 107*w - 101*w. Let x(g) be the first derivative of 0*g + 5 + w*g**2 + 1/5*g**5 - 1/6*g**3 + 1/8*g**4. Solve x(y) = 0.
-1, 0, 1/2
Factor 0 - 2/3*y**2 + 20/9*y - 2/9*y**4 - 4/3*y**3.
-2*y*(y - 1)*(y + 2)*(y + 5)/9
Let b(t) be the second derivative of t**5/5 + t**4/3 - 4*t**3/3 + 49*t. Suppose b(d) = 0. Calculate d.
-2, 0, 1
Suppose -4*c = -5*m - 42 + 222, c - 59 = -2*m. Factor -61*h**3 + m*h**3 + 2*h**4 + 31*h**3.
2*h**3*(h + 1)
Suppose 0 = -25*b + 113 - 38. Factor 2/7*v**b - 1/7*v**5 + 1/7*v**4 + 1/7 - 2/7*v**2 - 1/7*v.
-(v - 1)**3*(v + 1)**2/7
Let -1/2 - 3*k + 27/8*k**5 + 41/8*k**3 - 21/8*k**2 + 69/8*k**4 = 0. Calculate k.
-1, -2/9, 2/3
Let n(h) be the first derivative of 15 + 5*h**2 - 5*h - 5/3*h**3. Suppose n(a) = 0. What is a?
1
Let m(k) be the second derivative of 3/40*k**5 - 1/4*k**3 + 3/4*k**2 - 10*k - 1/8*k**4 + 0. Factor m(z).
3*(z - 1)**2*(z + 1)/2
Let u = 63962/13 - 4920. Factor 4/13*i - 2/13*i**2 - u.
-2*(i - 1)**2/13
Let o(a) be the second derivative of a**6/2700 + 7*a**5/900 + a**4/30 - 2*a**3/3 + 9*a. Let v(s) be the second derivative of o(s). Factor v(l).
2*(l + 1)*(l + 6)/15
Suppose 0 = 4*l - 4*v, -5*l - 2*v - v = -24. Factor 6*a + 14*a**3 - 9*a**l + 3*a**2 - 8*a**3 - 3*a - 3.
-3*(a - 1)**2*(a + 1)
Factor -1/5*j**2 + 2/5*j + 7.
-(j - 7)*(j + 5)/5
Let m be (27/21 - 1)*25/10. Find k such that m*k**2 + 9/7*k + 2/7 - k**4 - 9/7*k**3 = 0.
-1, -2/7, 1
Suppose 5*k = 21 - 1, 4*u = 2*k + 4. Suppose 0 = 4*t + 3*c, 0*c = u*t + 2*c. Factor t + 2*l**2 + 3 - 8 + 3*l**2.
5*(l - 1)*(l + 1)
Let y(n) = -10*n**5 + 30*n**4 - 230*n**3 - 75*n**2 + 225*n. Let p(r) = r**5 + 2*r**4 + r**2. Let k(t) = 15*p(t) + y(t). What is s in k(s) = 0?
-15, -1, 0, 1, 3
Factor 4*s**4 + 17784*s**2 - 207*s**3 - 363856*s + 127040*s + 219488 - 253*s**3.
4*(s - 38)**3*(s - 1)
Factor -1222507 - n**4 + 511*n**3 + 3783065*n - 3690493 + 1216635*n - 87210*n**2.
-(n - 170)**3*(n - 1)
Factor -20*o - 49/4*o**2 + 3 + 43/4*o**3.
(o - 2)*(o + 1)*(43*o - 6)/4
Let z(y) be the first derivative of 6*y**5/35 - 53*y**4/14 + 198*y**3/7 - 69*y**2 - 56*y + 2. Suppose z(j) = 0. Calculate j.
-1/3, 4, 7
Let s(v) = -v**3 - 3*v**2 + 7. Let b(f) = f**3 + 2*f**2 - f - 6. Let z(m) = 3*b(m) + 4*s(m). Factor z(t).
-(t - 1)*(t + 2)*(t + 5)
Let v(d) = 3*d - 11. Let m be v(8). Let x = m + 10. Factor -3*q - x*q**3 + 17*q**3 + q + 8*q**3.
2*q*(q - 1)*(q + 1)
Let v = -187 + 187. Let o(c) be the second derivative of 1/40*c**5 + 0*c**2 - 1/48*c**4 + v*c**3 - 1/120*c**6 + 0 - 5*c. Factor o(h).
-h**2*(h - 1)**2/4
Let q = -60 + 46. Let r be ((-4)/(-1))/((-28)/q). Factor -2/3*t - 1/3 - 1/3*t**r.
-(t + 1)**2/3
Let q(w) = -20 + 7 - w + 1 + 5*w. Let u be q(4). Find o, given that 3/4*o**u + 0 + 3*o - 9/4*o**3 + 0*o**2 = 0.
-1, 0, 2
Solve 2/15*a**3 - 6/5*a + 24/5 - 8/15*a**2 = 0 for a.
-3, 3, 4
Let g(z) be the third derivative of -z**8/728 + 4*z**7/273 - 9*z**6/260 - 31*z**5/195 + z**4 - 24*z**3/13 - 2*z**2 + 11*z. Determine s, given that g(s) = 0.
-2, 2/3, 2, 3
Suppose -5*z + 6*l - 2*l - 54 = 0, 2*z - 3*l = -23. Let p be z - -11 - 3/5. Factor -4/5*k**2 - 2/5*k - p*k**3 + 0.
-2*k*(k + 1)**2/5
Solve 17/7*w - 2/7*w**2 - 1/7*w**5 + 10/7*w**4 - 16/7*w**3 - 8/7 = 0 for w.
-1, 1, 8
Let z(y) = -y**3 - 3*y**2 - 3*y - 4. Let o be z(-3). Determine g, given that 6*g**3 - 2*g**4 + 4*g**o - 5*g**5 - 7*g**4 + 4*g**5 = 0.
0, 1, 2
Let g = 38 + -26. Factor 12*p + g*p**2 - 2 + 10 - 8*p**2.
4*(p + 1)*(p + 2)
Factor 5*t**4 + 5003 - 52*t**3 + 132*t**2 - 2*t**4 + t**4 - 124*t - 4963.
4*(t - 10)*(t