 -3*k**4 - 60*k**3 - 324*k**2 - 648*k. Let z(s) = -5*o(s) + 3*t(s). Factor z(q).
-3*q*(q + 6)**3
Suppose 7 + 14 = 3*z. Find u, given that z*u**2 + u**3 - 13*u**2 + 6*u - u**2 = 0.
0, 1, 6
Let x = 4 - 1. Factor -12*u**x - 6*u**3 + 16*u**3 + 2*u**2 + 4*u.
-2*u*(u - 2)*(u + 1)
Determine c so that 5*c**2 - 5*c**4 + 33*c - 74*c + 41*c = 0.
-1, 0, 1
Let q(s) = 2*s**3 - 4*s**2 + 2*s + 3. Let t(u) = 2*u**3 - 4*u**2 + 2*u + 4. Let l be (-8)/(-3)*36/24. Let v(o) = l*q(o) - 3*t(o). Determine x so that v(x) = 0.
0, 1
Let g be ((-6)/(-3297))/((-255)/335699). Let k = 2/471 - g. Factor 3/5*t**2 + k*t + 12/5.
3*(t + 2)**2/5
Suppose 0*d + 1/10*d**2 - 2/5 = 0. What is d?
-2, 2
Let g(w) be the third derivative of -w**7/1260 + w**6/80 + w**5/360 - w**4/16 - 172*w**2. Factor g(m).
-m*(m - 9)*(m - 1)*(m + 1)/6
What is t in 2*t**2 + 33/5*t**3 + 8*t**4 + 0 + 1/5*t + 16/5*t**5 = 0?
-1, -1/4, 0
Let v(q) be the second derivative of -q**6/300 + q**5/75 + q**4/60 - 2*q**3/15 + 7*q**2 + 15*q. Let p(t) be the first derivative of v(t). Factor p(b).
-2*(b - 2)*(b - 1)*(b + 1)/5
Let s(l) be the first derivative of l**7/840 - l**6/360 - l**5/120 + l**4/24 + 19*l**3/3 - 14. Let c(a) be the third derivative of s(a). Factor c(q).
(q - 1)**2*(q + 1)
Let k(r) = -3*r**5 - 10*r**4 - 7*r**3 - 3*r**2 + 3. Let s(d) = -32*d**5 - 110*d**4 - 78*d**3 - 34*d**2 + 34. Let z(l) = 68*k(l) - 6*s(l). What is y in z(y) = 0?
-1, -2/3, 0
Factor 4/7*z**5 + 52/7*z - 24/7*z**3 - 16/7*z**2 + 8/7*z**4 - 24/7.
4*(z - 1)**3*(z + 2)*(z + 3)/7
Let c = 724 + -720. Find v, given that -4/11*v - 8/11*v**3 + 2/11*v**c + 10/11*v**2 + 0 = 0.
0, 1, 2
Let h = -4391/18 + 244. Let p(z) be the first derivative of -h*z**3 + 0*z - 3 - 1/6*z**2. Suppose p(n) = 0. What is n?
-2, 0
Let u(q) = q**2 - q**3 + 3*q**4 - 2*q**4 - 2*q**5 + 3*q**5. Let x(v) = 2*v**4 + 2*v**2. Let f = -267 - -268. Let c(l) = f*x(l) - 2*u(l). Factor c(b).
-2*b**3*(b - 1)*(b + 1)
Let d(w) = -w**3 - w**2 + 2. Let o(k) = 4*k**4 + 8*k**3 + 5*k**2 + k + 2. Let q(i) = -d(i) + o(i). Determine j so that q(j) = 0.
-1, -1/4, 0
Let d(i) be the second derivative of -25*i + 0*i**2 + 1/21*i**4 + 0 - 2/7*i**3. Factor d(w).
4*w*(w - 3)/7
Let m(w) = -2*w**4 + 20*w**3 + 13*w**2 + 5. Let z(b) = -9*b**4 + 99*b**3 + 66*b**2 + 24. Let y(s) = -24*m(s) + 5*z(s). Solve y(n) = 0 for n.
-3, -2, 0
Let u be ((-24)/(-30))/((-2)/(-10)). Suppose -4*w = -5*x - u, 5*x + 2*w + 3 = 5*w. What is d in 0 - d + 0 + x*d - d**2 = 0?
-1, 0
Suppose -457 - 740 = -7*u. Let l = u + -1195/7. Find a, given that -4/7*a**5 - 4/7*a**3 + l + 8/7*a + 8/7*a**2 - 10/7*a**4 = 0.
-1, -1/2, 1
Factor -1/6*n**4 - 20/3*n - n**2 - 25/6 + 4/3*n**3.
-(n - 5)**2*(n + 1)**2/6
Factor 2/5*s**2 - 212/5*s + 5618/5.
2*(s - 53)**2/5
Let o(a) = -a**3 - a**2 + a. Let x(b) = -b**3 + 161*b**2 - 2186*b + 2028. Let j(s) = -2*o(s) - x(s). Factor j(y).
3*(y - 26)**2*(y - 1)
Let z(b) = -3*b + 4*b - b**2 + 0 - b**3 - 1. Let a(q) = -3*q**4 + 3*q**3 + 6*q**2 + 9*q - 9. Let v(n) = -a(n) + 9*z(n). What is o in v(o) = 0?
-1, 0, 5
Let p(y) = -y**2 + 50*y + 2291. Let j be p(-29). What is a in -1/7*a**2 + 2/7*a + j - 1/7*a**3 = 0?
-2, 0, 1
Let f = -201067 + 53685599/267. Let w = 2/267 + f. Find r, given that 8*r**2 + 0 + w*r + 10/3*r**3 = 0.
-2, -2/5, 0
Determine d, given that -24*d**2 - 19 + 43 + 4*d**3 - 24 = 0.
0, 6
Let u be ((-16)/8 - 353/(-178))/(-3). Let g = 4631/534 - u. Find i such that -22/3*i - 8/3*i**3 - 4/3 - g*i**2 = 0.
-2, -1, -1/4
Let f(y) = 2*y**5 + 34*y**4 - 68*y**3 + 14*y**2 + 48*y - 36. Let g(v) = v**5 + v**4 - 2*v**3 + v**2 - 2*v. Let i(o) = -f(o) + 6*g(o). Solve i(j) = 0 for j.
-1, 1, 3
Let x(c) = c**3 + 5*c**2 - 8*c - 9. Let s = -10 + 4. Let m be x(s). Determine h so that -5*h**3 - 12*h**2 + 2*h**m + 9*h + 6*h**3 = 0.
0, 1, 3
Let v(b) be the third derivative of -b**9/3780 - b**8/1680 + b**7/315 + b**4/12 + 6*b**2. Let o(q) be the second derivative of v(q). Factor o(h).
-4*h**2*(h - 1)*(h + 2)
Let m be (-27 + 22)*(-1)/15. Find a, given that -8/3*a**3 + 0 - m*a**2 - 5/3*a**4 + 2/3*a = 0.
-1, 0, 2/5
Let f(w) be the first derivative of 2*w**3/3 + 172*w**2 + 14792*w + 395. Let f(z) = 0. What is z?
-86
Factor 2/11*y**4 + 0 - 14/11*y**3 + 2*y**2 - 10/11*y.
2*y*(y - 5)*(y - 1)**2/11
Let b be 169/39 - (-1)/(-3). Suppose 0 = -c - b*p + 5, 5*c - 2*c = 4*p + 15. What is w in -2*w**2 + w**4 - 4*w**4 - 6*w**3 + 6*w**5 + c*w**4 = 0?
-1, -1/3, 0, 1
Let i(h) be the first derivative of -h**3/3 - 11*h**2/2 + 22*h + 5. Let k(j) = 2*j**2 + 34*j - 65. Let x(l) = -11*i(l) - 4*k(l). Factor x(d).
3*(d - 3)*(d - 2)
Let b(v) be the first derivative of -29 - 25*v**3 + 126*v**2 - 108*v + 3/2*v**4. Factor b(w).
3*(w - 6)**2*(2*w - 1)
Let u(r) be the first derivative of r**6 - 94*r**5/5 + 82*r**4 + 168*r**3 - 704*r**2 - 512*r + 49. Determine p so that u(p) = 0.
-2, -1/3, 2, 8
Let s be 664/83 + (-48)/7. Factor -s*t**2 - 2/7*t**3 - 8/7*t + 0.
-2*t*(t + 2)**2/7
Let i = -9850 - -9860. Factor -5/2*c**4 - 15*c**2 + i*c**3 + 10*c - 5/2.
-5*(c - 1)**4/2
Suppose 3*l = 9*l - 42. Let h be (-13)/(-2) + (-35)/l. Let -3/2*d**3 - d**2 + h*d + 1 = 0. Calculate d.
-1, -2/3, 1
Let c(a) be the first derivative of -a**5/15 + 5*a**4/12 + 22*a**3/9 + 8*a**2/3 + 26. Find p, given that c(p) = 0.
-2, -1, 0, 8
Let l(o) be the first derivative of 48/7*o - 10 + 12/7*o**2 + 1/7*o**3. Let l(w) = 0. Calculate w.
-4
Let q(n) be the first derivative of n**7/560 - n**6/80 + 3*n**5/160 + n**4/16 - n**3/4 - 29*n**2/2 + 12. Let p(x) be the second derivative of q(x). Factor p(k).
3*(k - 2)**2*(k - 1)*(k + 1)/8
Let s(v) = -100*v**2 - 68*v - 10. Let f(k) = 100*k**2 + 69*k + 10. Let r be 1 + 0 + (-10 - -8). Let j be 3*(r + -2)/3. Let c(b) = j*f(b) - 4*s(b). Factor c(u).
5*(4*u + 1)*(5*u + 2)
Let g(s) = -3*s**5 + 6*s**4 - 27*s**3 - 36*s**2. Let k(y) = 4*y**5 - 6*y**4 + 26*y**3 + 36*y**2. Let v(i) = -7*g(i) - 6*k(i). Determine t so that v(t) = 0.
-4, -1, 0, 3
Let t(b) be the third derivative of -5/32*b**4 - 12*b**2 + 1/480*b**6 + 0 + 0*b - 1/3*b**3 - 1/40*b**5. Find i, given that t(i) = 0.
-1, 8
Let b(m) = -m**3 + 2*m. Let y(i) = -14*i**4 + 161*i**3 - 30*i**2 - 164*i + 44. Let g(o) = -6*b(o) - 2*y(o). Suppose g(j) = 0. Calculate j.
-1, 2/7, 1, 11
Let i(r) = -2*r**3 + r**2 - r. Let u(s) = -12*s**3 + 232*s**2 - 4336*s + 27436. Let x(f) = 4*i(f) - u(f). Factor x(g).
4*(g - 19)**3
Let b = 16 - 11. What is p in -5*p**2 + 4*p**2 - 24*p**3 + 21*p**3 - p**b - 3*p**4 = 0?
-1, 0
Let t = 215 + -215. Let n(b) be the third derivative of 0*b - 1/600*b**6 + 0*b**3 + 3*b**2 + 0*b**5 + 1/120*b**4 + t. Factor n(x).
-x*(x - 1)*(x + 1)/5
Let k(h) = h**3 + 19*h**2 - 35*h + 27. Let x(m) = 8*m**3 + 132*m**2 - 244*m + 192. Let l(y) = -44*k(y) + 6*x(y). Solve l(r) = 0.
1, 9
Suppose -3*f - 4*a = -2*f + 6, -12 = -5*f + a. Factor -2*n**2 + 1 + n + n**5 + 3*n**4 - 2*n**3 - f*n**4 - 6*n + 6*n.
(n - 1)**2*(n + 1)**3
Let g(q) = 11*q**3 - 10*q**2 + 11*q + 6. Let u(v) = v**3 + v + 1. Let p be (-6)/(0 + -3) + 4. Let d(x) = p*u(x) - g(x). Determine l so that d(l) = 0.
0, 1
Let k be 51/(-306) - (113/6 - 1). Let q be ((-416)/(-180))/4 + (-4)/k. Factor 0 - q*o + 2/5*o**2.
2*o*(o - 2)/5
Let t(v) be the first derivative of -245*v**4 + 700*v**3 - 285*v**2/2 + 10*v - 23. Factor t(k).
-5*(k - 2)*(14*k - 1)**2
Let x(s) be the third derivative of -s**7/945 + s**6/90 - s**5/270 - 2*s**4/9 - 16*s**3/27 - 83*s**2. Find g, given that x(g) = 0.
-1, 4
Suppose 2*m + 4*u - 14 = -2, u = -2*m + 6. Determine g so that 4*g**3 - g**4 - 2*g**3 - 8*g**2 + 13*g**m - 2*g - 4*g**2 = 0.
-1, 0, 1, 2
Let t be 9/(-3) - (-6)/2. Suppose -1 - 3 = -2*l + 3*r, t = 5*r. Solve 0 + 1/4*c**l - 1/4*c = 0.
0, 1
Let x be ((-5 + 0)/(-5))/(3/9). Let p(m) be the second derivative of 0*m**2 + 1/4*m**4 + 3*m + m**x + 0. Factor p(d).
3*d*(d + 2)
Let p be (-1 + 69/63)*33/110. Let i(m) be the first derivative of -54/7*m**2 + p*m**5 - 2 + 18/7*m**3 - 3/7*m**4 + 81/7*m. Factor i(z).
(z - 3)**4/7
Suppose 0 = -15*p + 158 + 82. Let u be 1 + (p/27)/(8/(-12)). Factor -2/9*r**3 + 2/9*r + u*r**2 - 1/9.
-(r - 1)*(r + 1)*(2*r - 1)/9
Let g(i) = i**4 + 28*i**3 + 286*i**2 + 1258*i + 2025. Let p(z) = -5*z**4 - 140*z**3 - 1430*z**2 - 6289*z - 10125. Let s(x) = 33*g(x) + 6*p(x). Factor s(l).
3*(l + 5)**2*(l + 9)**2
Let o be (-6)/(-15) - (4392/(-30))/(-6). Let v be (-38)/o - (-50)/75. Determ