/6 - b**2. Let y(z) be the first derivative of u(z). Find m, given that y(m) = 0.
-6, 1
Let z = 661 + -1975/3. Factor -1/3 - z*k**2 - 7/3*k + 16/3*k**3.
(k - 1)*(4*k + 1)**2/3
Let q be (6 - 4)*146/(-204). Let y = q + 30/17. Factor 0*f - 5/3*f**3 + 0 - y*f**2 - 4/3*f**4.
-f**2*(f + 1)*(4*f + 1)/3
Let h(d) be the first derivative of -d**5/100 + d**4/15 + d**3/30 - 2*d**2/5 + 43*d - 17. Let b(a) be the first derivative of h(a). Factor b(w).
-(w - 4)*(w - 1)*(w + 1)/5
Let v(b) be the second derivative of -4/9*b**3 + 2*b**2 - 8*b + 0 + 1/36*b**6 - 2/9*b**4 + 7/90*b**5. Let g(n) be the first derivative of v(n). Factor g(l).
2*(l - 1)*(l + 2)*(5*l + 2)/3
Let q = 3/98 + 187/294. Let b(j) be the first derivative of 4 + q*j**3 + 4*j + 3*j**2. Factor b(c).
2*(c + 1)*(c + 2)
Let q = -1269 + 1269. Factor -2/3*m**3 + q - 8/3*m**2 - 2*m.
-2*m*(m + 1)*(m + 3)/3
Let y(d) be the first derivative of d**5/10 - 3*d**4/8 - 5*d**3/6 + 3*d**2/4 + 2*d - 61. Suppose y(f) = 0. What is f?
-1, 1, 4
Factor 183/7 + 26*i - 1/7*i**2.
-(i - 183)*(i + 1)/7
Let c(v) be the first derivative of 4*v**5/5 - 6*v**4 + 12*v**3 - 8*v**2 - 82. Factor c(x).
4*x*(x - 4)*(x - 1)**2
Suppose -21*h + 91 = -14. Factor c**4 + h + 3*c**4 - 6 - 8*c**3 - 12*c**2 + 32*c - 15.
4*(c - 2)*(c - 1)**2*(c + 2)
Suppose 2 = m - 2. Let j be (16/(-6))/((-16)/24). Factor 3*p**4 + 2*p**4 - 2*p**m - 2*p**j.
p**4
What is i in 0 + 0*i - 3/2*i**3 - 6*i**2 = 0?
-4, 0
Let o(d) = d**2. Let w(l) = -10*l**4 + 6*l**3 + 49*l**2 + 50*l + 12. Let y(z) = 5*o(z) + w(z). Determine i so that y(i) = 0.
-1, -2/5, 3
Let u(z) be the third derivative of z**6/240 + 3*z**5/40 - z**4 + 13*z**3/3 - 64*z**2. Find b, given that u(b) = 0.
-13, 2
Let g(a) be the third derivative of -1/540*a**6 + 0 - 1/135*a**5 + 0*a + 2/945*a**7 + 0*a**3 + 0*a**4 + 1/1512*a**8 + 14*a**2. Suppose g(p) = 0. What is p?
-2, -1, 0, 1
Let x(j) be the second derivative of j**6/10 - 3*j**5/2 + 8*j**4 - 19*j**3 + 45*j**2/2 - 3*j - 32. Factor x(q).
3*(q - 5)*(q - 3)*(q - 1)**2
Let l(m) be the third derivative of 15*m**7/14 - m**6/2 - 221*m**5/60 + 5*m**4/2 - 2*m**3/3 - 3*m**2. Factor l(g).
(g - 1)*(g + 1)*(15*g - 2)**2
Let b(k) = 19*k**4 + 78*k**3 + 355*k**2 + 570*k + 300. Let y(q) = 9*q**4 + 39*q**3 + 177*q**2 + 285*q + 150. Let r(f) = 6*b(f) - 13*y(f). Factor r(j).
-3*(j + 1)*(j + 2)*(j + 5)**2
Let y(p) be the third derivative of -p**9/15120 + p**7/2520 + 7*p**4/24 + 4*p**2. Let f(z) be the second derivative of y(z). Determine r so that f(r) = 0.
-1, 0, 1
Let a(v) be the third derivative of v**5/30 + 2*v**4/3 + 4*v**3 + 4*v**2 - 2*v. Factor a(w).
2*(w + 2)*(w + 6)
Let s(y) = -6*y**2 - 4*y - 10. Let o(n) = -n**2 + n. Let t(v) = 5*o(v) - s(v). Let x be t(-8). Factor x*r**3 - 2*r**4 + 5*r**2 - 2*r**5 - 6*r**2 + 3*r**2.
-2*r**2*(r - 1)*(r + 1)**2
Let g(k) be the first derivative of 0*k - 6*k**2 + 4/3*k**3 + 19. Factor g(d).
4*d*(d - 3)
Let t(l) = -5*l**3 - 16*l**2 + 9*l + 16. Suppose 42*o - 38*o - 16 = 0. Let m(h) = 20*h**3 + 65*h**2 - 35*h - 65. Let w(z) = o*m(z) + 15*t(z). Solve w(b) = 0.
-4, -1, 1
Let a(v) be the third derivative of v**6/160 - 23*v**5/80 + 21*v**4/16 - 2*v**2 - 327*v. Factor a(r).
3*r*(r - 21)*(r - 2)/4
Let v(n) be the second derivative of 0*n**5 - 1/70*n**7 + 0 + 1/10*n**3 - 1/25*n**6 + 0*n**2 + 1/10*n**4 + 2*n. What is w in v(w) = 0?
-1, 0, 1
Let f(r) = -8*r**2 + 88*r + 108. Let w(k) = k**2 + k - 2. Let h(a) = f(a) + 6*w(a). Factor h(m).
-2*(m - 48)*(m + 1)
Suppose 0 = 5*p - 2*n - 80, 110 = 5*p - 0*p + 4*n. Let d be ((-24)/126)/(p/(-105)). Factor -2*k**5 + 0 + d*k**3 - 2/9*k**2 + 0*k - 2/3*k**4.
-2*k**2*(k + 1)*(3*k - 1)**2/9
Factor 23664*f**2 + 13128*f**2 + 5288*f**3 - 37044 + 4*f**5 - 356*f - 4936*f + 252*f**4.
4*(f - 1)*(f + 1)*(f + 21)**3
Let t(x) = x**2 + 13*x + 12. Let w be t(-1). Let d(z) be the third derivative of 0*z - z**2 + w - 1/120*z**5 - 1/24*z**3 - 1/32*z**4. Factor d(i).
-(i + 1)*(2*i + 1)/4
Let i(q) = 6*q**2 + 53*q + 42. Let d(j) = 3*j**2 + 27*j + 21. Let x = -72 + 77. Let u(n) = x*d(n) - 3*i(n). Factor u(t).
-3*(t + 1)*(t + 7)
Let r be (10/6)/5 - (4572/351 + -13). Factor 80/13*t - 2/13*t**4 + 64/13 - r*t**3 + 24/13*t**2.
-2*(t - 4)*(t + 2)**3/13
Let i(o) be the first derivative of -o**7/5880 + o**6/2520 + o**5/168 + o**4/56 + 7*o**3 + 20. Let r(b) be the third derivative of i(b). What is s in r(s) = 0?
-1, 3
Suppose 16*i = -7*i + 46. Let n(m) be the first derivative of -5 + 1/12*m**3 + 1/2*m - 3/8*m**i. Determine g so that n(g) = 0.
1, 2
Find u such that -22/3*u - 28/3*u**4 + 20/3*u**3 + 80/3*u**2 - 52/3 + 2/3*u**5 = 0.
-1, 1, 2, 13
Factor -128/13 - 336/13*o - 36/13*o**2 + 10/13*o**3.
2*(o - 8)*(o + 4)*(5*o + 2)/13
Suppose f - 3 + 5 = 0. Let u = 2 - f. Factor u*n**2 - 15*n**2 + 9*n**2 + 4*n.
-2*n*(n - 2)
Let s(b) be the first derivative of b**6/20 - 3*b**5/5 + 3*b**4 - 8*b**3 + 12*b**2 - 2*b - 1. Let h(z) be the first derivative of s(z). Factor h(g).
3*(g - 2)**4/2
Let p(i) = -i**3 - 3*i**2 - 6*i - 77. Let g be p(-5). Factor -4/3*x**g - 8/3*x**2 - 4/3*x + 0.
-4*x*(x + 1)**2/3
Let b(c) = -2*c**3 - 2*c**2 - 4*c + 5. Suppose 2 = -2*a - 8, 4*o - 6 = 2*a. Let r(w) = w**3 + w - 1. Let x(t) = o*b(t) - 3*r(t). Factor x(n).
-(n - 2)*(n - 1)*(n + 1)
Let v(g) be the second derivative of g**6/40 + g**5/80 - 17*g**4/48 + 19*g**3/24 - 3*g**2/4 + 12*g - 2. Factor v(x).
(x - 1)**2*(x + 3)*(3*x - 2)/4
Let b(g) be the second derivative of -g**6/50 + 6*g**5/25 - 13*g**4/20 + 3*g**3/5 + 110*g. Factor b(d).
-3*d*(d - 6)*(d - 1)**2/5
Let v(m) be the third derivative of m**8/16 - 9*m**7/14 + 77*m**6/40 - 31*m**5/20 - 3*m**4 + 8*m**3 - m**2 + 149. Let v(b) = 0. Calculate b.
-4/7, 1, 4
Let z(x) be the second derivative of x**5/450 + x**4/36 - 2*x**3/15 + 10*x**2 + 9*x. Let c(v) be the first derivative of z(v). Factor c(h).
2*(h - 1)*(h + 6)/15
Let x(u) be the third derivative of u**8/1008 + u**7/315 + u**6/360 - 5*u**2 + 3. Factor x(d).
d**3*(d + 1)**2/3
Let 3267/4*r**2 + 12 + 198*r = 0. Calculate r.
-4/33
Solve 2/7*i**2 + 52/7*i + 138/7 = 0 for i.
-23, -3
Suppose 268 = 5*d + 258. What is p in 1 + d*p**3 + 0 + 19*p**2 - 3*p - 3*p**3 - 16*p**2 = 0?
1
Let p be 6/(-180)*((-174)/12 - -7). Factor -3/2 - 1/4*a + p*a**2.
(a - 3)*(a + 2)/4
Suppose 0*a**2 + 0 - 5/4*a**5 - 5/2*a**4 - 5/4*a**3 + 0*a = 0. Calculate a.
-1, 0
Let k(g) be the third derivative of -g**5/140 - 15*g**4/14 - 450*g**3/7 - 531*g**2. Factor k(a).
-3*(a + 30)**2/7
Suppose 2*h = 3*z + 24, 8*h - 5*z = 3*h + 65. Let x be (-3)/((-108)/75) + h/(-20). Factor x + 2/3*l - 2/3*l**2.
-2*(l - 2)*(l + 1)/3
Let y = 36 + -34. What is v in -21*v + 0*v**4 + 2*v - 12*v**3 - 18*v**y + 7*v - 3*v**4 - 3 = 0?
-1
Let f = 55 - 52. Let q = 1 - -2. Factor -n**5 + 3*n**5 + f*n**3 + 10*n**4 + 2*n**2 + 3*n**q - 20*n**2.
2*n**2*(n - 1)*(n + 3)**2
Factor -10*u**5 + 23*u**4 - 16*u**4 + 284*u**3 - 116*u**2 + 288*u + 632*u**2 + 53*u**4 + 14*u**5.
4*u*(u + 1)*(u + 3)**2*(u + 8)
Let g(j) = 2*j**3 - 33*j**2 + 46*j - 12. Let v be g(15). Let c be ((-1)/3)/((-1)/6). Suppose -5 + c*w**2 - 11*w + w**3 + v + 10*w = 0. Calculate w.
-2, -1, 1
Let w(v) be the first derivative of 2*v**3/9 - 2*v**2 - 32*v/3 + 80. Let w(f) = 0. Calculate f.
-2, 8
Find n, given that -4/5*n**3 - 1968300 - 43740*n - 324*n**2 = 0.
-135
Solve -1/5*w**2 + 0 - 13*w = 0.
-65, 0
Let z be 700/(-15)*(-5)/(75/(-36)). Let y = z + 114. Factor -46/5*i**y - 9/5 + 33/5*i - 9/5*i**4 + 6*i**3 + 1/5*i**5.
(i - 3)**2*(i - 1)**3/5
Let h be ((-4)/(-18))/((-17)/(-765)*15). Solve 0 - 4/3*r**2 + 0*r + h*r**3 = 0 for r.
0, 2
Let x be ((-72)/63)/(-8) + 2/(-14). What is p in 0*p - 2/21*p**3 + x + 2/21*p**2 = 0?
0, 1
Let x(t) be the second derivative of 0*t**3 + 0 - 9*t - 1/60*t**5 + 0*t**2 + 1/72*t**4. Factor x(i).
-i**2*(2*i - 1)/6
What is i in -5*i**2 + 424*i - 474*i - 6 + 61 = 0?
-11, 1
Let d(c) = c**2 + 19*c - 457. Let k be d(-33). Find v, given that 0 + 1/8*v**k - 1/4*v**2 + 1/4*v**4 - 1/8*v + 0*v**3 = 0.
-1, 0, 1
Let p(o) be the first derivative of o**8/336 + o**7/140 - o**6/120 - 7*o**2 + 28. Let j(m) be the second derivative of p(m). Factor j(v).
v**3*(v + 2)*(2*v - 1)/2
Let t(f) be the first derivative of -3/10*f**2 - 1/5*f**3 + 0*f + 12. Factor t(b).
-3*b*(b + 1)/5
Let g = -559 - -2237/4. Let u(b) be the third derivative of g*b**5 + 0*b + 0 - 1/8*b**4 - 8*b**2 + 0*b**3. F