 5*j. Factor r(u).
3*u*(u - 4)*(7*u + 3)
Let a(j) be the third derivative of j**7/420 - 29*j**6/40 + 7741*j**5/120 - 1247*j**4/4 + 1849*j**3/3 - 507*j**2. Factor a(z).
(z - 86)**2*(z - 1)**2/2
Factor -60/7*b - 57/7 - 3/7*b**2.
-3*(b + 1)*(b + 19)/7
Factor 176/9 - 2/9*w**2 + 2/3*w.
-2*(w - 11)*(w + 8)/9
Factor -4/3*t**3 - 2*t**4 + 0*t + 0*t**2 - 2/3*t**5 + 0.
-2*t**3*(t + 1)*(t + 2)/3
Let b(r) be the first derivative of r**5/5 - 55*r**4/2 + 971*r**3 + 3080*r**2 + 3136*r + 653. Suppose b(p) = 0. Calculate p.
-1, 56
Let m = 8 - 8. Solve 2*y - 2*y - 4*y**4 + 4*y**2 - 4*y**3 + 4*y**5 + m*y**2 = 0 for y.
-1, 0, 1
Suppose -148/5*t + 248/5*t**2 - 68/5*t**3 + 24/5 - 56/5*t**4 = 0. Calculate t.
-3, 2/7, 1/2, 1
Let q(s) = 5*s**2 + 39*s + 94. Let k(x) = 30*x**2 + 235*x + 565. Let f(g) = 6*k(g) - 35*q(g). Factor f(l).
5*(l + 4)*(l + 5)
Let t(o) be the first derivative of -o**5/60 - o**4/12 - 9*o**2 + 19. Let b(q) be the second derivative of t(q). Suppose b(j) = 0. What is j?
-2, 0
Let w(m) = -m**3 + 2*m. Let k(u) = 4*u**4 + 11*u**3 + u**2 - 12*u. Let j(x) = -k(x) - 6*w(x). Factor j(d).
-d**2*(d + 1)*(4*d + 1)
Let w(h) = 5*h**3 + 4*h**2. Let c(t) = -9*t**3 - 39*t**2 + 19*t**2 - 17*t**3. Let o be (-96)/9*6/(-4). Let z(k) = o*w(k) + 3*c(k). Let z(g) = 0. Calculate g.
-2, 0
Let p(k) = -k**2 + 2. Let v(f) = -24 - 14*f + 2*f**2 + 8*f**2 + 4*f. Let b(t) = 12*p(t) + v(t). Find i such that b(i) = 0.
-5, 0
Factor 8706*s**2 + 110*s**3 - 18224*s + 2*s**4 + 49*s**3 + 109*s**3 + 9248.
2*(s - 1)**2*(s + 68)**2
Let q = -265 - -280. Suppose -3*h + 4*i + 10 = 0, h + 2*i + 4 = 2*h. Factor -11*a**2 - 5*a**h + 3 - 2*a + q*a**2.
-(a - 1)*(a + 3)
Suppose 0 = -5*x - t + 27, 2*x - 3*t - 2 = t. Let p be (-1 - -2) + (8 - x). Find s, given that -s + 16 - p*s - 5*s - 10*s + 4*s**2 = 0.
1, 4
Suppose 362*h + 9 = 365*h. Let c(w) be the third derivative of 0*w**h + 1/48*w**4 + 0 + 0*w + 1/120*w**5 - 2*w**2. Factor c(l).
l*(l + 1)/2
Suppose 63*y - 67*y + 36 = 0. Let j be (-707)/77 + y + 48/22. Find f, given that -3/4*f**5 + 1/2*f**3 - f**4 + 0 + 1/4*f + f**j = 0.
-1, -1/3, 0, 1
Solve -2/9*f**4 - 88/9*f - 22/3*f**2 - 20/9*f**3 - 40/9 = 0 for f.
-5, -2, -1
Factor -104 - 4/3*w**2 + 316/3*w.
-4*(w - 78)*(w - 1)/3
Let y(o) = -o**2 + 2*o. Let x(p) = 2*p**3 + 4*p**2 - 14*p + 2. Let s(z) = x(z) + 6*y(z). Suppose s(f) = 0. Calculate f.
-1, 1
Let t(g) be the second derivative of g**5/100 - g**4/30 - g**3/10 - 793*g. Factor t(r).
r*(r - 3)*(r + 1)/5
Suppose 19*q = 16*q - 2*y + 17, 3*y = q - 13. Let r(a) be the second derivative of -1/30*a**5 - q*a + 1/3*a**2 + 1/6*a**4 - 1/3*a**3 + 0. Solve r(z) = 0.
1
Let h = 599/5 - 1792/15. Solve -2/3*x + 0 + 2/3*x**3 + 1/3*x**2 - h*x**4 = 0 for x.
-1, 0, 1, 2
Suppose -5*z - 10 = -3*s + 22, -4*z - 24 = -2*s. Suppose 5*w - 249 = 2*w. Factor -b**s + 2*b**4 + 83*b**3 - b**2 - w*b**3.
b**2*(b - 1)*(b + 1)
Let p = 50 - 46. Factor -51*w**2 + 52*w**2 - 2 + 2 + w**p + 2*w**3.
w**2*(w + 1)**2
Suppose 2 = g + 3. Let j be ((2/6)/g)/(35/(-126)). Suppose -j + 2/5*m**2 - 4/5*m = 0. Calculate m.
-1, 3
Factor -3*m + 16*m**3 - 34*m**3 + 12*m**4 + 2*m**5 + 12*m**2 + 6*m**5 - 11*m**5.
-3*m*(m - 1)**4
Let y = -436199/7 + 62673. Let l = 360 - y. Determine r so that 12/7*r**2 + 0 + 6/7*r**3 + l*r + 1/7*r**4 = 0.
-2, 0
Let z(l) be the third derivative of -l**8/48 + 43*l**7/315 - 23*l**6/60 + 3*l**5/5 - 41*l**4/72 + l**3/3 - 89*l**2. Determine q, given that z(q) = 0.
3/7, 2/3, 1
Let h(o) be the first derivative of o**4/12 + o**3/9 - 4*o**2/3 - 4*o + 42. Solve h(j) = 0 for j.
-2, 3
Let n(r) be the second derivative of 7*r - 3*r**2 + 1/15*r**6 - 4/3*r**3 + 1/3*r**4 + 0 + 2/5*r**5. Find q, given that n(q) = 0.
-3, -1, 1
Suppose 0 = -3*r + 6, 2*b - 8 = 3*b - 5*r. Factor 4 - 9 - 6*t + t - 5*t**b - 5*t.
-5*(t + 1)**2
Let h = 2178 - 2173. Let j(p) be the second derivative of 0 - 1/48*p**4 + 3*p + 1/120*p**6 - 1/80*p**h + 1/24*p**3 + 0*p**2. Factor j(l).
l*(l - 1)**2*(l + 1)/4
Let d(b) be the first derivative of -3/10*b**2 - 2/5*b + 6 - 1/15*b**3. Suppose d(j) = 0. What is j?
-2, -1
Let z(n) be the second derivative of -n**5/15 + 4*n**4/9 - 8*n**3/9 - 80*n + 2. Factor z(d).
-4*d*(d - 2)**2/3
Let q(j) be the first derivative of -2*j**4/15 + 22*j**3/45 + 19*j**2/15 + 8*j/15 + 46. Let q(z) = 0. What is z?
-1, -1/4, 4
Suppose 0 = 4*m - 141 - 323. Suppose w - 42 = -g, w - 2*g = -2*w + m. Suppose 24*i**2 + 16*i - w + 4*i**4 + 6*i**3 + 8 - 26*i**3 = 0. Calculate i.
-1, 2
Let y(r) be the second derivative of -27/2*r**2 + 3*r**3 + 7*r - 1/4*r**4 + 0. Factor y(c).
-3*(c - 3)**2
Let t(c) be the first derivative of -c**4/9 + 536*c**3/9 - 35912*c**2/3 + 9624416*c/9 + 554. Factor t(l).
-4*(l - 134)**3/9
Let t(g) be the first derivative of 2*g**5/35 + 5*g**4/7 + 58*g**3/21 + 32*g**2/7 + 24*g/7 - 375. Factor t(u).
2*(u + 1)**2*(u + 2)*(u + 6)/7
Let -2/19*z + 2/19*z**3 - 2/19*z**2 + 2/19 = 0. What is z?
-1, 1
Let g(v) = 6*v**2 - 49*v + 192. Let a(d) = -3*d**2 + 24*d - 99. Let o(k) = -11*a(k) - 6*g(k). Let o(n) = 0. Calculate n.
3, 7
Let 10/3*t - 4*t**2 + 2/3*t**3 + 0 = 0. Calculate t.
0, 1, 5
Let c be 5/(-45)*-3 - (-1)/6. Suppose 0 = x + 2 - 7. What is o in o**4 - c*o**x + 0*o**2 + 0 + 0*o - 1/2*o**3 = 0?
0, 1
Let z(t) = 13*t**3 - 14*t**2 + 49*t - 6. Let x(n) = 28*n**3 - 28*n**2 + 98*n - 13. Let h(w) = 6*x(w) - 13*z(w). Let h(p) = 0. What is p?
0, 7
Let n(l) = 2*l + 10. Let x be n(7). Let r be ((-6)/9)/((-4 + 0)/x). Factor -18*o + 97/2*o**2 + 2 - 36*o**3 + 8*o**r.
(o - 2)**2*(4*o - 1)**2/2
Let j(h) be the first derivative of 22 + 30/7*h**2 + 50/21*h**3 + 18/7*h. Factor j(k).
2*(5*k + 3)**2/7
Let z = 48 + -46. Suppose 9 = 4*b - 3. Factor -m**2 - m**b + z*m**4 - 2*m**3 - m**4 + 2*m**3 + m.
m*(m - 1)**2*(m + 1)
Let y be 34/357 + 3/42*4. Let x(g) be the second derivative of -g + 0*g**2 - 4/15*g**6 + y*g**7 + 0 + 0*g**3 - 1/12*g**4 - 7/20*g**5. Solve x(s) = 0.
-1/4, 0, 1
Let w(u) be the first derivative of -5/6*u**3 + 3/2*u**2 - u - 8 + 1/20*u**5 + 1/12*u**4. Let q(r) be the first derivative of w(r). Let q(m) = 0. What is m?
-3, 1
Let w(o) = 5*o**2 - 2*o + 1. Let a = 3 - 2. Let j be w(a). Determine d so that d**3 - 4*d**5 + 3*d**3 + 4*d**2 - 3*d**j + 2*d**4 - 3*d**4 = 0.
-1, 0, 1
Let s be (16/10)/((-42)/(-105)). Factor 7*k**4 - 22*k**2 - 2*k**s - 20*k**3 + 37*k**2.
5*k**2*(k - 3)*(k - 1)
Let z = 263 + -259. Suppose -z*c + 19 = f, -5*f - 18 = c - 37. Find x, given that 2/19 + 2/19*x**c + 0*x + 0*x**3 - 4/19*x**2 = 0.
-1, 1
Let a(r) = r - 1. Let k be a(9). Let l = k + -6. Suppose -8*t**2 - 5*t**3 - 3*t**2 + 2*t**2 - t**l + 5*t**4 = 0. What is t?
-1, 0, 2
Let d be ((-6)/(-9))/((-48)/(-540)). Determine y so that 3/2*y - d*y**3 + 6*y**2 + 0 = 0.
-1/5, 0, 1
Let v(p) be the first derivative of p**8/4200 - p**7/2100 - 6*p**3 - 12. Let w(o) be the third derivative of v(o). What is y in w(y) = 0?
0, 1
Let n(o) be the first derivative of 2*o**5/35 - o**4/2 - 4*o**3/21 + 60*o**2/7 - 144*o/7 - 318. Factor n(q).
2*(q - 6)*(q - 2)**2*(q + 3)/7
Let j(a) be the third derivative of -a**5/160 - 5*a**4/16 - 25*a**3/4 + a**2 + 27. Factor j(m).
-3*(m + 10)**2/8
Suppose w + 26*w - 135 = 0. Let b(f) be the second derivative of 1/60*f**w - 1/18*f**3 + 1/6*f**2 - 4*f + 0 - 1/36*f**4. Find x, given that b(x) = 0.
-1, 1
Let v(i) = 2*i**4 - i**3 - 2. Let s(c) = -5*c**4 - 2*c**3 + 16*c**2 + 16*c - 44. Let o(h) = s(h) + 2*v(h). Factor o(n).
-(n - 2)**2*(n + 2)*(n + 6)
Let g be 9/15*(-270)/(-54). What is f in 3/5*f**5 - 3/5*f**2 + 6/5*f - 9/5*f**g + 3/5*f**4 + 0 = 0?
-2, -1, 0, 1
Let o = 2/465 + 149/1395. Solve 2/9*h**3 - 1/3*h**2 + o*h + 0 = 0.
0, 1/2, 1
Let u(l) be the first derivative of -8/39*l**3 + 25 + 0*l - 1/26*l**4 - 4/13*l**2. Solve u(b) = 0.
-2, 0
Factor -20*d - 31*d**3 - 15*d - 15*d + 36*d**3 - 15*d**2.
5*d*(d - 5)*(d + 2)
Let y(s) be the second derivative of -12*s**2 - 21*s - 29/3*s**4 + 46/3*s**3 + 0 + 12/5*s**5. Find u, given that y(u) = 0.
2/3, 3/4, 1
Suppose 14*n = 20*n. Suppose n = 7*x + 2*x. Factor -8/5 + x*f + 2/5*f**2.
2*(f - 2)*(f + 2)/5
Suppose 5*v - 18 = 2*v. Let n be (-6)/4 - 9*v/(-12). Factor 3/2*k - 1 + 1/2*k**4 + 1/2*k**2 - 3/2*k**n.
(k - 2)*(k - 1)**2*(k + 1)/2
Let n = 83 + -81. Factor 100*m - m**2 + 7*m**n - 25*m**3 - 9*m**2 - 7*m**2 + 120 - 5*m**4.
-5*(m - 2)*(m + 2)**2*(m + 3)
Let x = 3 - 17. Let c = 24 + x. Fac