4
Let p(z) be the third derivative of -z**10/75600 - z**9/12600 - z**8/8400 + 11*z**4/6 - 11*z**2. Let y(b) be the second derivative of p(b). Factor y(h).
-2*h**3*(h + 1)*(h + 2)/5
Factor 0 - 4/3*q**3 + 20/3*q**2 + 0*q.
-4*q**2*(q - 5)/3
Factor 5*o**3 - 5*o - 1 - 16 + 20 + 15*o**2 - 18.
5*(o - 1)*(o + 1)*(o + 3)
Let u be 2/(-11) - 128/(-220). Let t(b) = -29*b + 90. Let l be t(3). Factor 0 + 2/5*g - u*g**4 + 6/5*g**l - 6/5*g**2.
-2*g*(g - 1)**3/5
Let w(b) = -b - 1. Let a(j) = 10. Let s(u) = -a(u) - 5*w(u). Let q be s(2). Find d, given that -1/2*d**4 + 1/2*d + 1/2*d**q - 1/2 - d**3 + d**2 = 0.
-1, 1
Let a(i) be the second derivative of -5/6*i**3 + 5/12*i**4 + 0*i**2 + 0 - 15*i. Factor a(q).
5*q*(q - 1)
Suppose 0 - 1/5*v**3 + 52/5*v**2 - 676/5*v = 0. What is v?
0, 26
Let g(r) be the second derivative of r**4/108 - 46*r**3/27 + 1058*r**2/9 - 168*r. Factor g(k).
(k - 46)**2/9
Let x = 1755 + -1753. Factor 12/11*h**x - 6/11 - 34/11*h.
2*(h - 3)*(6*h + 1)/11
Suppose -15*w - 628 + 658 = 0. Suppose -48/5 - 28/15*b**w + 8*b + 2/15*b**3 = 0. What is b?
2, 6
Let d(g) be the first derivative of 5*g**3/24 - 177*g**2/16 + 35*g/4 - 623. Factor d(t).
(t - 35)*(5*t - 2)/8
Suppose 4*r = -2*m + 12, 3*r + 0*m - 10 = -m. Factor -4*w**4 - 3*w**3 + 4*w + 3*w**4 - 2*w**4 + r*w**4.
w*(w - 2)**2*(w + 1)
Let v(r) be the second derivative of 3*r**6/10 + 6*r**5 + 463*r**4/12 + 78*r**3 + 70*r**2 + 3*r - 70. Factor v(c).
(c + 5)*(c + 7)*(3*c + 2)**2
Let d(x) be the first derivative of x**3/18 - 8*x**2/3 - 34*x/3 + 188. Factor d(q).
(q - 34)*(q + 2)/6
Factor 20/3*t - 20/3 - 5/3*t**2.
-5*(t - 2)**2/3
Let b(m) be the first derivative of -5*m**3/3 + 345*m**2 - 23805*m - 256. Solve b(d) = 0 for d.
69
Let s(n) be the third derivative of n**8/84 + 4*n**7/35 - n**6/10 - 16*n**5/15 + 2*n**4 - 459*n**2. Factor s(r).
4*r*(r - 1)**2*(r + 2)*(r + 6)
Let t(k) be the third derivative of k**6/280 - k**5/28 - k**4/56 + 5*k**3/14 + 34*k**2. Determine q so that t(q) = 0.
-1, 1, 5
Let b(z) be the third derivative of 2/27*z**3 + 0*z + 0 - 1/135*z**5 + 3*z**2 + 0*z**4. Find y such that b(y) = 0.
-1, 1
Let o = -184 + 193. Let c be (18/9)/(30/o). Factor 1/5*b**3 - 3/5*b**2 - 1/5*b + c.
(b - 3)*(b - 1)*(b + 1)/5
Let w(x) = 2*x**3 + 3*x**2 - 11*x - 11. Suppose -6 = -2*i - 4. Let h(u) = 13*u**3 + 6*u**3 - 18*u**3 - i - u. Let g(q) = h(q) + w(q). Factor g(o).
3*(o - 2)*(o + 1)*(o + 2)
Let u be (3/9 - 17/6)*12/(-55). Factor u*z**2 - 36/11*z + 30/11.
6*(z - 5)*(z - 1)/11
Let t(w) be the first derivative of 5*w**3/3 + 30*w**2 + 175*w + 103. Factor t(u).
5*(u + 5)*(u + 7)
Suppose 16*d + 434 = 18*d. What is p in 512*p + 2*p**4 + 192*p**2 + 32*p**3 - d + 320 + 409 = 0?
-4
Factor 4*h - 16*h**3 - 34*h + 10*h - 82*h**3 - 200*h**2 + 12*h.
-2*h*(h + 2)*(49*h + 2)
Let w(m) be the third derivative of 0 + 1/150*m**5 - 1/900*m**6 + 0*m**4 + 0*m + 6*m**2 - 1/2*m**3. Let t(b) be the first derivative of w(b). Factor t(v).
-2*v*(v - 2)/5
Suppose 2*z = -t - 2, -7*t - 5*z + 23 = -8*t. Let c be (t/10 + 2)*(-4)/(-3). Solve 4/5*x**3 + 0*x + 0*x**2 + 0 - c*x**4 = 0 for x.
0, 1/2
Let h(j) = 10*j**3 + 2105*j**2 + 23805*j - 35. Let m(i) = -i**3 - 234*i**2 - 2645*i + 4. Let c(w) = -4*h(w) - 35*m(w). Determine t, given that c(t) = 0.
-23, 0
Let x(o) be the first derivative of -4/3*o**3 + 0*o - 3*o**4 + 4*o**2 + 20 + 2/3*o**6 + 4/5*o**5. Factor x(s).
4*s*(s - 1)**2*(s + 1)*(s + 2)
Let d(i) be the third derivative of 0*i - 1/40*i**6 + 3/10*i**5 + 3*i**3 - 11/8*i**4 + 0 - 6*i**2. Factor d(g).
-3*(g - 3)*(g - 2)*(g - 1)
Let -2/11*n**4 + 6/11*n - 2/11*n**2 + 4/11 - 6/11*n**3 = 0. Calculate n.
-2, -1, 1
Factor -28*u + 14*u**3 + u**4 - 20*u - 16*u**2 + 2*u**4 - 2*u**3 + u**4.
4*u*(u - 2)*(u + 2)*(u + 3)
Let f = 16956/7 + -2422. Find d, given that -2/7*d**3 - f*d**2 + 4/7*d**4 + 0 + 0*d = 0.
-1/2, 0, 1
Let n(x) be the first derivative of 3*x**5/5 + 3*x**4/4 - 23*x**3 + 117*x**2/2 - 54*x - 107. What is a in n(a) = 0?
-6, 1, 3
Let r(s) be the second derivative of -s**4/54 - 2*s**3/9 - 492*s. Solve r(m) = 0 for m.
-6, 0
Let k = -767 + 7671/10. Factor -k*y**2 + 0 - 1/5*y + 1/10*y**3.
y*(y - 2)*(y + 1)/10
Suppose 66 = 6*q - 9*q. Let j = -14 - q. Determine u, given that -u**4 - 16*u**3 - 8*u**2 - j*u**2 + 5*u**2 - 6*u**4 - 2*u = 0.
-1, -2/7, 0
Let q(l) be the third derivative of l**6/480 + 3*l**5/80 + l**4/12 - 5*l**3/2 + l**2 + 39. Factor q(r).
(r - 2)*(r + 5)*(r + 6)/4
Let v(a) be the second derivative of 3*a**4/4 + 250*a**3 + 498*a**2 - 3*a - 71. Factor v(n).
3*(n + 166)*(3*n + 2)
Let t(o) = 11*o - 63. Let v be t(6). Let p(j) be the third derivative of 0*j**v - 7*j**2 + 1/210*j**7 + 1/60*j**6 + 0*j**4 + 0*j + 0 + 1/60*j**5. Factor p(s).
s**2*(s + 1)**2
Determine q, given that 5/6*q - 1/6*q**2 + 11 = 0.
-6, 11
Let x(t) be the first derivative of -t**7/1400 - t**6/75 + 4*t**3/3 - 2*t + 22. Let g(s) be the third derivative of x(s). Factor g(c).
-3*c**2*(c + 8)/5
Let y = 13 + -113/9. Let b(u) be the first derivative of -2/27*u**3 - 8/9*u - y*u**2 + 2. Factor b(d).
-2*(d + 2)**2/9
Let w(p) be the third derivative of 1/270*p**5 + 0 + 2/27*p**3 + 0*p - 19*p**2 - 1/270*p**6 + 5/108*p**4. Factor w(r).
-2*(r - 2)*(r + 1)*(2*r + 1)/9
Suppose 1/7*y**2 + 1/7*y**3 + 0 - 2/7*y = 0. What is y?
-2, 0, 1
Let q = -141 + 148. Let v(l) be the third derivative of 0*l**3 + 1/210*l**q + 0 - 1/1008*l**8 + 0*l + 0*l**4 + 1/180*l**5 - 1/120*l**6 + l**2. Factor v(h).
-h**2*(h - 1)**3/3
Factor -4/3*t**3 + 16/3*t**2 + 0 + 20/3*t.
-4*t*(t - 5)*(t + 1)/3
Factor 0*u + 10*u - 6 - 6 + 1111*u**2 + u - 1110*u**2.
(u - 1)*(u + 12)
Let z be 52*4/792 + (-1067)/121 + 9. Let -z*j**3 - 4/9*j + 0 + 10/9*j**2 = 0. What is j?
0, 1/2, 2
Let o = -1 + 3. Suppose 0 = 3*b - j - 17, 0 = 2*b + 2*b + 2*j - 36. Factor -b + 7 - k**2 + 3*k**o.
2*k**2
Let o(t) be the second derivative of -t**4/72 + t**3/6 + 7*t**2/12 + 238*t. Factor o(p).
-(p - 7)*(p + 1)/6
Let n(a) be the third derivative of a**7/1260 + a**6/360 - 7*a**5/90 + 23*a**4/72 - 7*a**3/12 - 12*a**2 - 5. Factor n(m).
(m - 3)*(m - 1)**2*(m + 7)/6
Suppose 27/2*q - 1/4*q**2 - 729/4 = 0. What is q?
27
Suppose 0 = -0*x - 4*x + 2*q + 32, 2*q + 39 = 5*x. Let b = 10 - x. Suppose 6*n**3 + 0*n**b - 9*n**4 + 3*n**2 + 0*n**3 = 0. Calculate n.
-1/3, 0, 1
Let n(l) be the first derivative of -3*l**3 - 15*l**2 - 114*l - 6. Let q(g) = -g**2 + g - 1. Let y(b) = n(b) - 6*q(b). Factor y(m).
-3*(m + 6)**2
Let o(d) be the first derivative of -2/5*d**3 + 3/20*d**4 + 24/5*d - 9 - 6/5*d**2. What is r in o(r) = 0?
-2, 2
Let q be 2/(-9) - 902/(-495). Factor 52/5*f - 16/5*f**5 - 29*f**3 + q + 38/5*f**2 + 88/5*f**4.
-(f - 2)**3*(4*f + 1)**2/5
Let f = 33559/3 - 11041. Let v = -144 + f. Determine m, given that 2*m**2 + 1/3*m**4 + 1/3 + 4/3*m + v*m**3 = 0.
-1
Let t be (-354)/15 - (-92 - -68). Suppose 0 - 1/5*n**5 - 3/5*n - 2/5*n**2 + t*n**4 + 4/5*n**3 = 0. What is n?
-1, 0, 1, 3
Let g(u) be the first derivative of 7/20*u**4 - 3/10*u**6 + 0*u - 9/50*u**5 - 1/10*u**2 + 1/10*u**3 + 19. Suppose g(i) = 0. What is i?
-1, -1/2, 0, 1/3, 2/3
Let m(z) = 2*z**4 - 8*z**3 - 4*z**2 - 4*z - 4. Let p(l) = -3*l**4 + 7*l**3 + 3*l**2 + 3*l + 3. Let h(u) = 3*m(u) + 4*p(u). Factor h(s).
-2*s**3*(3*s - 2)
Let c(i) = 2*i**2 - 2*i + 3. Let q be c(1). Solve -29*a + 2*a**q + 12 + 0*a + 15*a = 0 for a.
-3, 1, 2
Let n = -10577 + 10577. Solve n*y - 3/5 + 3/5*y**2 = 0.
-1, 1
Let p(n) be the third derivative of -n**7/945 - n**6/180 + 2*n**5/135 + 81*n**2. Suppose p(k) = 0. Calculate k.
-4, 0, 1
Let w(o) = o**5 + 19*o**4 + 183*o**3 + 341*o**2 + 176*o + 10. Let g(t) = t**5 - t**4 - t**3 + t**2 + 2. Let y(b) = -5*g(b) + w(b). Suppose y(x) = 0. What is x?
-2, -1, 0, 11
Let h(z) be the second derivative of 0 - 1/18*z**4 + 1/3*z**3 + 11*z - 2/3*z**2. Solve h(m) = 0.
1, 2
Let r = 21128/1585 - 168/317. Factor r*m + 2*m**2 + 24/5.
2*(m + 6)*(5*m + 2)/5
Let g(o) be the second derivative of o**5/50 - 11*o**4/15 + 32*o**3/5 + 288*o**2/5 - o + 238. Find z, given that g(z) = 0.
-2, 12
Let a(q) be the second derivative of -q**4/12 + 9*q**3/2 - 19*q**2 - 2*q + 7. Let d be a(25). Let j - 12*j**2 + 2/3 - d*j**4 - 73/3*j**3 = 0. What is j?
-1, -1/4, 2/9
Let y = 577 + -575. Let c(z) be the second derivative of 0 - 1/21*z**4 - 8*z + 2/7*z**y + 0*z**3. Factor c(t).
-4*(t - 1)*(t + 1)/7
Let u(p) be the second derivative