 - -52. Suppose -o*l = -3*l - 18. Factor 5*s**5 - 9*s**3 - 15*s**2 - 18*s**4 + 8*s**4 - 26*s**l - 5*s**2.
5*s**2*(s - 4)*(s + 1)**2
Solve -3*d**2 - 345*d - 2268 + 197*d + 544*d + 369*d = 0 for d.
3, 252
Let h(z) be the third derivative of z**8/60480 + z**7/5040 + 7*z**5/10 - 23*z**2. Let f(r) be the third derivative of h(r). Determine i, given that f(i) = 0.
-3, 0
Suppose q - 12 = -3*p, 2*p - 12 = -0*q - 2*q. Factor 8*u - 2*u**4 + 16 - 33*u**3 - 16*u**2 + u**2 + u**4 + 25*u**q.
-(u - 1)*(u + 1)*(u + 4)**2
Suppose 1882*p**2 - 2*p**3 + 3798*p**2 - 46*p**3 - 169 + 397 - 2*p**3 + 2278*p = 0. What is p?
-1/5, 114
Let s(g) be the third derivative of g**8/2184 - g**7/91 + 14*g**6/195 + 12*g**5/65 - 36*g**4/13 - 144*g**3/13 - 667*g**2. Suppose s(c) = 0. Calculate c.
-2, -1, 6
Let o(y) = -y**4 - 115*y**3 - 1851*y**2 - 8112*y + 10079. Let c(a) = -a**4 - a**3 + a**2 + 1. Let m(g) = -2*c(g) - 2*o(g). Determine z so that m(z) = 0.
-35, -12, 1
Let j(b) be the third derivative of 0 + 77*b**2 + 0*b**3 - 11/15*b**5 + 0*b + 5/3*b**4 + 1/30*b**6. Solve j(h) = 0 for h.
0, 1, 10
Let c(w) be the first derivative of -w**6/6 - 129*w**5/5 + w**4/4 + 43*w**3 + 4892. What is z in c(z) = 0?
-129, -1, 0, 1
Let w(k) = 31*k**2 + 63*k + 91. Let q(y) = 18*y**2 + 33*y + 45. Let n(a) = -5*q(a) + 3*w(a). Find x such that n(x) = 0.
-4
Let u(x) be the first derivative of x**6/360 + x**5/24 - x**4/4 - 48*x**3 + 102. Let y(k) be the third derivative of u(k). Factor y(w).
(w - 1)*(w + 6)
Factor -19*v**2 + 29*v + 33*v**2 - 12*v - 15*v**2.
-v*(v - 17)
Let s be 1/(-5) + ((-35485)/141)/(-151). Factor -52/15 + 2/15*n**2 - s*n.
2*(n - 13)*(n + 2)/15
Let x(m) be the second derivative of m**7/840 + m**6/120 + m**5/48 + m**4/48 - 2*m**2 - m + 17. Let g(a) be the first derivative of x(a). Factor g(q).
q*(q + 1)**2*(q + 2)/4
Suppose -2*o + 121 = -35. Let -3*j**2 - o - 3745*j - 13 + 3616*j - 35 = 0. What is j?
-42, -1
Let v(f) be the first derivative of -4*f**3/9 + 1004*f**2 - 756012*f + 651. Factor v(u).
-4*(u - 753)**2/3
Let v(g) be the third derivative of -g**7/210 + g**6/10 - 13*g**5/20 + 7*g**4/6 + 27*g**2 - 31. Find s such that v(s) = 0.
0, 1, 4, 7
Let q(c) be the first derivative of 38 + 0*c**2 + 27/4*c - 1/4*c**3. Let q(a) = 0. Calculate a.
-3, 3
Let k(d) be the third derivative of -d**7/42 - 151*d**6/24 - 1327*d**5/3 + 12415*d**4/2 - 20280*d**3 - 2619*d**2. Determine u, given that k(u) = 0.
-78, 1, 4
Let l(n) be the second derivative of -n**6/120 - 3*n**5/2 - 39*n**4/16 + 119*n**3/12 + 69*n + 6. Factor l(f).
-f*(f - 1)*(f + 2)*(f + 119)/4
Solve 0 - 48/7*v**3 + 2/7*v**5 - 16/7*v**4 + 64/7*v**2 + 160/7*v = 0.
-2, 0, 2, 10
Factor 4*p + 48/5 + 2/5*p**2.
2*(p + 4)*(p + 6)/5
Let j(t) = -3*t**2 - 50*t - 179. Let g be j(-10). Let u(y) be the first derivative of -6/35*y**5 + 0*y - 3/7*y**2 - g - 6/7*y**3 - 9/14*y**4. Factor u(k).
-6*k*(k + 1)**3/7
Suppose o + 10 = -n - 2*o, 4*n + 25 = -9*o. Let p = 527/2 - 255. Determine z so that -27/4*z**n - p*z**2 + 19/4*z - 18*z**3 + 3/2 + 27*z**4 = 0.
-1/3, 2/3, 1, 3
Let o(q) be the first derivative of -q**4/36 + 5*q**3/9 - 8*q**2/3 - 144*q - 90. Let k(n) be the first derivative of o(n). Suppose k(h) = 0. What is h?
2, 8
Solve -108 + 980*y - 270*y - 267*y - 4*y**2 - 164 - 359*y = 0.
4, 17
Let i be -2*2/2*195/(-10). Suppose 0 = 4*l + 3*k - i, 2*l + l - 3*k = 24. Factor -1754*g**3 + 0 - 6 + l*g + 1751*g**3.
-3*(g - 1)**2*(g + 2)
Let s be 10/6 + 144/108. Suppose r + 8 - 11 = h, -s*r = -9. Factor -28*a**3 + 6*a**2 - 8/3*a**5 + 0*a + h + 50/3*a**4.
-2*a**2*(a - 3)**2*(4*a - 1)/3
Suppose 0 = 12*n - 31 - 17. Factor 11*k**4 - 40*k + 60*k**2 - 24*k**3 - 6*k**3 - 6*k**n.
5*k*(k - 2)**3
Let d(r) be the second derivative of -r**6/360 + r**5/40 + 49*r**3/6 - 51*r. Let b(h) be the second derivative of d(h). Let b(p) = 0. Calculate p.
0, 3
Let f(u) be the first derivative of -2*u**5/35 + 2*u**4/7 + 8*u**3/3 + 32*u**2/7 + 614. Find b, given that f(b) = 0.
-2, 0, 8
Let d(t) be the second derivative of -17*t - 10/3*t**3 + 0*t**4 - 6*t**2 + 1/12*t**5 + 0. Let b(x) be the first derivative of d(x). Factor b(r).
5*(r - 2)*(r + 2)
Let o be (6 - 12) + (-3)/(-2) + (-135)/(-6). Let b(x) be the first derivative of o - 5/2*x**2 + 5/6*x**3 + 0*x. Find z, given that b(z) = 0.
0, 2
Let a(x) be the third derivative of x**7/4200 - x**6/225 - 101*x**3/6 - 121*x**2. Let n(s) be the first derivative of a(s). Find o such that n(o) = 0.
0, 8
Factor 5162/15*d + 2/5*d**3 - 1682/15 - 70/3*d**2.
2*(d - 29)**2*(3*d - 1)/15
Determine s, given that -696/7*s - 40 + 10/7*s**2 = 0.
-2/5, 70
Factor 4096*f + 93 - 7*f**2 - 4186*f + 0*f**2 + 4*f**2.
-3*(f - 1)*(f + 31)
Factor 6*f**4 + 0*f**4 - 7*f**3 - 2*f**4 + 120*f**2 + 63*f**3 - 68*f**2.
4*f**2*(f + 1)*(f + 13)
Let b(h) be the second derivative of -57*h**5/100 - 93*h**4/20 - 52*h**3/5 + 18*h**2/5 - 2*h + 728. What is p in b(p) = 0?
-3, -2, 2/19
Let q(c) be the third derivative of -3*c**5/10 - c**4/2 - 3*c**3/2 - 11*c**2 + 1. Let l(r) = 19*r**2 + 9*r + 10. Let j(w) = -3*l(w) - 4*q(w). Factor j(d).
3*(d + 1)*(5*d + 2)
Let u(v) be the first derivative of 7*v**6/5 - 267*v**5/25 + 147*v**4/10 + 169*v**3/5 - 168*v**2/5 - 48*v - 6261. Solve u(m) = 0 for m.
-1, -1/2, 1, 20/7, 4
Let v(u) = u**2 - u - 28. Let j be v(-5). Suppose -8*l - 17 = -11*l - j*i, l + 1 = i. Factor -4/7 + 2/7*r**5 + 4/7*r**4 - 4/7*r**l - 16/7*r**2 - 2*r.
2*(r - 2)*(r + 1)**4/7
Let j be (-7)/(-2)*105/49. Factor -25*q + j*q**2 - 125/2.
5*(q - 5)*(3*q + 5)/2
Factor 119*f - 203*f - 9*f**3 - 5*f**2 + 0*f**4 - 7*f**2 + f**4 + 104*f.
f*(f - 10)*(f - 1)*(f + 2)
Factor 2349/4*r**2 - 7203 - 3*r**3 - 28665*r.
-3*(r - 98)**2*(4*r + 1)/4
Let d(u) be the first derivative of -2*u**3/27 + 15*u**2 + 1112*u/9 - 120. Suppose d(o) = 0. Calculate o.
-4, 139
Let r(l) be the first derivative of -6*l + 1/2*l**3 + 33/16*l**4 - 115 + 9/10*l**5 - 9/2*l**2 + 1/8*l**6. Let r(v) = 0. What is v?
-2, -1, 1
Let l(h) be the first derivative of 95 - 1/8*h**2 - 1/8*h**3 - 1/32*h**4 + 0*h. Determine o so that l(o) = 0.
-2, -1, 0
Let 0 + t**4 + 1/4*t**3 - 17/6*t**2 - 1/12*t**5 - 2*t = 0. Calculate t.
-1, 0, 2, 12
Let x(i) = 2*i**3 + 74*i**2 + 72*i + 3. Let d be x(-36). Factor 154*n**2 - 17*n - 160*n**2 + 17*n + 3*n**d.
3*n**2*(n - 2)
Let y = -1792173 + 5376586/3. Factor 0 - y*h + 1/3*h**2.
h*(h - 67)/3
Suppose 0 = -43*j + 36*j + 21. Solve 2587 + 4857 + 78*r**2 - 2028*r - 2*r**3 + 3071 + 7061 + r**j = 0.
26
Let d(u) be the first derivative of -3/8*u**4 - 96*u - 17/2*u**3 - 8 - 60*u**2. Solve d(y) = 0.
-8, -1
Suppose 84/5*k - 3/5*k**5 - 81/5*k**3 + 48/5*k**4 + 0 - 48/5*k**2 = 0. Calculate k.
-1, 0, 1, 2, 14
Let w(y) be the first derivative of 3*y**4/4 - 13*y**3 + 51*y**2 + 144*y - 883. Factor w(k).
3*(k - 8)*(k - 6)*(k + 1)
Let a be (66/385)/((-2)/(-180)) + 912/(-152). Suppose -34/7*f - 30/7*f**3 + a*f**2 - 2/7*f**4 + 0 = 0. Calculate f.
-17, 0, 1
Suppose -4*y = -5*i, -8 = -7*i + 10*i - 4*y. Factor -32/3*w + i*w**3 + 26/3*w**2 - 2.
2*(w - 1)*(w + 3)*(6*w + 1)/3
Let d(r) = -7*r**2 - 3736*r - 699368. Let b(v) = -15*v**2 - 7470*v - 1398730. Let g(m) = 2*b(m) - 5*d(m). Factor g(z).
5*(z + 374)**2
Let b be (18/(-42))/((-240)/115640). Factor -49/2*p**4 - b*p**3 - 18*p + 124*p**2 + 0.
-p*(p + 9)*(7*p - 2)**2/2
Suppose -214*y - 3933 = -233*y. Find v such that y*v**2 - 57*v - 32 + 185*v**2 - 31*v - 412*v**2 = 0.
-4, -2/5
Find y, given that -256*y + 667*y**2 - 48 - 663*y**2 - 126 - 86 = 0.
-1, 65
Let t(o) = -3*o**3 - 9*o**2 - 15*o - 9. Let z(l) = -12*l**3 - 38*l**2 - 63*l - 37. Let j(p) = -11*t(p) + 3*z(p). Find x such that j(x) = 0.
-2, -1
Let s(v) be the third derivative of 1/24*v**4 - 1/18*v**5 + 0*v + 1/30*v**6 - 1/105*v**7 + 0*v**3 + 1/1008*v**8 - 29*v**2 + 0. Factor s(b).
b*(b - 3)*(b - 1)**3/3
Let a(f) be the third derivative of -3*f**8/280 + 72*f**7/175 - 41*f**6/75 - 479*f**5/75 - 707*f**4/60 - 46*f**3/5 - 6*f**2 + 358. Let a(o) = 0. Calculate o.
-1, -2/3, -1/3, 3, 23
Let y(r) be the third derivative of r**5/48 - 55*r**4/24 - 115*r**3/6 - 181*r**2. Factor y(k).
5*(k - 46)*(k + 2)/4
Let t be 21/((-63)/(-2))*138. Let j = 1018/11 - t. Suppose -2/11*g**2 + 0 + j*g = 0. Calculate g.
0, 3
Let b(q) = -5*q**2 - 6*q + 7. Let v be b(3). Let t = 56 + v. Factor -w**2 - 4*w + t*w**2 - w**2 + 6*w**2.
4*w*(w - 1)
Factor -1925/3*l + 640 + 5/3*