6*o**2 - 617*o - 84. Let x(a) = 2*n(a) - 27*t(a). Factor x(d).
3*(d + 4)*(d + 7)*(7*d + 1)
Let g(j) be the third derivative of 8/9*j**3 + 1/15*j**5 - 39*j**2 + 0*j + 1/3*j**4 + 1/180*j**6 + 1. Factor g(i).
2*(i + 2)**3/3
Let -5*x**3 - 5*x**3 + 5*x**3 + 818 - 21*x**2 - 800 + 2*x**3 + 3*x + 3*x**4 = 0. What is x?
-2, -1, 1, 3
Let l(w) be the second derivative of -5*w**4/12 - 1315*w**3/3 + 7935*w**2/2 - 1200*w + 2. Factor l(z).
-5*(z - 3)*(z + 529)
Let t(z) be the third derivative of -z**8/84 + 766*z**7/105 - 5762*z**2 - 2*z. Factor t(p).
-4*p**4*(p - 383)
Let i(v) be the second derivative of 1/2*v**4 + 16/3*v**3 - 1/10*v**5 + 67*v + 0 + 12*v**2. Determine u so that i(u) = 0.
-2, -1, 6
Suppose 6*o - j - 25 = 4*o, -34 = -2*o - 2*j. Let f be 8/(-22)*(-21)/o. Factor -f*a**2 + 6/11*a + 2/11*a**3 - 2/11.
2*(a - 1)**3/11
Let i(r) = r**4 + r**2 + r. Let n(o) = 9*o**4 + 89*o**3 + 212*o**2 + 180*o + 45. Let m(f) = 6*i(f) + 2*n(f). Determine g so that m(g) = 0.
-3, -1, -5/12
Let t be 6/17 + (-290410)/30583 - (-9)/((-36)/(-40)). Factor -t*i**2 - 20/7*i - 16/7.
-2*(i + 2)*(3*i + 4)/7
Suppose 4*k - 739 = -3*t, -3*k + 0*k + 518 = -5*t. Let u = 279 - k. Determine c, given that 94*c**2 - u*c**2 - 22 + 24*c - 10 = 0.
2, 4
What is k in 8430 - 65405 - 2130*k - 119344 - 5*k**2 + 77222 - 127748 = 0?
-213
Let x(s) be the second derivative of 2*s + 9 + 1/90*s**4 - 1/15*s**3 + 2/15*s**2. Factor x(z).
2*(z - 2)*(z - 1)/15
Let r = -1414/45 + 344/9. Let k(a) be the first derivative of -62/15*a**3 - 39 - 3/4*a**4 - 8/5*a - r*a**2. Factor k(p).
-(p + 2)**2*(15*p + 2)/5
Let 3/4*m**3 + 0 - 255/2*m + 507/4*m**2 = 0. Calculate m.
-170, 0, 1
Let l = -471 + 473. Let w be l*44*(-5)/(-60). Factor 0*z - 10/3*z**2 + w*z**3 - 14/3*z**4 + 2/3*z**5 + 0.
2*z**2*(z - 5)*(z - 1)**2/3
Let b(q) be the first derivative of -q**3/15 - 1357*q**2/5 - 1841449*q/5 - 1132. Solve b(z) = 0.
-1357
Let v(n) = -3*n**2 + 12*n + 2. Let y be v(4). Factor 1680*q**4 + 0*q**2 - q**3 - 841*q**4 + 6*q**y - 840*q**4.
-q**2*(q - 2)*(q + 3)
Let b(j) = 4*j**2 - 24*j + 8. Let x be b(-7). Let m = x + -372. Factor -108*n**3 - 81/4*n**5 + 81*n**4 - 12*n + 60*n**2 + m.
-3*n*(n - 2)*(3*n - 2)**3/4
Let j be (-6 - (-2 - 3)) + (-3)/(-1). Suppose -58*z**4 + 160*z**3 - 47*z**4 - 10*z - 65*z**j + 20*z**4 = 0. Calculate z.
-2/17, 0, 1
Let m be (9/(-4))/(15/(-10)). Let t = -10/22667 + 22687/45334. Factor -1 + 1/2*v**4 - 3/2*v + t*v**2 + m*v**3.
(v - 1)*(v + 1)**2*(v + 2)/2
Let u(a) be the first derivative of -a**5/240 + a**4/24 + 5*a**3/24 - 85*a**2 + 161. Let v(q) be the second derivative of u(q). Factor v(d).
-(d - 5)*(d + 1)/4
Let m(h) = 125 - 11*h + 12*h + 24*h. Let n be m(-5). Suppose -2/9*l**3 + n + 2/9*l - 2/9*l**2 + 2/9*l**4 = 0. What is l?
-1, 0, 1
Let j be (-23)/(-3) - ((-22)/3 - -7). Suppose -603 = -j*y - y. Factor -2*k**3 - y*k**2 + k**3 + 57*k**2.
-k**2*(k + 10)
Suppose 14 = 41*i - 34*i. Factor 76*c**2 + 78*c**2 - 120*c - 232*c**i + 74*c**2.
-4*c*(c + 30)
Let p(n) be the second derivative of 0*n**3 + 2 - 1/30*n**4 + 1/150*n**5 + 4/15*n**2 - 2*n. Factor p(z).
2*(z - 2)**2*(z + 1)/15
Let y = 46849 + -46849. Determine h, given that -6/13*h**4 + 2*h**2 + 76/13*h**3 + 0 + y*h = 0.
-1/3, 0, 13
Let z(f) be the first derivative of 5/6*f**4 - 92 - 2/9*f**3 - 8/3*f**2 + 2/15*f**5 - 8/3*f - 1/9*f**6. Factor z(p).
-2*(p - 2)**2*(p + 1)**3/3
Let m be (-28)/(-322) - (-980)/(-2806). Let n = 542/671 + m. What is q in 0*q - 2/11*q**3 - n*q**2 + 0 = 0?
-3, 0
Let c = -2/591951 + 2367818/4143657. Suppose c*q - 48/7 + 10/7*q**2 = 0. What is q?
-12/5, 2
Let m be -6*91/78 + 7. Let r(a) be the second derivative of 0*a**4 - 2/21*a**7 - 4/15*a**6 + 0*a**2 - 1/5*a**5 + 0 - 29*a + m*a**3. Factor r(i).
-4*i**3*(i + 1)**2
Let n(h) be the third derivative of h**6/240 - 281*h**5/10 + 78961*h**4 - 355008656*h**3/3 - 10*h**2 + 2*h - 44. Find m such that n(m) = 0.
1124
Suppose -4*q = -v + 4, 2*v - 9 = v + 3*q. Suppose 0 = -3*s + 9 + v. Factor -8*h**2 + s*h**3 - 18*h**4 + h**3 - 14*h**4 + 28*h**4.
-4*h**2*(h - 2)*(h - 1)
Let u(t) be the first derivative of t + 1/20*t**5 + 0*t**3 + 0*t**2 + 1/6*t**4 - 1. Let a(n) be the first derivative of u(n). Factor a(l).
l**2*(l + 2)
Let i(d) be the second derivative of 1/210*d**7 + 1/75*d**6 + 1/100*d**5 + 0*d**3 + 0*d**2 + 0*d**4 + 3 + 2*d. Factor i(k).
k**3*(k + 1)**2/5
Let h(m) = -6*m + 402. Let b be h(67). Let w(z) be the third derivative of b*z**3 + 0 - 18*z**2 + 1/6*z**6 - 1/3*z**4 + 0*z - 1/5*z**5. Factor w(i).
4*i*(i - 1)*(5*i + 2)
Let j(r) = 25041*r + 350578. Let h be j(-14). Determine a, given that 0 - 2/7*a**5 - 6/7*a**h + 2*a**2 + 6/7*a**3 - 12/7*a = 0.
-3, -2, 0, 1
Let l be 0/(-2)*285/570. Let c(j) be the third derivative of 0*j**6 + 0*j**4 + 0*j + 2/105*j**7 - 4/15*j**5 + l*j**3 + 19*j**2 + 0. Solve c(w) = 0.
-2, 0, 2
Determine o so that -3/8*o**2 + 105/2 + 417/8*o = 0.
-1, 140
Let l(v) be the first derivative of 3*v**4/4 - 42*v**3 - 2372. Factor l(p).
3*p**2*(p - 42)
Suppose 5*i + 40*g = 45*g + 75, -2*i + 5*g = -15. Let t be (i/90)/((-4)/(-72)). Find p, given that 0 - 32/21*p**2 - 2/7*p**t + 26/21*p**3 + 8/21*p = 0.
0, 1/3, 2
Suppose 530/3*d**4 - 1840/3*d**2 - 1120/3 + 4520/3*d - 1060/3*d**3 - 35/6*d**5 = 0. What is d?
-2, 2/7, 2, 28
Let k(i) be the first derivative of 50*i**2 - 5/3*i**3 + 105 + 105*i. Factor k(s).
-5*(s - 21)*(s + 1)
Let d be ((-4)/(-46))/(19984/114908). Solve 1/2*f**3 + 0 + 0*f + d*f**4 - f**2 = 0 for f.
-2, 0, 1
Let o(b) = -2*b**3 - 17*b**2 + 13*b - 28. Let v be o(8). Let d = v - -2042. Factor 57/2*u**2 - 33/2*u - d*u**3 - 6.
-3*(u - 4)*(u - 1)*(4*u + 1)/2
Let l be 30/(-180) + (2/5)/((-48)/(-30)). Let i(b) be the third derivative of 0*b**3 + 0*b + 0 - 35/24*b**4 - l*b**5 + 8*b**2. Factor i(q).
-5*q*(q + 7)
Suppose -d = -g - 4*d + 4, -2*g + 8 = -5*d. Factor 24*l**3 - 95*l - 26*l**2 + 81*l + 2*l**g - 34*l**3.
2*l*(l - 7)*(l + 1)**2
Factor 16*r**2 + 2808 - 63 - 56*r**2 + 5*r**2 + 2234*r + 4156*r.
-5*(r - 183)*(7*r + 3)
Let z(k) be the second derivative of 35 + k + 8/25*k**5 + 0*k**2 + 7/75*k**6 + 2/15*k**4 + 0*k**3. Factor z(c).
2*c**2*(c + 2)*(7*c + 2)/5
Let 46*g**2 + g**4 - 252430*g + 18*g**3 + 10*g**2 + 32 + 252502*g + g**4 = 0. Calculate g.
-4, -2, -1
Let k(h) be the third derivative of 1/3*h**3 + 0 - 228*h**2 + 0*h + 1/240*h**5 - 1/16*h**4. What is c in k(c) = 0?
2, 4
Suppose -68 = -77*t + 75*t. Factor -t*d**2 - 9*d**3 + d**4 - 24*d + 9 + 68 - 77.
d*(d - 12)*(d + 1)*(d + 2)
Let t(s) = 2*s**2 - 9*s + 15. Let c(j) = 2*j**2 - 10*j + 16. Suppose 223 + 71 = 6*p. Let i = p - 47. Let u(o) = i*t(o) - 3*c(o). Suppose u(x) = 0. Calculate x.
3
Suppose -3 - 157 = 16*t. Let k be (-8)/(-10)*t/(-4). Factor 22*m**k - 38*m**2 - 2*m**3 + 14*m**2.
-2*m**2*(m + 1)
Let h(p) be the third derivative of 0*p + 1/1155*p**7 + 0*p**3 + 0 - 1/165*p**5 - 37*p**2 + 1/660*p**6 + 0*p**4. Solve h(a) = 0.
-2, 0, 1
Let h = 8485/21 + -66305/168. Factor h + 3/8*b**2 + 15/4*b.
3*(b + 5)**2/8
Suppose -2*c - 10*c = 13*c - 100. Let s(q) be the third derivative of 1/30*q**5 + 0*q - 2*q**3 - 18*q**2 + 0 + 5/12*q**c. Factor s(t).
2*(t - 1)*(t + 6)
Let s(x) be the third derivative of -11*x**7/70 - 7*x**6/30 + 29*x**5/60 + 7*x**4/6 + 2*x**3/3 + 64*x**2. Find m, given that s(m) = 0.
-1, -2/3, -2/11, 1
Let f(z) be the second derivative of 140*z + 0 + 0*z**2 - 1/10*z**4 + 0*z**3 - 1/100*z**5. Let f(v) = 0. What is v?
-6, 0
Let g = -539666/13 - -41534. Let j = -763/39 + g. Factor -1/3*x**3 - 2 + 2/3*x**2 + j*x.
-(x - 3)*(x - 1)*(x + 2)/3
Let c(n) be the first derivative of 3*n**4/4 + 354*n**3 + 62658*n**2 + 4929096*n - 608. Let c(x) = 0. What is x?
-118
Let m(p) be the third derivative of -11/24*p**4 + 4/3*p**3 - 29*p**2 + 0*p + 0 + 1/20*p**5. Let o(b) = b**2 - b. Let i(q) = -2*m(q) + 10*o(q). Factor i(h).
4*(h - 1)*(h + 4)
Factor 2/9*g**3 + 38*g + 46/9*g**2 + 90.
2*(g + 5)*(g + 9)**2/9
Suppose -5*z + 7*m = 5*m - 235, -235 = -5*z - 3*m. Factor -206 + 833*r - 64 - 82*r**2 + 2*r**3 - 530 + z*r.
2*(r - 20)**2*(r - 1)
Let k(w) be the first derivative of -16/33*w**3 - 1/11*w**4 + 0*w**2 + 37 + 0*w + 2/55*w**5. Find o, given that k(o) = 0.
-2, 0, 4
Let s(o) be the second derivative of 0 + 0*o**2 - 5/3*o**3 + 19*o - 25/24*o**4 - 1/72*o**6 + 1/4*o**5. Let b(q) be the second derivative of s(q). Factor b(x).
-5*(x - 5)*(x - 1)
Suppose