3. Suppose 3*q - 2*u - 16 = 0, 5*q - 5 = -2*u + 11. Let s be j(q). Factor 71 + s*m**2 - 33 + 10 + 24*m.
3*(m + 4)**2
Suppose -856*w + d = -851*w - 2, 3*w + d + 2 = 0. Factor 8/5*o**2 + 24/5*o - 2/5*o**3 + w.
-2*o*(o - 6)*(o + 2)/5
Let p = 716897 - 2150690/3. Determine j, given that 1/3*j**5 - 2/3*j + 0 + j**4 - j**2 + p*j**3 = 0.
-2, -1, 0, 1
Let q = -17632/45 - -3527/9. Let x(o) be the third derivative of o**4 + 5 - 10/3*o**3 - q*o**5 + 0*o + 2*o**2. Suppose x(t) = 0. What is t?
1, 5
Let q = 347/12 + -331/12. Factor -2 - q*r + 2/3*r**2.
2*(r - 3)*(r + 1)/3
Let j(x) be the second derivative of x**6/165 + 184*x**5/55 + 367*x**4/66 + 394*x. Factor j(p).
2*p**2*(p + 1)*(p + 367)/11
Let n(p) be the first derivative of -p**5/30 + p**4/4 - 2*p**2 - 34. Let w(t) be the second derivative of n(t). Factor w(u).
-2*u*(u - 3)
Let k be (-54)/(-81) + (17/3)/(-1). Let q be (-25)/(-7) - k/(30/(-18)). Factor 13/7*h - 3/7 - q*h**2.
-(h - 3)*(4*h - 1)/7
Let i(m) be the first derivative of 2/15*m**3 - 2/5*m**2 - 6/5*m + 35. Factor i(d).
2*(d - 3)*(d + 1)/5
Let m(d) be the third derivative of -d**8/840 - 16*d**7/525 - 13*d**6/50 - 74*d**5/75 - 121*d**4/60 - 12*d**3/5 + 1097*d**2. Determine x, given that m(x) = 0.
-9, -4, -1
Suppose -108*g - 99*g + 128*g + 158 = 0. What is f in -58/13*f**3 - 86/13*f**g - 16/13 - 18/13*f**4 - 2/13*f**5 - 60/13*f = 0?
-4, -2, -1
Let l(j) = -2*j**3 + 16*j**2 - 32*j + 2. Let x be (76/(-95))/((-4)/(-10)). Let f(b) = -2*b**3 + 16*b**2 - 32*b + 3. Let v(n) = x*f(n) + 3*l(n). Factor v(d).
-2*d*(d - 4)**2
Factor 15*p**2 - 22*p**4 + 22*p**2 - 14*p**4 + 35*p**4 + 21*p**2 + 40*p + 17*p**3.
-p*(p - 20)*(p + 1)*(p + 2)
Suppose 203992*l - 203956*l - 108 = 0. Factor -4/5*b**l + 1/5*b**2 + 4/5*b + 0 - 1/5*b**4.
-b*(b - 1)*(b + 1)*(b + 4)/5
Let h(k) = -k**3 - 13*k**2 - 11*k + 20. Let w be h(-10). Let i = w - -693/4. Suppose -15/4*u - 1/2 - i*u**2 = 0. Calculate u.
-1, -2/13
Let r be 7/(-18)*-3*(-60)/495. Let k = 8/99 - r. Factor -k*h**2 - 2/3*h - 4/9.
-2*(h + 1)*(h + 2)/9
Let y be (-27 + 1644/60)/((40/(-6))/(-5)). Let l(j) be the first derivative of 23 + 1/15*j**3 - 4/5*j + y*j**2. Factor l(u).
(u - 1)*(u + 4)/5
Determine j so that -7/2*j**3 + 7/2*j - 19/2*j**2 + 9 + 1/2*j**4 = 0.
-2, -1, 1, 9
Let p(c) = -7*c**3 - 2*c**2 + 2 - 5*c**2 - c - 4*c**2 + 4*c**2 - 29. Let i(t) = -t**3 - t**2 - t - 4. Let q(m) = 6*i(m) - p(m). Suppose q(j) = 0. What is j?
-3, 1
Suppose 29 = 4*w - 2*h + 299, -h - 129 = 2*w. Let r = w - -70. Factor r*c**4 - 11*c + 4*c**2 + 1 + 8*c**3 + 4*c**3 - 9 - c.
4*(c - 1)*(c + 1)**2*(c + 2)
Let v = 433258/722095 - 1/722095. Find r, given that 0*r + 18/5*r**3 + 0 - 18/5*r**5 + v*r**2 - 3/5*r**4 = 0.
-1, -1/6, 0, 1
Let u(c) be the first derivative of c**6/120 + c**5/16 + c**4/8 + 28*c - 80. Let q(j) be the first derivative of u(j). Factor q(i).
i**2*(i + 2)*(i + 3)/4
Let r(o) = -o**2 + 14*o - 18. Let n be r(11). Factor -n + 13 - 34 - 14*y + 2*y - y**2.
-(y + 6)**2
Let p(s) be the first derivative of -s**3/3 + 11*s**2/2 + 26*s - 590. Suppose p(t) = 0. What is t?
-2, 13
Let n(m) = 13*m**2 - 19*m + 6. Let s(y) = y**2 + 9*y. Let z(g) = -5*g**2 - 29*g - 1. Let x(v) = 7*s(v) + 2*z(v). Let d(b) = 2*n(b) + 9*x(b). Factor d(r).
-(r - 6)*(r - 1)
Let y be (-530)/1060 - (-3)/4. Let i be 12/(-30) - (-24)/10. Let -1/2 - 1/4*w + y*w**i = 0. Calculate w.
-1, 2
Let a(p) be the second derivative of -p**5/40 + 41*p**4/12 - 152*p**3/3 + 296*p**2 - 53*p + 23. Determine m, given that a(m) = 0.
4, 74
Let t(o) be the first derivative of 1/3*o**6 - o**2 + 0*o**4 + 0*o - 104 - 4/3*o**3 + 4/5*o**5. Solve t(n) = 0 for n.
-1, 0, 1
Find o such that -1176/5 - 3/5*o**3 - 18*o**2 - 756/5*o = 0.
-14, -2
Let c(n) be the first derivative of 7*n**6/1620 - 187*n**5/540 - n**4/2 - 36*n**3 - 262. Let b(l) be the third derivative of c(l). Determine w so that b(w) = 0.
-2/7, 27
Suppose 3*u + n = 13, 5*u - 5*n = 4*u - 1. Let 506*w**3 + 4998*w**u - 5219*w**3 - 686*w**5 - 96 + 768*w**2 + 448*w - 719*w**3 = 0. What is w?
-2/7, 2/7, 1, 6
Let n(x) be the third derivative of x**5/20 - 23*x**4/2 + 1058*x**3 + 71*x**2 - x. Find a such that n(a) = 0.
46
Let q(j) be the second derivative of -17/5*j**2 + 58*j + 0 + 1/15*j**4 - 11/5*j**3. Solve q(g) = 0 for g.
-1/2, 17
Let o(d) be the second derivative of d**4/30 + 7*d**3/3 - 396*d**2/5 - 6701*d. Factor o(u).
2*(u - 9)*(u + 44)/5
Let q be (-6)/(-20)*36/(-27)*-1. Let h(s) be the first derivative of -9 - q*s**3 + 6/5*s + 3/20*s**4 - 3/10*s**2. Factor h(n).
3*(n - 2)*(n - 1)*(n + 1)/5
Let f = 1440625/8 - 180071. Find c such that 3*c**3 + 0 + 3/8*c**4 + f*c**2 + 9/2*c = 0.
-4, -3, -1, 0
Let c(h) be the first derivative of 45/14*h**4 + 0*h + 12/7*h**2 - 25 + 6/7*h**5 - 4/7*h**6 - 40/7*h**3. What is y in c(y) = 0?
-2, 0, 1/4, 1, 2
Let r(a) be the third derivative of -a**7/42 - 31*a**6/24 - 2*a**2 - 47*a + 3. Let r(s) = 0. What is s?
-31, 0
Let f = -24 + 30. Let n be (-1)/6 - (f + 110/(-12)). Solve -12*k + 12 + 24*k - 3*k**2 + 4*k**3 - 7*k**n = 0 for k.
-2, -1, 2
Suppose 14*i - 25 = -53. Let w(j) = j**3 - 2*j**2 + j. Let r(k) = -6*k**4 + 7*k**3 + 14*k**2 - 11*k. Let c(o) = i*r(o) - 6*w(o). Determine l so that c(l) = 0.
-1, 0, 2/3, 2
Let t(o) = 127*o**2 + 1028*o - 27. Let n(v) = -4*v**2 + v + 3. Let f(m) = 5*n(m) - t(m). Find b, given that f(b) = 0.
-7, 2/49
Let t be 2*(12635/(-57))/(-35). Factor t*j + 1/3*j**2 + 361/3.
(j + 19)**2/3
Let k(p) be the first derivative of -129 + 8/21*p**3 + 2*p**2 + 24/7*p. Factor k(d).
4*(d + 2)*(2*d + 3)/7
Let d be 6/(18/15) - 7. Let v be (-4 + 2)*47/d. Determine o so that 19*o**3 + 51*o**2 + 192 - v*o + 287*o - 16*o**3 = 0.
-8, -1
Let j(w) be the first derivative of w**4/6 + 100*w**3/9 - 71*w**2 + 108*w + 6948. Let j(o) = 0. Calculate o.
-54, 1, 3
Let w(c) be the third derivative of -c**5/90 + 293*c**4/3 - 343396*c**3 + c**2 - 27*c + 4. Factor w(g).
-2*(g - 1758)**2/3
Let d(y) = -5*y**3 - 18*y**2 + 3*y + 8. Let k(f) = 6*f**3 + 20*f**2 - 5*f - 7. Let p(m) = 7*d(m) + 6*k(m). Suppose p(o) = 0. Calculate o.
-2, 1, 7
Let d = -2525 - -1259. Let m = d - -1268. Determine h so that 16/7*h + 16/7 - 200/7*h**5 - 20*h**m + 340/7*h**4 - 32/7*h**3 = 0.
-2/5, 1/2, 1
Suppose 1042*n - 549 - 980 = -434 + 989. Solve 7*x + 0 - 1/2*x**3 - 5/2*x**n = 0 for x.
-7, 0, 2
Let b(v) be the third derivative of v**8/1120 - v**7/280 - v**6/90 - 17*v**5/30 + 25*v**2 + v. Let x(y) be the third derivative of b(y). Factor x(n).
2*(3*n - 4)*(3*n + 1)
Let p be (96/288)/((1/30)/((-12)/(-70))). Let z(r) be the first derivative of -54/7*r + 13 - 1/21*r**6 + p*r**3 - 2/5*r**5 + 27/7*r**2 - 5/7*r**4. Factor z(q).
-2*(q - 1)**2*(q + 3)**3/7
Let b(h) be the third derivative of -h**5/150 + 7*h**4/30 + 17*h**3/5 + 7117*h**2. Factor b(q).
-2*(q - 17)*(q + 3)/5
Factor 94/17 - 88/17*t - 6/17*t**2.
-2*(t - 1)*(3*t + 47)/17
Let z = -109 + 109. Factor -90 + 140 - 80*g + 211 + 59 + 5*g**2 + z*g**2.
5*(g - 8)**2
Suppose 0 = -4*v - 5*f - 4, 5*v - 40 = 5*f. Let c be 2/v + (10 - 627/110). Determine u so that 4/5*u**2 - c - 4/5*u = 0.
-2, 3
Let t(p) be the second derivative of -p**5/30 - 335*p**4/18 + p**3/9 + 335*p**2/3 - 2623*p. Solve t(x) = 0.
-335, -1, 1
Suppose 0 = 4*v - 3*o + 5*o - 18, 0 = 2*v - 2*o. Determine r, given that 12*r + 7 + r**v - 12*r**2 + 3*r**3 - 13 + 2 = 0.
1
Let v be 33 + 22 + (-6440)/120. Factor 4/3*r**2 + 0 + v*r**4 + 0*r + 10/3*r**3.
2*r**2*(r + 2)*(2*r + 1)/3
Let o(l) = -8*l**4 + 986*l**3 + 3191*l**2 + 2767*l + 549. Let j(t) = 5*t**4 + t**3 + t**2 - t + 1. Let z(c) = 3*j(c) + o(c). Solve z(m) = 0.
-138, -2, -1, -2/7
Let k(a) be the second derivative of 34/105*a**6 + 4/35*a**5 - 8/147*a**7 + 18/7*a**2 - 50/21*a**4 - 16/7*a**3 + 0 - 22*a. Let k(c) = 0. Calculate c.
-1, 1/4, 3
Let m(t) = -t**3 + 108*t**2 - 1394*t - 93. Let p be m(93). Let r(n) be the second derivative of 0*n**3 + p + 0*n**2 - 27*n + 1/54*n**4. Factor r(a).
2*a**2/9
Let o(j) be the second derivative of 4/3*j**4 + 1/5*j**5 + 12*j**2 - 1 - 17*j - 22/3*j**3. Factor o(h).
4*(h - 1)**2*(h + 6)
Factor -45*k**3 + 285*k**2 + 24141*k + 100 - 12244*k - 12217*k.
-5*(k - 5)*(3*k - 2)**2
Let h(c) be the second derivative of -1/6*c**6 - 2*c**2 - 15*c + 5/4*c**4 + 1/10*c**5 + 2/3*c**3 + 1. Determine r so that h(r) = 0.
-1, 2/5, 2
Let f = 83/915 - -13/305. Let k(p) be the first derivative of 0*p 