 1)
Let n = -11/3965 + 63561/43615. Factor 0 + 2/11*i**2 - n*i.
2*i*(i - 8)/11
Let c(t) be the second derivative of t**4/3 - 16*t**3 + 280*t**2 + 119*t - 3. Factor c(y).
4*(y - 14)*(y - 10)
Factor -245/2*q + 1830 - 5/2*q**2.
-5*(q - 12)*(q + 61)/2
Let a(u) be the third derivative of 1/66*u**4 + 1/33*u**3 + 0*u + 1/330*u**5 - 46*u**2 + 0. Suppose a(t) = 0. What is t?
-1
Suppose -20*t - 252 = -11*t. Let c be (-2 - (-22)/3) + (t - -23). Factor c*z**3 + 0 + 1/3*z**2 - 2/3*z.
z*(z - 1)*(z + 2)/3
Let t = -1/2031572 - -4063151/14221004. Factor 0 + t*r**3 - 6/7*r**2 - 20/7*r.
2*r*(r - 5)*(r + 2)/7
Solve -35/3*x - 1/6*x**3 + 71/6*x**2 + 0 = 0.
0, 1, 70
Suppose 3678 = -4*c - 2*z, 2*z + 1105 = -3*c - 1653. Let b be 6/21 - c/210. Factor 10/3*u**2 - 4/3 - 8/3*u**3 + b*u.
-2*(u - 2)*(u + 1)*(4*u - 1)/3
Let v = 55 + 16. Factor 67*g**3 - v*g**3 - 223 + 59*g**2 - 320*g + 17*g**2 - 177.
-4*(g - 10)**2*(g + 1)
Let n be (-45)/40 - (-2412)/2144. Factor n + 1/7*s**2 - 2/7*s.
s*(s - 2)/7
Let q(d) = -d**4 - 93*d**3 - 580*d**2 - 1002*d - 517. Let h(c) = -5*c**4 - 187*c**3 - 1158*c**2 - 2002*c - 1033. Let z(b) = -6*h(b) + 14*q(b). Solve z(l) = 0.
-2, -1, 65/4
Let s(d) = -526*d**3 - 6*d**2 - 3*d + 2. Let z be s(-1). Factor 135*f + 56*f**3 - 109*f**3 - 9*f**2 + z + 50*f**3.
-3*(f - 7)*(f + 5)**2
Let z(x) be the second derivative of 0*x**2 + 70*x + 0*x**3 + 0*x**5 + 0 + 1/20*x**6 + 0*x**4. Factor z(r).
3*r**4/2
Let -9 - 856*f + 729*f**2 - 23 + 1734*f + 2586*f + 139*f**2 = 0. Calculate f.
-4, 2/217
Suppose -943*j = 96*j - 2078. Factor -162*n**j + 3*n**3 - 657/4*n - 165/4.
3*(n - 55)*(2*n + 1)**2/4
Let z be (24 - (-30400)/(-1254))*-9. Solve z*i**2 + 2/11*i**5 + 0 + 38/11*i**3 + 0*i + 16/11*i**4 = 0.
-4, -3, -1, 0
Let a(j) = -j**2 - 3*j**2 + 24*j - 128 - j**2 + 5*j. Suppose -2*b + 6*b + 12 = 0. Let v(k) = k**2 + k. Let d(w) = b*v(w) - a(w). Suppose d(y) = 0. What is y?
8
Factor 96*z + 234/5*z**2 + 9*z**3 + 3/5*z**4 + 288/5.
3*(z + 1)*(z + 4)**2*(z + 6)/5
Let w = -253 - -244. Let k be (1305/260)/w*-8. Factor -k*y + 14/13 + 8/13*y**2.
2*(y - 7)*(4*y - 1)/13
Let l(b) be the third derivative of b**8/1680 + 13*b**7/1050 + 41*b**6/600 + 47*b**5/300 + 3*b**4/20 - 283*b**2. Solve l(j) = 0 for j.
-9, -2, -1, 0
Solve 7260*f + 513*f**4 - 2845*f**3 - 4180*f**2 - 287*f**4 - 5*f**5 - 456*f**4 = 0 for f.
-22, -3, 0, 1
Let l(o) = -o**2 + 2*o. Suppose -14*x + 9*x = -5. Let m(i) = -6*i + 5. Let r(u) = x*l(u) + m(u). Solve r(f) = 0 for f.
-5, 1
Suppose 5*i = 4*b + 15, 3*i - 6*i + 3*b = -9. Determine s, given that -3*s**2 + 0*s**i - s**3 - 28 + s + 21 + 10 = 0.
-3, -1, 1
Let n = -2419199/120 + 20160. Let b(j) be the second derivative of 1/80*j**5 + 13*j + n*j**6 + 0 + 0*j**2 - 1/24*j**3 - 1/48*j**4. Factor b(x).
x*(x - 1)*(x + 1)**2/4
Let l(v) be the first derivative of -3*v**4/4 + 1818*v**3 - 1652562*v**2 + 667635048*v - 1774. Determine o, given that l(o) = 0.
606
Let n(l) be the first derivative of -l**7/4200 - l**6/360 + 4*l**3/3 - 189. Let r(d) be the third derivative of n(d). Factor r(a).
-a**2*(a + 5)/5
Suppose 291*z - 3*w = 296*z - 36, 4*z - 4*w = -16. Let -8/3*t**2 - 8/3*t**z + 2/3*t**5 + 2/3*t**4 + 0*t + 0 = 0. What is t?
-2, -1, 0, 2
Let o(u) = 12*u**2 - 4*u - 10. Let q(m) = m**2 + m - 1. Let l = 25 + -77. Let a = -50 - l. Let s(r) = a*o(r) - 44*q(r). Solve s(g) = 0 for g.
-3, 2/5
Suppose 5/2*a**3 + 65*a - 40 - 55/2*a**2 = 0. What is a?
1, 2, 8
Let h = 8828/15 + -8732/15. Factor 28/5*t - 4/5*t**2 + h.
-4*(t - 8)*(t + 1)/5
Suppose -20/7*q**3 + 0 - 184/7*q**2 - 36/7*q = 0. What is q?
-9, -1/5, 0
Let o be (73/146)/((-6)/(-9))*64/78. Let -2/13*w**5 - 6/13*w**3 + 0*w**2 + 0*w + o*w**4 + 0 = 0. What is w?
0, 1, 3
Let g(k) be the third derivative of -k**5/60 - 213*k**4/8 - 2188*k**2. Find x, given that g(x) = 0.
-639, 0
Suppose -3*i + 2*f = -31, -1665 + 1621 = 4*f. Determine m, given that 3/4 + 3/4*m**4 + 15/4*m + 15/4*m**5 - 15/2*m**i - 3/2*m**2 = 0.
-1, -1/5, 1
Let h(i) = 5*i**3 + 26*i**2 - 33*i + 14. Let k(c) = 7*c**3 + 26*c**2 - 32*c + 14. Let a(t) = 5*h(t) - 4*k(t). Solve a(r) = 0 for r.
2/3, 1, 7
Find j, given that 46353*j**3 + 5*j**5 + 53980*j**2 - 196000*j - 995*j**4 + 2627*j**3 + 10253 - 210253 = 0.
-2, -1, 2, 100
Let u(x) be the first derivative of 2*x**5/25 + 89*x**4/20 - 182*x**3/3 - 477*x**2/10 + 476. Determine f, given that u(f) = 0.
-53, -1/2, 0, 9
Suppose -u + y = -2*u - 1, 2*y + 6 = 0. Let 23*t**2 - 8*t**3 - 35*t**2 - 4*t**4 + 24*t**u = 0. What is t?
-3, 0, 1
Let l(o) be the second derivative of o**5/10 - 8*o**4/3 - 55*o**3/3 - 38*o**2 + 683*o. Solve l(v) = 0.
-2, -1, 19
Factor -87 - 263/2*j - 45*j**2 - 1/2*j**3.
-(j + 1)*(j + 2)*(j + 87)/2
Let v(r) = r**3 + 200*r**2 + 847*r - 1068. Let p(j) = -2*j**3 - 391*j**2 - 1692*j + 2135. Let b(h) = 4*p(h) + 10*v(h). Factor b(t).
2*(t - 1)*(t + 5)*(t + 214)
Let v = 53/5359 - 369150045/69667. Let q = -5296 - v. What is p in -2*p**2 - 2/13*p**4 + 14/13*p**3 + q - 6/13*p = 0?
-1, 2, 3
Suppose 2*h + 16*b - 11*b = 30, -3*h = 4*b - 38. Let c be 5 + -15 - -1*h. Factor -1/3*p - 1/3*p**2 + c.
-p*(p + 1)/3
Let f(y) = -5*y**3 - y**2. Let q be f(-1). Suppose 0 = q*i - 5*v - 96, -4*v = 2*i - 5*i + 71. Factor 24*z**2 + 6*z - i*z**2 + 3*z + z.
-5*z*(z - 2)
Let c(r) be the third derivative of r**5/300 - 11*r**4/40 - 74*r**3/15 + 423*r**2. Let c(w) = 0. Calculate w.
-4, 37
Let x(u) be the third derivative of u**7/840 + u**6/90 + 119*u**3/6 - 55*u**2 - 3*u. Let l(j) be the first derivative of x(j). Factor l(t).
t**2*(t + 4)
Let f(v) be the first derivative of 34*v**5/5 - 86*v**4 + 890*v**3/3 - 50*v**2 - 1070. Factor f(i).
2*i*(i - 5)**2*(17*i - 2)
Let j(q) be the third derivative of -4075/84*q**4 + 6883/42*q**5 + 3872/735*q**7 + 109*q**2 - 19681/420*q**6 + 0 + 125/21*q**3 - 32/147*q**8 + 2*q. Factor j(w).
-2*(w - 5)**3*(16*w - 1)**2/7
Suppose 3*f + 15 = -5*p, -f - 593 = 2*p - 588. Let h(c) be the first derivative of p*c + 3/16*c**2 - 1/2*c**3 - 3 + 3/8*c**4. Factor h(k).
3*k*(2*k - 1)**2/8
Suppose -3*n - 2*o + 12 + 12 = 0, 4*n + 3*o = 34. Let p be 1*(-5 - 1)/(-2). Factor 1/2*q**2 + n - p*q.
(q - 4)*(q - 2)/2
Let c(y) = -4*y + 8. Let b be c(3). Let o = b - -6. Factor 8*v**2 + 3*v**3 - o*v**3 - 10*v**2.
v**2*(v - 2)
Let 75*x**2 + 170*x + 26*x**2 - 18*x**2 - x**3 = 0. What is x?
-2, 0, 85
Let x(g) be the first derivative of -g**6/1080 - 7*g**5/360 + 25*g**3/3 - 60. Let a(r) be the third derivative of x(r). Factor a(m).
-m*(m + 7)/3
Let z(q) be the first derivative of 4*q**2 - 18/7*q + 129 - 2/7*q**3. Let z(y) = 0. What is y?
1/3, 9
Factor -5/4*r**3 - 935/4*r**2 - 43245/4 - 44175/4*r.
-5*(r + 1)*(r + 93)**2/4
Let u(l) be the second derivative of -l**7/945 + l**6/36 - 7*l**5/135 - 73*l**2/2 - 39*l. Let h(f) be the first derivative of u(f). Let h(b) = 0. What is b?
0, 1, 14
Let o(h) be the second derivative of 2*h**7/63 + 8*h**6/45 - 2*h**5/5 - 4*h**4 - 6*h**3 - 827*h. Determine z so that o(z) = 0.
-3, -1, 0, 3
Let c = -4/6655 - -267/1331. Let j(f) be the third derivative of 0*f - 1/40*f**4 + 0 + c*f**3 - 1/100*f**5 + 13*f**2. Solve j(s) = 0 for s.
-2, 1
Let a(m) be the third derivative of 20/3*m**3 - 95/6*m**4 + 33/2*m**5 + 55*m**2 + 0*m - 27/8*m**6 + 0. Solve a(o) = 0 for o.
2/9, 2
Suppose -5*k + 4 = -x - 13, x + 1 = k. Find v such that 4*v**4 + 3*v**5 + 75*v - 2*v**3 + 24*v**3 + 120*v**2 - 28*v**4 - k*v**3 = 0.
-1, 0, 5
Let s(y) be the first derivative of -y**6/6 + 8*y**5/15 + 7*y**4/3 + 2*y**3/3 - 25*y**2/6 - 14*y/3 + 4957. Solve s(h) = 0 for h.
-1, 1, 14/3
Let d be (25956/(-135))/14 + 14. Let v(j) be the third derivative of 0*j + 0 + 1/150*j**5 - 2*j**2 + 1/20*j**4 - d*j**3. Solve v(q) = 0.
-4, 1
Factor -22*q**3 + 11*q**3 + 34*q**2 - 209*q + 10*q**3 + 58*q + 174.
-(q - 29)*(q - 3)*(q - 2)
Let p be ((-16)/(-52))/(10/65). Let j be (5/(-10))/(6/(-8)). Factor -j*s**p + 32/3*s - 128/3.
-2*(s - 8)**2/3
Find c such that 237/2*c**5 + 94/3*c + 417/2*c**2 + 2665/6*c**3 + 2/3 + 2309/6*c**4 = 0.
-1, -2/9, -2/79
Let n(w) = 14*w + 6. Let j be n(11). Suppose 5*v - j = -4*o, -100 = -4*v + 2*o + 28. Factor 14*k**2 + k**5 + 28 - 7*k**2 - v - 3*k**4 - k**3.
(k - 2)**2*(k - 1)*(k + 1)**2
Let s be 16*494/832 + 210/(-28). Find r, given that 250/9*r - 4 - 8/9*r**5 - 526/9*r**s - 118/9*r**4 + 146/3*r**3 = 0.
-18, 1/4, 1
Let f be ((-75)/(-42))/((-72)/(-126)) - (-23)/(-184)