3)
Let u be (718/5026)/(2/7). Find c such that 6 + u*c**2 + 4*c = 0.
-6, -2
Let u be ((-21)/(-138))/(5 - (-21)/(-4)). Let w = 208/115 + u. Factor -3/5*s**5 - 3/5*s + w*s**3 + 0 + 0*s**2 + 0*s**4.
-3*s*(s - 1)**2*(s + 1)**2/5
Let h = -416 + 418. Determine x, given that -3*x**2 + 174*x + 5*x**h - 76 - 45*x - 55*x = 0.
-38, 1
Let i(y) = -2*y**2 + 101*y + 160. Let u be i(52). Suppose -3*v + 10 = -r, 10 = 3*r - 6*r + u*v. Factor 21/2*t**r + 18 - 24*t - 3/2*t**3.
-3*(t - 3)*(t - 2)**2/2
Let i = 319903 - 319838. Find n such that 0 + 845/2*n + i*n**2 + 5/2*n**3 = 0.
-13, 0
Let b(u) be the first derivative of -u**3/6 - 741*u**2/2 - 549081*u/2 + 1740. Let b(v) = 0. What is v?
-741
What is q in -3*q**2 - 11/2*q**3 - 5/2*q**4 + 0 + 0*q = 0?
-6/5, -1, 0
Let l = 359 + -361. Let c be (l/7 + 66/280)*-6. Factor 1/10*z + 1/2*z**2 + 0 + 7/10*z**3 + c*z**4.
z*(z + 1)**2*(3*z + 1)/10
Let g(f) be the third derivative of -f**7/630 + 29*f**6/180 + 118*f**5/45 - 557*f**4/36 + 65*f**3/2 + 97*f**2 + 22*f. Factor g(z).
-(z - 65)*(z - 1)**2*(z + 9)/3
Let v(m) be the third derivative of m**5/180 + 53*m**4/24 + 2*m**2 + 51*m - 3. Determine c, given that v(c) = 0.
-159, 0
Let z(w) = 2*w**3 + 2*w - 1. Let f(m) = 25*m**3 + 5*m**2 + 50*m - 35. Let s(l) = f(l) - 15*z(l). Factor s(i).
-5*(i - 2)*(i - 1)*(i + 2)
Let l(t) be the third derivative of t**6/80 - 82*t**5/15 + 145*t**4/16 + 109*t**3/6 + 486*t**2 - 3. Solve l(q) = 0 for q.
-1/3, 1, 218
Let s be (1092/65)/6 - (24/(-5))/4. Let c(m) be the first derivative of -3/10*m**s + 4 - 8/5*m**3 - 3*m**2 - 12/5*m. Factor c(y).
-6*(y + 1)**2*(y + 2)/5
Let c(x) = x**3 - 50*x**2 + 149*x - 104. Let g be c(2). Factor -1/10*y**g - 12/5 - y.
-(y + 4)*(y + 6)/10
Suppose 9*d + 296 = -82. Let t = d + 47. Factor -8*n**2 + 2*n**2 + 3*n**t + 6 + 223*n - 214*n - 12*n**3.
3*(n - 2)*(n - 1)*(n + 1)**3
Let h(i) = 170*i + 3740. Let z be h(-22). Let f(u) be the second derivative of 0*u**2 + 5/3*u**3 + 5/4*u**4 + z + 1/4*u**5 + 13*u. Factor f(m).
5*m*(m + 1)*(m + 2)
Let t = -2/1751 + 5293/35020. Let p(k) be the second derivative of -t*k**5 - 1/2*k**4 + 0 + 3*k**2 + 1/2*k**3 - 16*k. Factor p(r).
-3*(r - 1)*(r + 1)*(r + 2)
Let a(w) be the second derivative of 2*w**6/15 - 14*w**5/5 + 68*w**4/3 - 260*w**3/3 + 150*w**2 + 100*w - 57. Factor a(t).
4*(t - 5)**2*(t - 3)*(t - 1)
Let r = -1773 + 1013. Let q = r + 3803/5. Factor -1/5*n**4 + 3/5*n**3 - q*n**2 + 0 + 1/5*n.
-n*(n - 1)**3/5
Let p(j) be the third derivative of j**7/630 + j**6/90 - 79*j**5/60 - 485*j**4/18 - 850*j**3/9 - 2100*j**2. Factor p(u).
(u - 17)*(u + 1)*(u + 10)**2/3
Factor -102 - 32 + s**2 - 2485*s - 117 + 2583*s + 51.
(s - 2)*(s + 100)
Let m(i) = -2*i**5 - i**4 - i. Let q(s) = 20*s**5 - 355*s**4 + 5114*s**3 + 11570*s**2 - 29257*s - 23064. Let o(k) = 7*m(k) + q(k). Suppose o(d) = 0. What is d?
-3, -2/3, 2, 31
Let a(n) = -n**3 - 23*n**2. Let u be a(-23). Suppose -17*d + 22*d - 140 = u. Factor 24 + d*x + 4*x**3 + 16*x + 28*x**2 - 4.
4*(x + 1)**2*(x + 5)
Suppose 15043 + 18821 = 17*z. Let -z*a**2 - 736*a - 4 + 1972*a**3 + 3468*a**4 - 28 + 208*a = 0. Calculate a.
-1, -2/17, 2/3
Suppose 2*a + 5*l + 18 = 3, 5*a = -3*l + 10. Suppose -3*s = 3, 5*s = -a*p + 3*p - 5. Factor 2/5*f**5 + 4/5*f**2 + p*f**4 + 0*f + 0 - 6/5*f**3.
2*f**2*(f - 1)**2*(f + 2)/5
Let x(i) be the first derivative of -i**8/10920 + i**7/2730 - i**6/2340 - 115*i**3/3 - 93. Let w(z) be the third derivative of x(z). Factor w(n).
-2*n**2*(n - 1)**2/13
Let g(o) be the second derivative of -o**4/4 - 75*o**3/2 + 1134*o**2 + 2159*o. Factor g(i).
-3*(i - 9)*(i + 84)
Suppose 185*k + 100 = 215*k + 5*q, 0 = -5*k - 5*q + 50. Factor -3/8*c**3 + 0 - 9/8*c**k - 3/4*c.
-3*c*(c + 1)*(c + 2)/8
Let m(w) = 17*w**5 + 42*w**4 - 17*w**3 - 58*w**2 + 12*w. Let f(a) = -69*a**5 - 169*a**4 + 69*a**3 + 231*a**2 - 44*a. Let n(q) = 2*f(q) + 9*m(q). Solve n(s) = 0.
-2, 0, 1/3, 1
Let i(u) be the first derivative of -u**6/6 - 9*u**5/5 - 13*u**4/2 - 6*u**3 + 27*u**2/2 + 27*u - 1340. Let i(q) = 0. What is q?
-3, -1, 1
Let f be -19 + 44 + -63 + 38. Determine a, given that 6/7*a**4 + 2/7*a**5 + 0*a**2 + 0 + f*a + 4/7*a**3 = 0.
-2, -1, 0
Find i such that 32/7 + 132/7*i**2 + 536/7*i = 0.
-4, -2/33
Let k(t) be the first derivative of t**7/147 + t**6/21 + 4*t**5/35 + 2*t**4/21 - 21*t - 23. Let o(v) be the first derivative of k(v). Let o(g) = 0. Calculate g.
-2, -1, 0
Let w(x) be the first derivative of -x**6/180 + x**5/40 - x**4/24 + x**3/36 - 8*x - 81. Let r(y) be the first derivative of w(y). Factor r(c).
-c*(c - 1)**3/6
Let k(c) be the third derivative of c**8/1512 + 4*c**7/945 - 11*c**2 + 57. Solve k(t) = 0.
-4, 0
Let i(z) be the first derivative of -3*z**2 - 14*z - 47. Let v be i(-3). Solve -10*p**3 - v*p + 5*p + p**3 + 3*p**2 + p - 10*p**4 = 0.
-1, -2/5, 0, 1/2
Let k(o) be the second derivative of -o**5/12 + 5*o**4/3 - 35*o**3/6 + 24*o**2 + 7*o. Let h(d) be the first derivative of k(d). Factor h(q).
-5*(q - 7)*(q - 1)
Let s = 2/376553 + 7154501/1129659. Determine h so that -54*h**4 + s*h - 1/6 - 397/6*h**2 + 114*h**3 = 0.
1/18, 1
Let d(q) be the second derivative of 5*q**4/21 - 62*q**3/21 + 12*q**2 - 657*q + 1. Determine t so that d(t) = 0.
2, 21/5
Let i(s) be the first derivative of 1/2*s**2 - 22 + 1/42*s**3 - 1/420*s**5 + 0*s + 0*s**4. Let b(h) be the second derivative of i(h). Factor b(a).
-(a - 1)*(a + 1)/7
Factor 8*n - 80*n**3 + 5*n**2 - 27*n**2 - 15*n**4 - 24*n**2 - 13*n**4 + 2*n**2.
-4*n*(n + 1)*(n + 2)*(7*n - 1)
Let h(q) = -2*q**4 - 7*q**3 + 17*q**2 - 12*q + 4. Let s(r) = -r**4 - 8*r**3 + 18*r**2 - 13*r + 4. Let f(g) = 3*h(g) - 4*s(g). Factor f(t).
-(t - 2)**2*(t - 1)*(2*t - 1)
Let o = 241 - 239. Let q = -1529/4 - -383. Factor -3*m - q*m**o - 9/4.
-3*(m + 1)*(m + 3)/4
Factor -2/7*v**3 + 250/7 - 150/7*v + 30/7*v**2.
-2*(v - 5)**3/7
Suppose -4*i + 0*i = -141 + 29. Let d(u) be the first derivative of -i - 2/3*u**3 + 0*u + 4*u**2. Factor d(v).
-2*v*(v - 4)
Let t(v) be the second derivative of v**6/135 - 7*v**5/30 + 19*v**4/27 - 57*v + 2. Solve t(z) = 0.
0, 2, 19
Let k(m) be the first derivative of -2*m**5/5 + 49*m**4/12 - 38*m**3/9 - 79*m**2/6 + 14*m/3 - 192. Find b, given that k(b) = 0.
-1, 1/6, 2, 7
Suppose -v + 1 = 2*w - 13, -w - 2*v + 1 = 0. Let g(y) = -y**3 + 11*y**2 - 18*y + 12. Let n be g(w). Solve -n*f**2 + 15*f**3 - 4*f**3 - 27*f**3 = 0 for f.
-3/4, 0
Let r(t) be the first derivative of t**4/40 - 19*t**3/15 - 39*t**2/20 - 3426. Solve r(b) = 0.
-1, 0, 39
Let x(y) be the third derivative of 0 + 0*y + 6*y**3 + 169/60*y**5 - 13/2*y**4 - 146*y**2. What is k in x(k) = 0?
6/13
Let q = -258586/5 - -51722. Let -q - 3/5*p**3 + 24/5*p**2 + 3/5*p = 0. Calculate p.
-1, 1, 8
Let g(h) = h**3 - 6*h - 5. Let f = -195 + 196. Let k(x) = x + 1. Let v(o) = f*g(o) - k(o). Determine l so that v(l) = 0.
-2, -1, 3
Suppose 6*a - 4 = -10. Let r(g) = g. Let d(y) = 4*y**2 - 8*y + 8. Let s(b) = a*d(b) + 4*r(b). Factor s(x).
-4*(x - 2)*(x - 1)
Let p(r) be the third derivative of r**7/1470 + 11*r**6/168 + 248*r**5/105 + 736*r**4/21 - 4*r**2 - 38*r - 2. Determine l, given that p(l) = 0.
-23, -16, 0
Suppose 5 = -4*f - 3. Let l be (f/(-8))/1 + (-532)/(-112). Factor -4 - 15*o**2 + l*o**3 + 2*o + 4*o - 1 + 9*o.
5*(o - 1)**3
Let a = 304124 - 304124. Suppose -1/2*j**5 + 0 + a*j + 0*j**2 + 1/2*j**4 + j**3 = 0. What is j?
-1, 0, 2
Let q(h) be the third derivative of h**6/480 - 11*h**5/240 + h**4/4 + 3*h**3/2 + 162*h**2 + 3*h. Factor q(x).
(x - 6)**2*(x + 1)/4
Factor 61/8*a**3 - 899/8*a**2 + 0 - 961/8*a - 1/8*a**4.
-a*(a - 31)**2*(a + 1)/8
Let n(c) = -c**3 + 19*c**2 - 9*c - 10. Let j be n(18). Factor -60*k**2 - 148*k**3 - j*k**3 - 250 + 295*k**3 - 225*k.
-5*(k + 2)*(k + 5)**2
Let d be (-5253)/1545 - ((-1)/(-4))/(4/(-112)). Let -94/5 + d*f**3 - 834/5*f**2 - 562/5*f = 0. What is f?
-1/3, 47
Suppose -10*y + 66 = -34. Let m be 49/147*24/y. Suppose 16/5*v + 0 - m*v**2 = 0. What is v?
0, 4
Let w(p) be the second derivative of -p**4/66 - 656*p**3/33 - 107584*p**2/11 + 928*p. Factor w(s).
-2*(s + 328)**2/11
Let d be (-1219)/161 - ((-6)/(-36) - 110/12). Let -12/7*f**3 + 12/7*f + 2/7*f**4 + 8/7*f**2 - d = 0. Calculate f.
-1, 1, 5
Let s be 15 - (-5)/((-55)/143). Let i(m) be the third derivative of -1/15*m**5 + 1/3*m**4 + 2*m**3 + 0 + 2*m**s + 0*m. Factor i(f).
-4*(f - 3)*(f + 1)
Solve -2/7*k**2 - 1552/7*k - 30