 90. Let m(g) = 3*j(g) - 2*z(g). Solve m(x) = 0 for x.
2/9, 22
Let g(q) be the second derivative of -q**5/150 + 7*q**4/45 + 17*q**3/45 - 2*q**2 - 1176*q. Determine u so that g(u) = 0.
-2, 1, 15
Factor 63/2*i**4 + 1535*i**3 + 2883/2 + 1/6*i**5 + 13253/3*i**2 + 8711/2*i.
(i + 1)**3*(i + 93)**2/6
Let m be -6 - (-13 + 5 + -1). Determine x, given that -48*x**2 + 4*x**5 + 435*x**m - 134*x**3 + 28*x**4 - 144*x**3 - 141*x**3 = 0.
-6, -2, 0, 1
Suppose -399*t - 3 + 0 = 1072*t - 3. Factor 12321/2*m**3 + 3/4*m**5 + 111*m**4 + 151959*m**2 + 5622483/4*m + t.
3*m*(m + 37)**4/4
Let b be 3*(0 + 1/2). Suppose 215*r - 8838 = -55*r - 712*r. Factor -b*g**2 - 27/2 + r*g.
-3*(g - 3)**2/2
Factor 2/15*c**2 + 166/15*c + 32.
2*(c + 3)*(c + 80)/15
Let g(v) be the first derivative of v**7/504 - v**6/36 + v**5/6 - 5*v**4/9 - 34*v**3/3 - 2*v - 44. Let d(c) be the third derivative of g(c). Factor d(t).
5*(t - 2)**3/3
Suppose 0 = -6*w + 2*w - 100. Let o = 116 + w. Solve -16*u - 48*u**4 + 29*u**3 + 46*u + o*u**3 - 99*u**2 - 3 = 0.
1/4, 1
Suppose -30 = 11*v - 8. Let d be (-2)/(-4) + v/4. Factor -3 + 24*q + 22*q + d - 42*q - q**2.
-(q - 3)*(q - 1)
Let a(w) be the second derivative of -3/2*w**6 + 6*w**3 + 0*w**2 + 0 + 117/20*w**5 - 37/4*w**4 + 151*w + 1/14*w**7. Factor a(j).
3*j*(j - 12)*(j - 1)**3
Let d(u) be the third derivative of 1/60*u**6 - 1/15*u**5 - 8*u**2 + 0 + 1/105*u**7 - 3*u + 0*u**3 + 0*u**4. Factor d(l).
2*l**2*(l - 1)*(l + 2)
Suppose -2*z + 2*g - 7*g + 29 = 0, 0 = 5*g - 25. Factor -12*b - 3*b**2 + 9*b**2 - z*b**2.
4*b*(b - 3)
Let h(l) be the second derivative of 0 - 11/6*l**4 + 48*l + 4*l**3 + 2/5*l**5 - 1/30*l**6 - 9/2*l**2. Find u, given that h(u) = 0.
1, 3
Suppose -165776 - 1222*u + 165288 - u**4 - 981*u**2 + 109*u**3 - 357*u**3 = 0. Calculate u.
-244, -2, -1
Let k be ((-847)/33 - -9)*(-10)/(-12). Let j = -95/9 - k. Factor 2/3*p**3 + 0 + j*p**2 + 0*p.
2*p**2*(p + 5)/3
Let z(r) be the first derivative of 4*r**5/5 + 17*r**4 + 176*r**3/3 + 56*r**2 + 3492. Factor z(s).
4*s*(s + 1)*(s + 2)*(s + 14)
Let q be (-24)/228 + (-203)/(-2470). Let r = 4169/390 + q. Factor -r - 16*h**2 - 16/3*h**3 - 64/3*h - 2/3*h**4.
-2*(h + 2)**4/3
Factor 130416*z + 64896 + 3/2*z**4 + 132291/2*z**2 + 627*z**3.
3*(z + 1)**2*(z + 208)**2/2
Let y be 5/7*7 + -1. Suppose -y*s - z = -14, 0 = z - 22 + 24. Find m, given that -24/7*m**2 + 0 + 0*m + 92/7*m**3 + 16/7*m**s = 0.
-6, 0, 1/4
Let a(y) be the third derivative of 0*y**6 + 0*y - 48*y**2 + 0*y**4 + 0*y**5 - 1/112*y**8 + 1/70*y**7 + 0*y**3 + 2. Factor a(q).
-3*q**4*(q - 1)
Suppose 272*j**2 - 24*j - 129*j**2 - 146*j**2 = 0. What is j?
-8, 0
Suppose -5*w - 16 = -21. Let o be 17 + 2 + -3*w. Factor -2*u**3 - u - 8*u**4 - o + 10*u - u + 20*u**2 - 2*u**5.
-2*(u - 1)**2*(u + 2)**3
Let y be (12/(-5))/((-21)/10). Let b = -17377 + 17379. What is a in -y*a - 2/7*a**b - 8/7 = 0?
-2
Suppose 0 = 4*d + 22 - 34. Determine u so that -14 - 36 - 2*u**3 - 10*u**2 + u**3 - 65*u + 7*u**d - u**3 = 0.
-2, -1, 5
Let 291/2*l - 423/2 + 1/2*l**3 - 53/2*l**2 = 0. What is l?
3, 47
Let a = -31254 - -31256. Let 1/4 - 1/8*w - 1/8*w**a = 0. What is w?
-2, 1
Let k = 13509/188 + -3342/47. Factor 9/8*g**3 - k*g**2 - 3/8*g**4 + 0*g + 0.
-3*g**2*(g - 2)*(g - 1)/8
Let d = 5181 - 5181. Let f(g) be the second derivative of d*g**4 + 3/80*g**5 + 46*g - 1/8*g**3 + 0 + 0*g**2. Find v, given that f(v) = 0.
-1, 0, 1
Let s be -14 + ((-13246)/666 - -34). Solve -s*o**3 + 7/3*o - 38/9 + 2*o**2 = 0.
-2, 1, 19
Factor -25732*v + 25600*v + 134*v**2 - 5 + 3.
2*(v - 1)*(67*v + 1)
Let v(x) be the third derivative of -x**8/60480 + 11*x**7/15120 - x**6/72 + x**5/30 + 74*x**2. Let j(i) be the third derivative of v(i). What is t in j(t) = 0?
5, 6
Let z(v) = -v**3 - 2*v**2 - 8*v - 64. Let g(q) = q**2 + 4*q. Let s(j) = -6*g(j) - z(j). Let s(x) = 0. What is x?
-4, 4
Find w such that 4*w**2 - 51/2 + 133/2*w = 0.
-17, 3/8
Let k(w) be the second derivative of w**6/135 - 7*w**5/15 + 277*w**4/54 - 40*w**3/9 - 1700*w**2/9 - 1701*w. Solve k(g) = 0.
-2, 5, 34
Let g(k) be the first derivative of 3*k**3/2 - 113*k**2/2 + 120*k - 5900. Factor g(f).
(f - 24)*(9*f - 10)/2
Let l(c) be the third derivative of c**7/525 - 2*c**6/75 + 13*c**5/150 - c**4/10 - 2*c**2 - 583. Factor l(o).
2*o*(o - 6)*(o - 1)**2/5
Let q = -77/18108 + 2089/18108. Factor -q*b**2 + 8/9*b - 4/3.
-(b - 6)*(b - 2)/9
Let p be (1515/(-108) - (-14 - -1)) + (-30)/(-24). Factor -p - 2/3*s + 8/9*s**2.
2*(s - 1)*(4*s + 1)/9
Let r = -4627 + 4632. Let o(d) be the second derivative of 13*d**4 + 7*d - 12*d**2 + 0 + 14/15*d**6 - 33/5*d**r - 14/3*d**3. Solve o(f) = 0 for f.
-2/7, 1, 3
Factor -2*x + 2*x**3 - 271*x**2 + 17*x + 347*x**2 + 3*x**3.
x*(x + 15)*(5*x + 1)
Factor 0*z + 1/5*z**4 + 0 + z**3 - 6/5*z**2.
z**2*(z - 1)*(z + 6)/5
Let j be 6/(-8) + 4/30*15. Let b(q) be the first derivative of -j*q**4 + 5/2*q**2 - 5*q + 5/3*q**3 - 1. Determine i, given that b(i) = 0.
-1, 1
Solve 1925/2*s - 160 - 15*s**2 = 0 for s.
1/6, 64
Suppose -2916*g = -2915*g - 12, -36 = -t - 3*g. Factor 3/7*i + 1/7*i**2 + t.
i*(i + 3)/7
Let w = 38 - 35. Suppose -w*p = -4*x - 4*p + 14, 2*x = -3*p + 12. Solve -2*i**2 + 324*i - 47 + 4*i**x - 70*i**2 + 47 = 0 for i.
0, 9
Let w(z) be the third derivative of -z**8/40320 + z**7/5040 - 13*z**5/12 - 68*z**2. Let s(b) be the third derivative of w(b). Factor s(j).
-j*(j - 2)/2
Let c(x) = -352*x**3 - x**2 + x. Let z be c(1). Let s = z - -8802/25. Factor 2 + s*b**2 - 4/5*b.
2*(b - 5)**2/25
Let k = 2 - 0. Let s = 35040 - 210239/6. Determine x, given that -1/3*x - 1/6 - s*x**k = 0.
-1
Let y(b) = -3*b + 19. Let m be y(9). Let o = m + 10. Suppose 689 + 1026 + 735*z + 5*z**3 + 71*z**2 - 8*z**2 + 42*z**o = 0. Calculate z.
-7
Let l(y) be the second derivative of -1/150*y**6 + 11/30*y**3 + 8*y + 5 + 13/100*y**5 - 23/60*y**4 + 0*y**2. Factor l(z).
-z*(z - 11)*(z - 1)**2/5
Let k(y) be the third derivative of y**5/510 - 11*y**4/2 + 6171*y**3 - 578*y**2. Factor k(a).
2*(a - 561)**2/17
Let p(k) = -26907*k + 80751. Let f be p(3). Suppose 0 = 3*y - 5 - 1. Factor -f*m + 150 + 3/2*m**y.
3*(m - 10)**2/2
Let c = 4515 - 22571/5. Let m(l) be the first derivative of -2*l**4 + l**2 + l**6 + 22 + 0*l - c*l**5 + 4/3*l**3. Suppose m(h) = 0. What is h?
-1, -1/3, 0, 1
Suppose 0*c - 5*c - 4*t = 12, -4*c + 5*t = -15. Let k be (3/(-2) + -1)/(21490/(-1228)). Suppose -k*v**2 + 4/7 + c*v = 0. Calculate v.
-2, 2
Let l(x) be the third derivative of x**6/1200 - 19*x**5/600 - x**4/60 + 19*x**3/15 + 2*x**2 - 2088. Factor l(p).
(p - 19)*(p - 2)*(p + 2)/10
Suppose 0 = -150*t - 225 + 825. Let z(v) be the first derivative of 0*v + 13 - 1/30*v**t + 0*v**3 + 2/75*v**5 + 0*v**2. Determine b, given that z(b) = 0.
0, 1
Let b(y) = -32*y**3 + 39*y**2 - 3*y - 9. Let c(x) = 4*x + 13. Let d be c(-2). Let g(q) = q**3 - q + 1. Let f(l) = d*g(l) + b(l). Factor f(i).
-(i - 1)*(3*i - 2)*(9*i + 2)
Let n = -239084 - -956345/4. Factor 3 - n*w + 3/8*w**2.
3*(w - 4)*(w - 2)/8
Let u(l) = -135*l**2 - 25445*l + 25030. Let c(y) = 5*y**2 + 942*y - 927. Let g(m) = -55*c(m) - 2*u(m). Factor g(x).
-5*(x - 1)*(x + 185)
Let n(c) be the first derivative of -4*c**5/5 + 41*c**4 - 1900*c**3/3 + 2166*c**2 + 211. Factor n(g).
-4*g*(g - 19)**2*(g - 3)
Let p = -15534 + 15534. Suppose -4*i + 1 = -5*o - 6, 0 = 5*i + 4*o - 19. Factor -9/4*h**i + 0*h - 3/2*h**2 - 3/4*h**4 + p.
-3*h**2*(h + 1)*(h + 2)/4
Let c(q) be the third derivative of -q**5/110 + 147*q**4/22 + 295*q**3/11 - 4*q**2 + 410*q + 1. Let c(x) = 0. Calculate x.
-1, 295
Let w(h) = 7*h**2 + 4*h. Let m(l) = 48*l**2 + 28*l. Suppose -13*t + 10*t - 3*n = -66, 0 = -3*t - 5*n + 70. Let o(y) = t*w(y) - 3*m(y). Factor o(g).
-4*g*(g + 1)
Let x = -4279 + 4282. Let i(h) be the first derivative of -115/4*h**x + 33/4*h**5 + 0*h + 35/24*h**6 + 55/16*h**4 + 8 + 45/4*h**2. Find r such that i(r) = 0.
-3, 0, 2/7, 1
Solve -20*m**2 + 5*m**3 + 110*m**2 - 610*m + 775*m + 80 = 0 for m.
-16, -1
Suppose 3*k - 5 = -5*o, -5*k - 4*o + 23 = 6. Factor -13 - k*x**3 + 5*x + x**2 - 7*x**2 + 26*x**2 - 7 + 0*x**2.
-5*(x - 4)*(x - 1)*(x + 1)
Let o(a) = a**3 - 3*a**2 - 38*a + 7. Let n be o(8). Suppose 11 - n = -6*y. Factor -6/7*i + 3/7*i**4 - 12/7*i**3 + 0 + 15/7*i**y.
3*i*(i - 2)*(i - 1)**2/7
Let s(o) be the second derivative of -1/9*o**4 + 28/135*o**6 + 0*o**2 + 0*o**3 - 40*o + 0 - 17/90*o**5. Suppose s(h) = 0. C