50. Let i be v(13). Let w(q) = 4*q**3 - 12*q**2 + 3. Let d be w(i). Factor 3*u**2 + 0 - 7/2*u + 1/2*u**d.
u*(u - 1)*(u + 7)/2
Factor -n**3 - 71/3*n**2 - 46/3*n + 0.
-n*(n + 23)*(3*n + 2)/3
Let q(z) be the first derivative of 0*z - 1/2*z**4 - 4/21*z**3 - 4/35*z**5 - 90 + 3/7*z**2. Solve q(n) = 0.
-3, -1, 0, 1/2
Let d(h) = -4*h**3 - 324*h**2 - 330*h + 5. Let j(k) = -k**3 + 3*k**2 + 2*k + 1. Let v(u) = d(u) - 5*j(u). Factor v(o).
o*(o - 340)*(o + 1)
Factor 675122/15 + 223492/5*y**2 + 2/15*y**4 + 464/3*y**3 - 269584/3*y.
2*(y - 1)**2*(y + 581)**2/15
Let f(q) be the third derivative of -q**7/70 + 13*q**6/40 - 27*q**5/10 + 9*q**4 + 22*q**2 + 28*q. Suppose f(y) = 0. What is y?
0, 3, 4, 6
Let k be ((-1157)/178)/(260/(-80)). Factor -4/3*i**k - 20 + 64/3*i.
-4*(i - 15)*(i - 1)/3
What is h in -18/7*h**2 + 428/7*h + 96/7 = 0?
-2/9, 24
Suppose -h - g = -72, g - 2*g = 4*h - 282. Determine t so that -2*t**4 - 3*t**3 - 22*t**2 + 17*t**3 + 59*t - 119*t + h*t = 0.
0, 1, 5
Let a(h) be the first derivative of -36 - 5*h**2 - 5/8*h**4 + 0*h + 10/3*h**3. Factor a(m).
-5*m*(m - 2)**2/2
Let w be -11 - ((-6409)/546 - (-2)/12). Let i(u) be the second derivative of 1/35*u**5 + 15*u + 1/21*u**4 + 0*u**2 - w*u**3 + 0. Factor i(b).
4*b*(b - 2)*(b + 3)/7
Let j = 119 + -4. Let v = -103 + j. Factor -22*z - 4*z**3 - 4 - v*z**2 + 4*z + 6*z.
-4*(z + 1)**3
Suppose 0 = -16*k + 15*k + 2. Suppose 3*a - 6 = 3*s, 2*s + 2*a - 8 = 8. Factor 0*i**s + 2/7*i**4 - 4/7*i**k + 0*i + 2/7.
2*(i - 1)**2*(i + 1)**2/7
Let i be (158/711)/(1 + 11/9). Let g(q) be the first derivative of 2/3*q**3 - 1/2*q**4 + i*q**5 - 2 + 0*q + 0*q**2. Factor g(w).
w**2*(w - 2)**2/2
Suppose -3*l = -219 + 162. What is g in -l*g**2 + 2*g**4 - 12*g**4 - 14*g**2 + 50 - 5*g + 9*g**4 - 11*g**3 = 0?
-5, -2, 1
Let s = 3428/143 - 3038/143. Factor 12/11*f**2 + 16/11 - s*f + 2/11*f**3.
2*(f - 1)**2*(f + 8)/11
Let s(w) be the second derivative of 7*w**6/30 - 13*w**5/5 + 19*w**4/3 + 3*w - 295. Factor s(f).
f**2*(f - 2)*(7*f - 38)
Let a = -16121 + 145441/9. Solve 488/9*w**3 + 104/3*w**4 + 8/9 + a*w**2 + 76/9*w**5 + 12*w = 0 for w.
-1, -2/19
Let u be (70/25 + -4)*(-2 + -3). Suppose -v = 3*w + 13, u*v - 3*w = 2*v + 23. Solve -2/3*h + 0 - 1/6*h**v = 0 for h.
-4, 0
Let h be 1/(((-3)/4)/(-3)). Let k = -24755415/17 + 1456201. Find o, given that 0*o + 4/17*o**3 - k*o**h + 0 + 0*o**2 = 0.
0, 2
Let z(n) = -n**2 + 1. Let h(c) = -2*c**2 + 9*c - 11. Let b(l) = h(l) - z(l). Let q be b(7). Factor -4*j - j**3 + 10*j**3 + j - 8*j**q + 2*j.
j*(j - 1)*(9*j + 1)
Let u(h) be the third derivative of h**7/42 + 5*h**6/24 - h**5/4 - 85*h**4/24 - 25*h**3/3 + 3835*h**2. Factor u(c).
5*(c - 2)*(c + 1)**2*(c + 5)
Let f = -16827 - -50503/3. Factor 1/3*d**2 + f*d + 121/3.
(d + 11)**2/3
Let f(i) be the first derivative of -i**4/7 + 436*i**3/21 + 1152*i**2/7 - 2736*i/7 + 2180. Solve f(v) = 0.
-6, 1, 114
Let s(i) = -15*i - 915. Let o be s(-61). Let m(g) be the second derivative of 0*g**3 - 1/4*g**4 - 3/4*g**5 + o - 3/5*g**6 + 0*g**2 - 20*g. Factor m(l).
-3*l**2*(2*l + 1)*(3*l + 1)
Factor 138*j**4 + 954*j**3 + 319*j**2 + 899*j + 884*j**2 + 825*j + 2*j**5 + 8*j**4 + 528 + 803*j**2.
2*(j + 1)**3*(j + 4)*(j + 66)
Let j be (-1)/(6 - 85/15). Let a be j + 42/12 - -1. Factor 9/4*l**2 + 3/4*l**3 + a*l + 0.
3*l*(l + 1)*(l + 2)/4
Suppose 0 = 38*g - 33*g - 80. Let j be (-4)/(-34) - ((-432)/1071)/g. Determine s, given that -9/7*s + j*s**4 + 15/7*s**2 + 0 - s**3 = 0.
0, 1, 3
Let o be (10 - (6 - 9))*-2. Let r be o/65*15/(-7). Factor 0 - 3/7*k**3 + 0*k - r*k**2.
-3*k**2*(k + 2)/7
Let o(a) = 9*a**2 - 31*a - 25. Let s(z) = 25*z**2 - 92*z - 75. Let k(l) = -11*o(l) + 4*s(l). Let q be k(28). What is i in -24*i**q - 39/2*i + 9 - 60*i**2 = 0?
-2, -3/4, 1/4
Let g(d) be the third derivative of -2*d**7/315 - d**6/360 + 4*d**5/45 + d**4/18 + 2602*d**2 - 2*d. Determine v so that g(v) = 0.
-2, -1/4, 0, 2
Let b(q) be the first derivative of -5*q**3/3 - 115*q**2/2 + 1050*q + 4113. Suppose b(h) = 0. What is h?
-30, 7
Let d(o) = 42*o**3 - 2*o**2 + 4*o + 10. Let v be d(3). Determine l so that v + 2*l**3 - 1138 - 4*l**4 - 8*l - 18*l**3 - 20*l**2 = 0.
-2, -1, 0
Let t = 6 - -19. Let s = t + -23. Factor 7*l**2 - 3 - 30*l + 28 - 2*l**s.
5*(l - 5)*(l - 1)
Let a(o) = -1548*o - 24765. Let j be a(-16). Find q such that 0*q**j - 5/6*q**4 - 5/3*q + 0 + 5/2*q**2 = 0.
-2, 0, 1
Let f = 15 - 2. Let v be (-3)/12 + f/4. Factor -8*s - v*s**3 + 12*s**2 + 15*s**3 + 24*s**3.
4*s*(3*s - 1)*(3*s + 2)
Let r(s) be the first derivative of -5*s**6/6 - 6*s**5 - 35*s**4/2 - 80*s**3/3 - 45*s**2/2 - 10*s + 1089. Solve r(x) = 0.
-2, -1
Suppose -4 - 8 = -4*a. Let m be a + 0 - 4 - -3. Factor -17*r**2 + 0*r**2 - 3*r + 16*r**m.
-r*(r + 3)
Let p(u) = u**3 - 22*u**2 + 100*u + 231. Let s be p(11). Factor 2*x**2 + 6/7*x + 10/7*x**3 + 2/7*x**4 + s.
2*x*(x + 1)**2*(x + 3)/7
Suppose 32 = 11*n - 86*n - 2*z, -2*n = -z - 16. Factor 0 + n*h - 12/5*h**2 + 19/5*h**3 + 1/5*h**5 - 8/5*h**4.
h**2*(h - 4)*(h - 3)*(h - 1)/5
Factor -87 + 30*g - 1/3*g**2.
-(g - 87)*(g - 3)/3
Let f(y) be the first derivative of -y**6/150 + 14*y**5/75 - 3*y**4/10 + 88*y**3/3 - 62. Let g(j) be the third derivative of f(j). Factor g(k).
-4*(k - 9)*(3*k - 1)/5
Suppose 9 = v + 12, -g + 67 = -3*v. Suppose g = 3*p - 140. Suppose -57/2*m - 3 - p*m**2 = 0. What is m?
-1/4, -2/11
Let x(h) be the second derivative of -1/5*h**5 + 2*h**4 - 6*h**3 + 6 + 15*h + 0*h**2. Solve x(d) = 0 for d.
0, 3
Factor -9003*a**3 + 18012*a**3 - 32*a**2 - 1092*a - 9005*a**3.
4*a*(a - 21)*(a + 13)
Solve -290*a + 2804*a**2 - 1402*a**2 + 96 - 1394*a**2 - 24 = 0 for a.
1/4, 36
Let m = 101 - 137. Let q be 0 - (5/(-1) + m/(-9)). Factor -7 + 9*x + q + 7*x**2 - 10*x**2.
-3*(x - 2)*(x - 1)
Let m(q) be the third derivative of -q**8/112 + 26*q**7/35 + 219*q**6/40 + 139*q**5/10 + 14*q**4 - 3195*q**2. Determine f so that m(f) = 0.
-2, -1, 0, 56
Let y(u) = u**2 + 629*u + 3740. Let i be y(-6). Let q(w) be the first derivative of 25/8*w**i - 5*w - 5/12*w**3 + 41. Factor q(h).
-5*(h - 4)*(h - 1)/4
Let v be (-49)/196 - 9/(-4). Factor -12*z**v - 50 + 40*z - 12 + 94.
-4*(z - 4)*(3*z + 2)
Suppose t = -7*u + 10*u - 48, 0 = -5*u - 3*t + 94. Let a(k) = -k**2 + 18*k - 9. Let v be a(u). What is r in -r**2 - v - 9 + 15 - 3*r = 0?
-2, -1
Let h = 1936084/7 + -276562. Suppose -3/7*k**2 - 1875/7 - h*k = 0. Calculate k.
-25
Factor 80/3 - 91/3*l + 10/3*l**2 + 1/3*l**3.
(l - 5)*(l - 1)*(l + 16)/3
Let f = 11560 + -11557. Let h(w) = 10*w**3 + 3*w**2 - 2*w + 5. Let y be h(5). What is d in -1320 + y + 27*d + f*d**2 = 0?
-9, 0
Suppose -67*l + 324*l - 2*l**3 + 78*l**2 - 5*l = 0. Calculate l.
-3, 0, 42
Let t(b) be the third derivative of -b**6/120 + 379*b**5/210 + 547*b**4/168 - 109*b**3/21 + 2*b**2 - 426*b. Solve t(u) = 0.
-1, 2/7, 109
Let c = -5807 - -5810. Factor -5/3*k**c + 0 + k**2 + 2/3*k.
-k*(k - 1)*(5*k + 2)/3
Let b = -11 - -16. Suppose -3*k + 0*k = 2*y, -b*y + 11 = 2*k. Suppose -3*m**2 - m + 2*m - 3*m + 2*m**y + 0*m**3 = 0. Calculate m.
-1/2, 0, 2
Let s(r) be the third derivative of -r**5/5 - 361*r**4/8 - 45*r**3 + r**2 + 3*r - 558. Factor s(a).
-3*(a + 90)*(4*a + 1)
Let h = 16077 + -16062. Let n(d) be the second derivative of -h*d + 0 - 1/20*d**5 + 0*d**2 - 1/42*d**4 + 2/105*d**6 + 0*d**3. Determine t, given that n(t) = 0.
-1/4, 0, 2
Let y(a) = -25*a**3 - 40*a**2 - 45*a - 30. Let t be (-12)/(-9) + 1/(-3). Let j(o) = -o**3 - o**2 - o - 1. Let x(r) = t*y(r) - 20*j(r). Solve x(k) = 0 for k.
-2, -1
Suppose 4*q - 8 = -w, -3*w + 4*w = 3*q - 13. Suppose 5*f + q = 13, 4*f = 2*b + 2. Let b*o**2 - 22*o + 7*o**2 + 8*o - 3*o**3 + 10*o - 8 = 0. Calculate o.
-2/3, 2
Let j(z) be the first derivative of 2*z**5/55 - 18*z**4/11 + 68*z**3/33 + 36*z**2/11 - 70*z/11 - 176. Let j(o) = 0. What is o?
-1, 1, 35
Let c = 109647 - 219285/2. Factor -11/2*k**3 + 0 - c*k - 1/2*k**4 - 19/2*k**2.
-k*(k + 1)**2*(k + 9)/2
What is s in 1593*s**3 - 52*s**4 + 18*s**5 + 262*s**4 - 25*s**5 + 4*s**5 + 1896*s**2 - 3696*s = 0?
-4, 0, 1, 77
Let x(z) = 171*z**2 + 41*z + 168. Let u(o) = 642*o**2 + 165*o + 672. Let l(f) = 4*u(f) - 15*x(f). Factor l(c).
3*(c + 7)*(c + 8)
Let u(c) = -5*c**2 - 167*c - 57. Let j be u(-33). Let q be ((-58)/(-30) + -2)*(j + -11). Suppose -40/3 + 8/3*o - q*o**2 = 0. What is o?
10
Let t(k) = -k**3 - 2*k**2 + 2*k - 1. Let x be t(-3). Factor -21 - 2*s