 + 4)
Let h be 54*3*16/(-3840)*-8. Factor 12/5*l + h*l**2 + 3/5*l**4 + 0 + 18/5*l**3.
3*l*(l + 1)**2*(l + 4)/5
Let i(w) be the first derivative of -4*w**5 - 5/6*w**6 + 0*w + 0*w**3 - 15/4*w**4 + 0*w**2 + 92. Let i(y) = 0. Calculate y.
-3, -1, 0
Suppose -693 = -38*k - 617. Factor 2/13*b**k - 32/13 - 12/13*b.
2*(b - 8)*(b + 2)/13
Let z(d) be the second derivative of -d**6/120 - 123*d**5/40 + 83*d**4/4 - 125*d**3/3 - 92*d + 8. Factor z(f).
-f*(f - 2)**2*(f + 250)/4
Let w(f) be the second derivative of 3*f**3 + 1/6*f**4 + 18*f**2 + 0 + 41*f. Factor w(q).
2*(q + 3)*(q + 6)
Let g(r) = -5*r**4 - 40*r**3 + 110*r - 80. Let q(u) = -u**3 + u**2 + 3*u - 2. Let a(y) = g(y) + 15*q(y). Factor a(k).
-5*(k - 1)**2*(k + 2)*(k + 11)
Factor -56*t**2 + 3 - 221/2*t.
-(t + 2)*(112*t - 3)/2
Let o be -5 + (-22 - (-6560)/350)/((-6)/10). Let r be ((-2)/(-7))/(-3 - -5). Determine j so that 2/7*j**2 + o*j + r = 0.
-1, -1/2
Suppose -5*y + 1 = -9. Let v = 99 + -96. Let -60*w**y + 65*w**2 - 5 + v*w - 3*w = 0. Calculate w.
-1, 1
Let d(v) be the second derivative of v**9/5544 + v**8/770 + v**7/385 + 2*v**3/3 + 3*v**2/2 + 24*v. Let l(p) be the second derivative of d(p). Factor l(r).
6*r**3*(r + 2)**2/11
Let d = 40 + -62. Let u be 4/d + (-15389)/(-121). Let -35*z**3 + 5 + u*z**2 - 1 + 6*z - 116*z**2 + 14*z = 0. Calculate z.
-2/5, -2/7, 1
Suppose 9*i + 9*i = -27*i. Let x(l) be the third derivative of 0*l + i - 1/10*l**4 + 0*l**3 - 1/350*l**7 - 10*l**2 + 3/200*l**6 + 0*l**5. Solve x(t) = 0.
-1, 0, 2
Let c(z) be the second derivative of -z**4/4 - 47*z**3/2 + 390*z**2 - 158*z + 1. Factor c(d).
-3*(d - 5)*(d + 52)
Factor -58 - 180 + 160*z - 19216*z**3 + 19212*z**3 - 98 + 12*z**2.
-4*(z - 7)*(z - 2)*(z + 6)
Let b be (123/(-4))/(8/(704/33)). Let c be (b/(-45) - 1) + 2/(-9). Factor -1/5*g**3 + g - 2/5 + 1/5*g**4 - c*g**2.
(g - 1)**3*(g + 2)/5
Suppose 15*b + 52 + 8 = 0. Let t be ((b + 4)/(-7))/2. Solve 3/2*o**4 + 0*o + 0*o**2 + 9/2*o**3 + t = 0.
-3, 0
Let y(u) = -10*u**2 + 40*u - 15. Let o(m) be the second derivative of m**4/12 - m**2 + 31*m. Let f(w) = -15*o(w) - y(w). Factor f(x).
-5*(x - 1)*(x + 9)
Let w(d) be the third derivative of d**6/240 - d**5/120 - 5*d**4/4 - 9*d**3 - 30*d**2 + 3. Solve w(x) = 0 for x.
-6, -2, 9
Let h(n) be the third derivative of -n**7/1365 - 7*n**6/156 + 23*n**5/78 + 35*n**4/156 - 38*n**3/13 + n**2 - 824*n. Find j, given that h(j) = 0.
-38, -1, 1, 3
Let n be ((-116)/8 - -11)*20/(-28). Factor -3/2*a - 9/2*a**4 - 1/2 - a**3 + n*a**5 + 5*a**2.
(a - 1)**3*(a + 1)*(5*a + 1)/2
Suppose -1/9*c**2 - 140/9*c + 284/9 = 0. What is c?
-142, 2
Let d(v) be the first derivative of v**6/120 - v**5/20 - v**4/4 + 4*v**3/3 + v**2/2 + 106*v - 262. Let i(a) be the second derivative of d(a). Factor i(q).
(q - 4)*(q - 1)*(q + 2)
Let m(v) be the third derivative of -13/40*v**4 - 16*v**2 - 9/100*v**5 + 0 + 2*v + 7/10*v**3 + 1/175*v**7 + 13/200*v**6. Find l, given that m(l) = 0.
-7, -1, 1/2, 1
Let w = 205151 + -1846357/9. Factor 0 - w*d**3 - 4/9*d - 2/3*d**2.
-2*d*(d + 1)*(d + 2)/9
Let n be (5695/(-68))/((-3)/20). Let t = n - 557. Factor 8*w + t*w**2 - 6 - 8/3*w**3 - 2/3*w**4.
-2*(w - 1)**2*(w + 3)**2/3
Let z be (-1185)/(-315) + -1 + (-8)/(-12). Factor -z + 3/7*u**2 + 3*u.
3*(u - 1)*(u + 8)/7
Let o be ((-56)/(-24))/(28/24). Determine a so that a**2 + 57*a - 1 - 59*a + o = 0.
1
Let m(y) be the second derivative of -1/120*y**5 + 69*y + 0*y**2 + 1/8*y**4 - 2/9*y**3 + 1. Solve m(q) = 0.
0, 1, 8
Let z(c) be the second derivative of 3/40*c**6 - 42*c + 3/80*c**5 - 17/16*c**4 - 2 - 9/4*c**2 + 19/8*c**3. Suppose z(m) = 0. Calculate m.
-3, 2/3, 1
Let z be 45/6*(273/7098)/((-9)/(-39)). Factor -6125/4 + 175/2*c - z*c**2.
-5*(c - 35)**2/4
Suppose -830*o + 2580 - 90 = 0. Factor -39*y**o + 0 + 27/2*y**2 - 9/2*y**4 + 0*y.
-3*y**2*(y + 9)*(3*y - 1)/2
Let o(n) be the first derivative of 22*n**3/3 - 134*n**2 + 720*n - 13854. Factor o(t).
2*(t - 4)*(11*t - 90)
Determine g so that 0 - 6/5*g + 9*g**2 = 0.
0, 2/15
Let g = -38 - -27. Let l(h) = -h - 9. Let j be l(g). Solve -4*a**4 + j*a**2 + 4*a - 17*a**3 + 13*a**3 + 2*a**2 = 0.
-1, 0, 1
What is t in -1240*t + 40*t**3 - 1922/3 - 2/3*t**4 - 1676/3*t**2 = 0?
-1, 31
Let f(n) be the third derivative of -n**8/392 + n**7/147 + n**6/420 - n**5/42 + n**4/42 - 1432*n**2. Determine r, given that f(r) = 0.
-1, 0, 2/3, 1
Let c = -113 + 135. Let m be 7/14 - 11/c. Solve -1/2*u**3 + 1/8*u + m + 3/8*u**2 = 0.
-1/4, 0, 1
Find t such that 9*t**2 - 13882 + 6*t**2 + 13987 + 71*t + t**3 = 0.
-7, -5, -3
Let d be (451/(-66) + 7)*8*6/20. Let v(y) be the second derivative of 0*y**3 + d*y**2 - 2/15*y**4 + 0 + 20*y + 0*y**5 + 2/75*y**6. Solve v(x) = 0 for x.
-1, 1
Factor -126/17*d - 2/17*d**2 - 1672/17.
-2*(d + 19)*(d + 44)/17
Let u(d) be the third derivative of d**7/840 - d**6/240 - 119*d**5/240 - 29*d**4/8 + 39*d**3/2 - 3995*d**2. Factor u(a).
(a - 13)*(a - 1)*(a + 6)**2/4
Factor 2120/7 - 2/7*v**2 - 192/7*v.
-2*(v - 10)*(v + 106)/7
Let u(t) be the third derivative of 5*t**8/336 - t**7/14 - 11*t**6/24 + t**5/4 + 25*t**4/12 + 158*t**2 + 7*t. Let u(r) = 0. What is r?
-2, -1, 0, 1, 5
Let o = -109772435/570988 - 2/142747. Let u = o - -193. Factor -3 - u*x**2 + 3*x.
-3*(x - 2)**2/4
Let c(w) = w**3 - 38*w**2 + 393*w - 1102. Let v be c(23). Solve -3/8*l**4 - 21/2*l + 9 + 21/8*l**3 - 3/4*l**v = 0 for l.
-2, 1, 2, 6
Let a(u) = u**4 + 4*u**2 + 2*u. Let r(c) = 4*c**5 + 60*c**4 + 140*c**3 - 120*c. Let t(j) = 12*a(j) - r(j). Suppose t(p) = 0. What is p?
-6, -1, 0, 1
Let r(j) be the third derivative of j**5/390 - 563*j**4/52 - 130*j**3/3 - 149*j**2 + 4*j + 4. Let r(n) = 0. Calculate n.
-1, 1690
Let w(j) be the second derivative of 14/33*j**3 - 2*j - 18/55*j**5 + 3/11*j**2 + 1/22*j**4 + 38. Solve w(r) = 0 for r.
-1/3, 3/4
Suppose 148*a - 4 = 146*a. Let m be ((-143)/65 - -1) + 2. Let 1/5*q**5 + 6/5*q**4 + m*q + 12/5*q**a + 0 + 13/5*q**3 = 0. Calculate q.
-2, -1, 0
Let n = -375 - -382. Let r be (-42)/(-48) - n/(-14). Solve 1/8*v**4 - r*v**3 - 8 - 2*v + 9/2*v**2 = 0 for v.
-1, 4
Let s(a) = 112*a**2 - 10*a + 13. Let j be s(2). What is b in 11*b**3 - j*b - 4*b**4 + b**3 + 509*b + 60*b**2 + 24 = 0?
-1, 6
Determine u, given that -5*u**5 - 42*u**4 + 104*u**2 - 28*u**3 + 30*u - 1406 + 3*u**5 + 6*u**4 + 1338 = 0.
-17, -2, -1, 1
Suppose 41*j - 30*j = -55. Let w be (j/(-24))/((-70)/(-42)). Determine r, given that w*r + 1/4 - 1/8*r**2 = 0.
-1, 2
Let f(h) be the third derivative of h**7/105 + 23*h**6/60 - 22*h**5/5 + 55*h**4/3 - 112*h**3/3 + 2482*h**2. Factor f(g).
2*(g - 2)**2*(g - 1)*(g + 28)
Let m be (-36)/(-96) - 123/328. Let 0*y + m + 1/5*y**2 = 0. What is y?
0
Let t = 2394 + -2389. Let g(p) be the second derivative of 0 - 1/110*p**t - 1/33*p**4 + 0*p**2 + 8*p - 1/33*p**3. Factor g(s).
-2*s*(s + 1)**2/11
Suppose -3*n + 4*f = -1308, -n - 22*f + 436 = -23*f. Let w be n/(-22) + 10 - -10. Factor -20/11 - 42/11*s - w*s**3 - 24/11*s**2.
-2*(s + 1)**2*(s + 10)/11
Suppose 2*p + 1 = -3*s - 90, -5*p + 2*s - 237 = 0. Let t be (-2 - (-22)/12)*(45 + p). Factor -1/3*a - t*a**3 + 0 + 2/3*a**2.
-a*(a - 1)**2/3
Let l = 1613/99 - 1580/99. Factor 0 + 1/3*g - l*g**2.
-g*(g - 1)/3
Let t(l) = 17*l**3 + 13*l**2 - 26*l - 28. Let q(u) = 37*u**3 + 27*u**2 - 57*u - 56. Let k(f) = 6*q(f) - 13*t(f). Suppose k(n) = 0. Calculate n.
-2, 2, 7
Let b(v) be the second derivative of -5*v**6/3 - 249*v**5/2 - 364*v**4 - 1156*v**3/3 - 192*v**2 + 11*v - 69. Let b(s) = 0. What is s?
-48, -1, -2/5
Let z be (615/14)/((-8)/84). Let w = z + 462. Factor -w - 3/2*t - 3/4*t**2.
-3*(t + 1)**2/4
Let a = 2060 + -1276. Let v = 2390/3 - a. Factor -14/3*h**4 - 50/3*h**2 - v*h**3 - 32/3*h - 8/3 - 2/3*h**5.
-2*(h + 1)**3*(h + 2)**2/3
Let z(x) be the second derivative of x**5/90 + x**4/9 + 4*x**3/9 - 8*x**2 + 140*x. Let q(a) be the first derivative of z(a). Suppose q(k) = 0. What is k?
-2
Let h(k) = k**2 - 4*k + 2. Let x be h(4). Suppose 0 = -57*o + 23*o + 238. Factor o*u + 2*u**2 + 3*u - 4*u**x - 6*u.
-2*u*(u - 2)
Let q(r) be the second derivative of r**5/5 - 55*r**4/3 + 1904*r**3/3 - 10584*r**2 + 43*r - 19. Find m, given that q(m) = 0.
14, 27
Let -190104 + 1068*q - 3/2*q**2 = 0. What is q?
356
Let b(i) be the first derivative of -i**4/4 - 7*i**3 - 3*i**2/2 - 36*i - 35. Let u be b(-21). Factor 11 + 12*c - u - 9*c**2 + 13*c**2.
4*(c - 1)*(c + 4)
Suppose 0 = 2*