33). Let 1/2 - 1/4*u - n*u**2 = 0. Calculate u.
-2, 1
Let i(a) be the third derivative of 0*a - 163*a**2 + 0*a**3 + 1/945*a**7 - 1/270*a**5 + 2/27*a**4 - 2/135*a**6 + 0. Suppose i(u) = 0. Calculate u.
-1, 0, 1, 8
Let l(m) be the first derivative of 16*m + 57*m**4 + 56*m**2 + 34 - 356/3*m**3. Factor l(g).
4*(g - 1)*(3*g - 2)*(19*g + 2)
Let o(g) be the third derivative of -g**5/40 - 49*g**4/2 + 371*g**2. Factor o(b).
-3*b*(b + 392)/2
Let l(n) = -104*n**3 - 5094*n**2 + 5156*n - 42. Let a(v) = 22*v**3 + 1019*v**2 - 1032*v + 9. Let p(f) = 14*a(f) + 3*l(f). Find d such that p(d) = 0.
-255, 0, 1
Let u be 5/10 + 1 + 7/2. Find m such that -9604 + 33*m**3 + 27*m**4 - 15092*m - 1321*m**3 - 4*m**u - 6664*m**2 - 143*m**4 = 0.
-7, -1
Factor 9 + 536471*k**3 - 31 + 53*k + 82*k**2 - 536464*k**3.
(k + 1)*(k + 11)*(7*k - 2)
Let w(y) = y**2 + y + 2. Let q be w(-2). Suppose 0 = 57*i - 128 + 14. Factor 3*h**i - 8*h**2 - q*h - 4 + 4*h**2.
-(h + 2)**2
Let x(l) = -531*l + 103016. Let o be x(194). Factor 20/9 + 14/9*d - 8/9*d**o - 2/9*d**3.
-2*(d - 2)*(d + 1)*(d + 5)/9
Factor -1/2*j**2 - 570 - 383/2*j.
-(j + 3)*(j + 380)/2
Let d = -357 + 362. Let f(k) be the second derivative of -1/98*k**7 - 1/210*k**6 - 14*k + 0*k**4 + 1/70*k**d + 0*k**2 + 0 + 0*k**3. Find m, given that f(m) = 0.
-1, 0, 2/3
Let q = -5382/37 + 48512/333. Factor 2/9*r**2 - 8/3 + q*r.
2*(r - 3)*(r + 4)/9
Let x = -407 + 409. Let w(k) = 3*k**4 + 5*k**3 + 8*k**2 - 28*k - 32. Let s(y) = -y**4 + y**3 - y**2 - 2*y. Let h(t) = x*w(t) + 4*s(t). Factor h(r).
2*(r - 2)*(r + 1)*(r + 4)**2
Suppose -2*l + 103 = 5*s - 36, 99 = 3*s - 4*l. Factor 18 - u**2 + 15 + 15*u - s - 12*u.
-(u - 4)*(u + 1)
What is h in 127/2*h - 67/2*h**3 - 82 + 3/4*h**4 + 445/4*h**2 = 0?
-1, 2/3, 4, 41
Let r = -856231 - -856233. Let 15/4*l**3 - 1/2*l**4 + 0 - 5*l - 1/4*l**5 - l**r = 0. Calculate l.
-5, -1, 0, 2
Factor -3847*a**3 - 48*a**5 - 1213*a**3 - 51*a**5 - 320*a - 2100*a**4 - 2400*a**2 - 45*a**5 - 101*a**5.
-5*a*(a + 4)**2*(7*a + 2)**2
Let z(f) be the third derivative of 2*f**2 + 0*f**3 - 5/112*f**8 + 0*f + 0*f**4 + 25/6*f**5 + 16/21*f**7 - 95/24*f**6 + 17. Factor z(r).
-5*r**2*(r - 5)**2*(3*r - 2)
Let b = -252 - -265. Suppose -12*w**4 + 3*w + 16*w**2 + b*w**3 - 21*w**3 - 4 + 5*w = 0. Calculate w.
-1, 1/3, 1
Let m = -475 - -482. Let a be -7 - (m - 260/16). Factor -3*b - a - 3/4*b**2.
-3*(b + 1)*(b + 3)/4
Let d be (-1 + (-56)/24)/((-1)/39). Suppose -d = 3*m - 13*m. Find h, given that m*h**3 - 14*h**3 - 3*h**2 + 6*h**2 = 0.
0, 3
Suppose -19*i + 17*i = 282. Let u = -4 - i. Determine q, given that 6*q**2 - 24 + 138*q**3 + 12*q + u*q**3 - 278*q**3 = 0.
-2, 2
Let y = -36 + 66. Suppose -4*l + 0*l + 12 = a, 5*a - y = -5*l. Let 4*c**a - 16*c - 121*c**2 + 9*c**3 + 3*c**3 + 121*c**2 = 0. Calculate c.
-2, 0, 1
Let a = 77 + -75. Factor -4962*v**3 - 5*v**a + 4954*v**3 - 2*v**4 - 2*v**4 + v**2.
-4*v**2*(v + 1)**2
Suppose -4*j - 7*r + 45 = -2*r, 4*j - 38 = 2*r. Suppose 2*h = -n - 6 + 2, j = 2*n - 2*h. Let -13/12*w + 1/4*w**n + 1/3 = 0. What is w?
1/3, 4
Factor 116*f**2 - 4*f**3 - 588*f**2 - 1517 - 2724*f - 2031 + 263 - 747.
-4*(f + 3)**2*(f + 112)
Let t(m) be the third derivative of m**8/168 + 2*m**7/21 - 19*m**6/20 - m**5/3 + 14*m**4/3 + 23*m**2 - 45*m. Suppose t(r) = 0. Calculate r.
-14, -1, 0, 1, 4
Suppose 0 = 32*r - 59*r + 108. Suppose 4*j - 3*j + 7 = -5*h, r*j - 20 = 4*h. Factor j*f**3 - 9/4*f**2 + 0*f - 3/4*f**4 + 0.
-3*f**2*(f - 3)*(f - 1)/4
Solve 16*b**3 + 390*b + 508*b + 380*b**2 - 290*b - 176 = 0.
-22, -2, 1/4
Let s(k) = -30*k**3 - 2643*k**2 + 580797*k + 583446. Let z(y) = -161*y**3 - 13215*y**2 + 2903985*y + 2917231. Let x(f) = 16*s(f) - 3*z(f). Factor x(p).
3*(p - 441)**2*(p + 1)
Let u(q) be the first derivative of 2*q**5/55 - q**4/22 - 2*q**3/11 + q**2/11 + 4*q/11 - 7949. Let u(v) = 0. Calculate v.
-1, 1, 2
Factor 124*d**2 + 3*d**3 + 384*d - 2*d**5 + 252 - 3*d**4 + d**5 + 13*d**3 + 17*d**3 + 75*d**2.
-(d - 7)*(d + 2)**2*(d + 3)**2
Let m(d) be the third derivative of -d**6/260 - 62*d**5/195 + 7*d**4/13 - 2*d**2 - 941. What is x in m(x) = 0?
-42, 0, 2/3
Suppose -180*l + 374 = 7*l. What is h in 0*h - 2/5*h**5 + 2/5*h**3 + 0*h**l + 0*h**4 + 0 = 0?
-1, 0, 1
Suppose 4*i = -39*i - 144 + 531. Let x(t) be the third derivative of -5/32*t**4 - 15/4*t**3 + 1/96*t**6 + 0 + 1/12*t**5 + i*t**2 + 0*t. Factor x(z).
5*(z - 2)*(z + 3)**2/4
Determine i, given that -54*i**3 - 24 - 30 + 234*i - 175*i**2 - 44*i**3 - 35*i**2 = 0.
-3, 3/7
Factor 107 + 155 + 55 + 67 - 500*z - 25*z**3 + 208*z**2 - z**4.
-(z - 3)*(z - 2)**2*(z + 32)
Suppose 0 = -4*g + 4*a + 40, 2*a - 6 = -5*g + 65. Suppose 0 = 4*o + 2*u - 40, -5*u + 17 - g = -2*o. Factor 6 - o*n + 8/3*n**3 + 2/3*n**4 - 4/3*n**2.
2*(n - 1)**2*(n + 3)**2/3
Let t(a) = a**2 + 7*a - 19. Let y be t(-16). Factor y*o**4 - 54*o**2 - 40*o - 150*o**3 - 60*o**2 - 66*o**2.
5*o*(o - 2)*(5*o + 2)**2
Factor 125*z**2 - 1187*z + 129*z**2 + 127*z**2 - 793*z - 326700 - 384*z**2.
-3*(z + 330)**2
Let q(p) be the second derivative of p**4/4 - 627*p**3 + 1179387*p**2/2 + 2985*p. Find c such that q(c) = 0.
627
Let o(j) = 91*j**4 + 49*j**3 - 20*j**2 + 3*j + 3. Let q(m) = 21*m**4 + m**3 + m + 1. Let v(a) = -o(a) + 3*q(a). Solve v(t) = 0 for t.
-2, 0, 5/14
Let s be 2120/318*30/9*6/25. Let x(l) be the first derivative of 12 - 121/6*l**4 + s*l + 44*l**3 + 28*l**2. Suppose x(b) = 0. Calculate b.
-2/11, 2
Suppose -3*d + 1051 = -5*o + 130, o + 201 = -5*d. Let x be -6 - (o/14 + (41 - 36)). Factor 216/7*w + 780/7*w**2 + 338/7*w**3 + x.
2*(w + 2)*(13*w + 2)**2/7
Let v = -2978977/2 + 1489491. Determine r so that v*r**2 - 11*r + 8 + 1/2*r**3 = 0.
-8, 1, 2
Let h(c) = -c**2 - c + 1. Suppose 3*v + 10 = -8*g + 13*g, 0 = -5*g + 2*v + 5. Let d(m) = m**2 - 14*m. Let n(x) = g*d(x) - 5*h(x). What is s in n(s) = 0?
-5, 1/4
Let o(m) be the first derivative of -m**4/40 - 2*m**3/15 + 3*m**2 + 658. Solve o(b) = 0.
-10, 0, 6
Suppose 10*d - 24 = -4. Suppose -3*l + 30 = -4*o, 27 = d*l + 3*o - 10. Let -265*p**2 - p - l*p + 3*p + 269*p**2 = 0. What is p?
0, 3
Let p(f) be the first derivative of -f**6/12 - 127*f**5/30 - 85*f**4/6 - 16*f**3 - 35*f**2 - 158. Let h(z) be the second derivative of p(z). Factor h(o).
-2*(o + 1)*(o + 24)*(5*o + 2)
Let o(m) = -17*m - 625. Let y be o(-37). Let x(d) be the second derivative of 2*d**y - 19*d + 0 - 21/2*d**3 + 27*d**2 - 3/20*d**5. Solve x(v) = 0 for v.
2, 3
Suppose -5*k + 17 = z - 16, -66 = -2*z - 4*k. Suppose 0 = 16*j + 1 - z. Solve -1/5*f - 1/10*f**j + 1/10 + 1/5*f**3 = 0 for f.
-1, 1/2, 1
Factor -2058/5*k**2 + 530448/5*k - 528392/5 + 2/5*k**3.
2*(k - 514)**2*(k - 1)/5
Suppose 2*j + 2*u - 10 = 24, -j + 2*u = -26. Solve 24 + 6*h**2 - 7*h**2 + j*h - 7*h**2 - 4*h**3 = 0 for h.
-3, -1, 2
Factor 337*k - 7701424*k**2 - 348*k - 19360 - 4*k**3 + 3047*k + 7701352*k**2.
-4*(k - 11)**2*(k + 40)
Factor 0 - 1/3*h**2 + 7*h.
-h*(h - 21)/3
Let z(o) be the first derivative of -o**4/84 + 2*o**3/3 - 14*o**2 + 43*o + 82. Let i(f) be the first derivative of z(f). Solve i(b) = 0 for b.
14
Let z(r) be the first derivative of -1/3*r**2 + 1/24*r**4 + 2/3*r - 1/18*r**3 - 57. Factor z(h).
(h - 2)*(h - 1)*(h + 2)/6
Factor -722/11 + 2/11*z**3 - 78/11*z**2 + 798/11*z.
2*(z - 19)**2*(z - 1)/11
Let h be (27/60)/((-3)/(-45)*3). Let n = h - 29/20. Let 7/5*o**3 - 3*o**2 - 1/5*o**4 - n + 13/5*o = 0. What is o?
1, 4
Let h(l) = -2*l**3 - 39*l**2 - 91*l - 102. Let s be h(-17). Factor -2/9*d**4 + 44/9*d**2 + 0*d - 14/3*d**3 + s.
-2*d**2*(d - 1)*(d + 22)/9
Determine n, given that -10*n**3 + 2/9*n**4 + 0 - 294*n + 126*n**2 = 0.
0, 3, 21
Suppose 0 = 1698*t - 1616*t - 164. Let n(o) be the second derivative of 0 - 3/40*o**5 - 5*o + 5/8*o**4 - 2*o**3 + 3*o**t. Determine s so that n(s) = 0.
1, 2
Let i(f) be the third derivative of -f**2 - 26 - 26/3*f**5 - 1/30*f**6 + 0*f**3 - 4225/6*f**4 + 0*f. Solve i(z) = 0.
-65, 0
Let p be (144/15)/(1/5). Suppose 21*u - p*u = -54. Solve 1/4 - 1/2*m + 1/4*m**u = 0 for m.
1
Factor -21*o**2 - 22 + 56*o - 3*o**3 - 11*o - 6 + 6*o**3 + 1.
3*(o - 3)**2*(o - 1)
Let j(n) = -19*n**2 - 4680*n - 1331. Let h(d) = 94*d**2 + 23400*d + 6656. Let q(w) = -5*h(w) - 24*j(w). Solve q(t) = 0 for t.
-334, -2/7
Let i(l) be the first derivative of l**6/15 - 52*l**5/25 + 129*l**4/10 - 368*l**3/15 + 16*l**2 - 6226. Let i(m) = 0. What is m?
0, 1, 4, 20
Let h(f) be the 