*h. Find l such that 28/9 + 74/9*l - 14/9*l**3 - 88/9*l**h = 0.
-7, -2/7, 1
Let h(j) be the first derivative of j**5/15 - j**4/12 - 5*j**3/9 - j**2/2 + 2754. Factor h(p).
p*(p - 3)*(p + 1)**2/3
Let g(y) be the third derivative of y**8/392 + 71*y**7/490 - 89*y**6/280 - 8191*y**5/70 - 3036*y**4/7 - 576*y**3 + 11*y**2 + 3*y + 5. Let g(l) = 0. Calculate l.
-24, -1, -1/2, 14
Let f(s) be the third derivative of -s**6/120 + 461*s**5/60 + 925*s**4/24 + 463*s**3/6 + 41*s**2 - 9. Solve f(q) = 0.
-1, 463
Let k(t) be the third derivative of -t**5/12 + 455*t**4/24 - 1340*t**3 - 10*t**2 + 8*t + 12. Find l such that k(l) = 0.
24, 67
Solve 19/4*v**2 - 162*v + 17 = 0 for v.
2/19, 34
Suppose 0 = 4*p + p - 2*t + 2, 0 = -2*p + 3*t - 3. Let q be 3/((-2 - -3) + p). Factor -6 - c**2 - 20*c - q*c**2 - 10 + 0*c**2.
-4*(c + 1)*(c + 4)
Let n = -16444/117 - -1830/13. Let -4/9*q**3 + 2/9*q**5 + 0*q**2 + 0*q**4 + 0 + n*q = 0. Calculate q.
-1, 0, 1
Suppose -8*m + 3231 = -17*m. Let q = -355 - m. Factor -c**3 + 1/2*c**q + 1/2 - c**2 + 1/2*c + 1/2*c**5.
(c - 1)**2*(c + 1)**3/2
Factor -306/5*s**3 + 0 + 0*s + 2/5*s**4 - 124*s**2.
2*s**2*(s - 155)*(s + 2)/5
Let z(n) be the first derivative of -n**3 + 9*n**2/2 + 324*n + 1843. Solve z(c) = 0.
-9, 12
Let m = 65673 + -65670. Factor 0 + 360*r - 60*r**2 + 5/2*r**m.
5*r*(r - 12)**2/2
Let h(v) = v**2 + 12*v + 11. Suppose 10*o + 145 = 175. Let w(f) = -f**2 - 11*f - 12. Let d(g) = o*h(g) + 4*w(g). Find m, given that d(m) = 0.
-5, -3
Let w = 308180 + -308177. Factor 4/5 + 4/5*h**2 - 22/15*h - 2/15*h**w.
-2*(h - 3)*(h - 2)*(h - 1)/15
Let a(d) = 4*d**2 - 66*d + 56. Let o(u) = 5*u**2 - 67*u + 54. Suppose 0 = -6*v + 4285 - 4261. Let c(r) = v*a(r) - 3*o(r). Suppose c(j) = 0. What is j?
1, 62
Let q(p) be the third derivative of p**5/180 + 92*p**4/9 + 67712*p**3/9 - 2571*p**2. Factor q(d).
(d + 368)**2/3
Suppose 125 = 5*b - 4*p, -2*b + 42 + 26 = 2*p. Let u = 31 - b. Factor 2 + 6*v**2 + 2*v - v**2 + u*v - 3*v**2.
2*(v + 1)**2
Suppose -v**4 + 43 + 35 - 65*v - 159*v + 61*v - 5*v**3 + 0*v**4 + 91*v**2 = 0. What is v?
-13, 1, 6
Let i(k) be the second derivative of k**4/21 - 26*k**3/21 + 72*k**2/7 - 639*k. Factor i(g).
4*(g - 9)*(g - 4)/7
Let m(k) be the first derivative of -8*k**2 + 180 - 1/3*k**3 - 28*k. Suppose m(c) = 0. Calculate c.
-14, -2
Let c(t) be the third derivative of -t**8/672 - 13*t**7/140 - 7*t**6/48 + 119*t**5/120 + 4*t**4 + 19*t**3/3 + 52*t**2 + 12. Determine m so that c(m) = 0.
-38, -1, 2
Let g(o) be the second derivative of -363*o**5/80 + 2255*o**4/16 + 104*o**3 + 57*o**2/2 - 1402*o. Factor g(b).
-3*(b - 19)*(11*b + 2)**2/4
Let -1/5*g**2 - 242/5 - 123/5*g = 0. Calculate g.
-121, -2
Determine o, given that 2/23*o**2 - 608/23*o + 1208/23 = 0.
2, 302
Let g(v) = -17*v**3 - 58*v**2 + 410*v + 11548. Let f(y) = -3*y**3 - 11*y - 2. Let k(b) = 6*f(b) - g(b). Factor k(a).
-(a - 34)**2*(a + 10)
Let l(f) be the second derivative of f**6/24 + 7*f**5/12 + 55*f**4/24 + 25*f**3/6 + 49*f**2 + 3*f - 4. Let q(v) be the first derivative of l(v). Factor q(i).
5*(i + 1)**2*(i + 5)
Suppose 82653*q - 82677*q + 48 = 0. Factor 0 + 1/2*g**4 + 0*g + 1/2*g**3 - g**q.
g**2*(g - 1)*(g + 2)/2
Find p such that -15*p**2 + 0 - 10*p + 0 - 10252*p**4 + 10257*p**4 = 0.
-1, 0, 2
Let z be 39 + (6291/(-243) - 12). Suppose z*h**4 - 34/9*h**2 - 44/9*h**3 + 20/9*h + 0 = 0. Calculate h.
-1, 0, 2/5, 5
Let l(f) be the third derivative of 1/15*f**5 + 4/3*f**3 - 4*f - 1/2*f**4 + 0 + 6*f**2. Factor l(a).
4*(a - 2)*(a - 1)
Let f(o) be the first derivative of 5*o**3/3 - 130*o**2 - 265*o + 1004. Factor f(v).
5*(v - 53)*(v + 1)
Let m(y) = -26*y**2 + 3274*y + 252. Let j be m(126). Determine f so that 4/3*f**2 - 1/3*f**3 + j - f = 0.
0, 1, 3
Suppose 3*w - 4*h - 1974 = 0, 2054 = 4*w - 3*h - 578. Find v, given that -w - 1876 - 279 - 240*v - 5*v**2 - 67 = 0.
-24
Let p be -3*9/54 + 133/2. Let q be (p/18 - 3)*(-5)/(-2). Find a, given that -4/3*a**2 - a**4 + 0 - 4*a**3 + 0*a + q*a**5 = 0.
-1, -2/5, 0, 2
Factor -82 + 163/2*s + 1/2*s**2.
(s - 1)*(s + 164)/2
Let n be 15/3 + (1 - 3). Let z be (10/(-15))/((-1)/n). Let 132*r**3 - 10*r**z - 4*r + 2*r**5 + r**5 + 2*r**4 - r**5 - 138*r**3 = 0. What is r?
-1, 0, 2
Let w(v) = 13*v + 2 - 5*v - 5*v. Let k be w(9). What is g in 3*g**3 - k*g + 29*g = 0?
0
Let b(n) = 16 + 5*n + 4 - 48. Let u be b(6). Determine r, given that u*r**3 + 2*r**4 - 9*r**3 + 4*r**3 + 4*r**4 - 3*r**5 = 0.
0, 1
Suppose 908 = 2*r + 1442. Let d = -265 - r. Solve 8/11*k + 0 + 2/11*k**d = 0.
-4, 0
Let w be (-18)/6 + 94 + 5. Find b, given that 4*b**4 + w*b**2 - 46*b - 32*b**3 - 42 + 106 - 82*b = 0.
2
Let a(x) = -62213*x + 248854. Let m be a(4). Determine s so that 0*s - 8/3*s**m + 0 - 4/3*s**4 + 2/3*s**5 - 14/3*s**3 = 0.
-1, 0, 4
Suppose -5*d - 447*d**3 + 5*d + 1108*d**3 + 13*d**4 - 72*d**2 - 511*d**3 = 0. Calculate d.
-12, 0, 6/13
Let v(i) be the first derivative of -3/10*i**4 + 0*i + 268 + 2/3*i**3 + 2/5*i**2. Solve v(u) = 0 for u.
-1/3, 0, 2
Let g be (15/12 - -3)/(2/8). Let w be 3*(-4)/(-102) + 32/g. Solve -49 - 9*u**3 + 3*u**2 + 8*u**3 + u**2 - 63*u - 19*u**w = 0 for u.
-7, -1
Let i = 1033659/275636 - 6/68909. Factor i*b - 3/4*b**2 + 18.
-3*(b - 8)*(b + 3)/4
Let z(f) = -f**3 - 7*f**2 - 39*f - 56. Let v be z(-2). Factor -1/5*a**4 - 12/5*a**v - 8/5*a - 6/5*a**3 + 0.
-a*(a + 2)**3/5
Factor -12*u**4 - 39366/7 + 2432/7*u**3 - 26406/7*u**2 + 1/7*u**5 + 63423/7*u.
(u - 27)**3*(u - 2)*(u - 1)/7
Factor -1/2*n**2 + 767/6*n - 85.
-(n - 255)*(3*n - 2)/6
Suppose 4*t + h - 6 = 0, 5 + 7 = t - 5*h. Determine l, given that 4*l**t + 12 - 4 + 32*l + 40 = 0.
-6, -2
Let z be (-6*(-5)/20)/((-2)/(-168)). Find t, given that -6*t**2 + t**2 + 16*t**2 + 111 + 16*t**2 + 36 + z*t = 0.
-7/3
Let s be 74/((5 + 0)/5). Suppose 2*z - 80 = -s. Factor -21*m - 27 - 4*m**z - 37 + 28*m**2 - 20*m + 9*m.
-4*(m - 4)**2*(m + 1)
Let k(l) be the third derivative of 2*l**7/15 + 16*l**6/5 - 56*l**5/15 - 64*l**4 + 224*l**3/3 + 101*l**2 - 7*l. Suppose k(w) = 0. Calculate w.
-14, -2, 2/7, 2
Factor 29/3*j**2 - 46/3*j - 8.
(j - 2)*(29*j + 12)/3
Let s(g) be the first derivative of g**6/2 - 192*g**5/5 - 597*g**4/4 - 134*g**3 - 8433. Determine i so that s(i) = 0.
-2, -1, 0, 67
Let f = -90881 + 90883. Factor 10 - 5/4*d**f - 5/2*d.
-5*(d - 2)*(d + 4)/4
Let h = -75 + 76. Let t be (-15)/30*(-3 - h). Factor 8/11*v**t - 6/11*v + 2/11*v**3 - 36/11.
2*(v - 2)*(v + 3)**2/11
Factor -31414853248 - 8811*m**2 - 8546140*m + m**3 + 34424047*m + 6080382295.
(m - 2937)**3
Suppose -211*a + 198*a = 1794. Let r = a + 141. Factor 0 + 6/7*x + r*x**2 + 9/7*x**3.
3*x*(x + 2)*(3*x + 1)/7
Let h(r) be the second derivative of r**5/30 - 7*r**4/3 + 115*r**3/3 + 2116*r**2/3 + 2018*r. Factor h(k).
2*(k - 23)**2*(k + 4)/3
Let v be 2/5*(1 - -9). Let q be (-78)/(-240) + (4 - 392/64) + 2. Factor q*l**v - 4/5*l**3 - l**2 + 0*l + 0.
l**2*(l - 5)*(l + 1)/5
Let l(f) be the second derivative of f**4/12 - 31*f**3/6 + 65*f**2 - 388*f. Let l(y) = 0. What is y?
5, 26
Let i be ((-156)/(-832))/(17/272). Factor -b**i - 1/2*b**2 + b**4 + 5/4*b - 1/4*b**5 - 1/2.
-(b - 2)*(b - 1)**3*(b + 1)/4
Suppose 6 + 27 = 3*f - 2*k, 0 = 3*k - 18. Let x(h) be the third derivative of 1/80*h**5 + 0 + 0*h - f*h**2 + 0*h**3 + 1/16*h**4. Suppose x(p) = 0. Calculate p.
-2, 0
Factor 543 + 194373*r - 2*r**3 - 66*r**2 + 35 - 194883*r.
-2*(r - 1)*(r + 17)**2
Let w(q) be the third derivative of -q**6/1320 + 6*q**5/11 - 1800*q**4/11 + 288000*q**3/11 - 1952*q**2. Factor w(g).
-(g - 120)**3/11
Determine f so that 3*f**2 - 136*f**3 - 2 + 239*f**3 - 94*f**3 - 21*f - 13 = 0.
-1, 5/3
Suppose -68*w = -73 - 131. Let k(j) be the third derivative of 0 - 32*j**2 + 0*j - 1/240*j**5 - 1/48*j**4 - 1/24*j**w. Factor k(f).
-(f + 1)**2/4
Let c(k) be the third derivative of k**6/30 + 58*k**5/15 - 122*k**4/3 + 496*k**3/3 - 912*k**2. Factor c(p).
4*(p - 2)**2*(p + 62)
Let y be 1 + 3 + (-1 - 2)/(-3). Suppose 2*h - 3 = y. Let -2*s**3 + s**h - 20*s**2 + 2*s + 32*s**2 - 13*s**2 = 0. What is s?
-1, 0, 1, 2
Let q(b) be the first derivative of -b**8/3360 + b**7/420 + b**6/144 + 37*b**3 + 91. Let c(y) be the third derivative of q(y). Solve c(a) = 0.
-1, 0, 5
Let w be (13/((-364)/144) + 5)*(-592)/74. Suppose -w*l - 2/7*l**4 + 32/7*l**3 + 104/7 - 78/7*l**2 = 0. Calculate l.
-1, 2, 13
Let x(b) = 5*b**3 - 17*b**2 - 3*b - 55. Let y(z) = z**3 - 1