. Factor 32*k + 44*k - 3*k**2 - i*k - 9.
-3*(k - 3)*(k - 1)
Factor -7268 + 4*f**2 - 52*f + 7268.
4*f*(f - 13)
Suppose 0 = 18*j - 4*j - 56. Let h be (2/j)/(145/696). Factor h - 6/5*n - 12/5*n**2 + 6/5*n**3.
6*(n - 2)*(n - 1)*(n + 1)/5
Let v(f) be the first derivative of -f**3/15 + 23*f**2/2 - 110*f + 6390. Find r, given that v(r) = 0.
5, 110
Let c(f) = f**3 - 2*f**2 - 4*f - 1. Let j(k) = -8*k**3 - 81*k**2 + 186*k + 52. Let h(l) = -12*c(l) - 3*j(l). Factor h(n).
3*(n - 2)*(n + 24)*(4*n + 1)
Let k(c) be the third derivative of c**5/60 + 27*c**4/8 - 1156*c**2. Factor k(l).
l*(l + 81)
Let s = -2/352411 + 1057237/704822. Factor -2*t + s + 5/8*t**2.
(t - 2)*(5*t - 6)/8
Let j(r) be the third derivative of r**5/15 + r**4/6 - 246*r**2 - 3. Suppose j(c) = 0. What is c?
-1, 0
Let z(p) be the first derivative of -6/5*p**2 + 18*p + 3/10*p**3 + 7 + 1/20*p**4. Let q(k) be the first derivative of z(k). Solve q(o) = 0 for o.
-4, 1
Let b(f) = 116*f**2 + 12933*f + 6933739. Let m(n) = -63*n**2 - 6468*n - 3466869. Let c(o) = -6*b(o) - 11*m(o). Factor c(p).
-3*(p + 1075)**2
Suppose 5*f = h - 22, 3*f + 22 + 0 = 5*h. Let j = 17 + -5. Factor x**3 + 18*x - j*x + 2*x**h - 10*x + x**3.
2*x*(x - 1)*(x + 2)
Let g(z) be the third derivative of 2*z**7/15 - 43*z**6/30 + 27*z**5/5 - 15*z**4/2 + 7*z**2 + 74*z. What is u in g(u) = 0?
0, 1, 15/7, 3
Suppose -17*l + 7912 = 7861. Let j(m) be the first derivative of -2/9*m**l + 8/3*m**2 + 6*m + 10. Factor j(v).
-2*(v - 9)*(v + 1)/3
Let q(o) be the third derivative of o**6/720 - 89*o**5/360 + o**2 + 8*o + 193. Factor q(m).
m**2*(m - 89)/6
Suppose 0 = 18*g - 17*g - 2. Find z such that -10*z + 7*z - 6 - 3*z**3 - 10*z**g + 6*z**3 + 7*z**2 + 9*z**2 = 0.
-2, -1, 1
Let c(r) = -21*r**4 + 191*r**3 + 201*r**2 - 11*r - 44. Let j(l) = -4*l**4 + 38*l**3 + 40*l**2 - 2*l - 8. Let p(m) = -4*c(m) + 22*j(m). What is g in p(g) = 0?
-1, 0, 19
Let f = 1 - -5. Suppose 4*g = f*g. Factor -4 - 4*y**2 + 2*y**2 - 6*y + g*y**2.
-2*(y + 1)*(y + 2)
Let d = -501 + 360. Let m = d - -141. Factor 44/9*k**3 - 16/9*k**4 + 2/9*k**5 + m + 2*k - 16/3*k**2.
2*k*(k - 3)**2*(k - 1)**2/9
Let m = -1957 + 1973. Suppose -3*l + 2*l - 2 = -4*g, 0 = 3*l - g - m. Determine x, given that -14*x - l - 23/2*x**2 - 1/2*x**4 - 4*x**3 = 0.
-3, -2, -1
Let s = -1139147 - -1139151. Determine c so that 2/5*c**3 - 2/5*c + 1/5*c**2 - 1/5*c**s + 0 = 0.
-1, 0, 1, 2
Let i(r) be the first derivative of r**4/32 - 83*r**3/3 - 1331*r**2/16 - 333*r/4 - 674. Factor i(w).
(w - 666)*(w + 1)**2/8
Let u(i) be the first derivative of -i**8/560 + i**6/40 + i**5/20 - 4*i**3 + 4*i + 182. Let g(b) be the third derivative of u(b). Suppose g(n) = 0. What is n?
-1, 0, 2
Suppose -15714 = 233*i - 17112. Factor 14/3*l**2 + i + 2/3*l**3 + 10*l.
2*(l + 1)*(l + 3)**2/3
Determine z so that -196/5 - 197/5*z - 1/5*z**2 = 0.
-196, -1
Let w be (864/63 + -12)/((-4)/(-14)). Let a(f) be the second derivative of 0*f**2 + 0 - 11/5*f**5 + 8/15*f**w + 34*f - 1/21*f**7 - 3*f**3 + 4*f**4. Factor a(j).
-2*j*(j - 3)**2*(j - 1)**2
Let z(s) = 32*s**2 + 11*s**3 - 14*s + 27*s**2 + 19 - s**3 - 46*s**2. Let y(h) = 9*h**3 + 12*h**2 - 15*h + 18. Let j(w) = 7*y(w) - 6*z(w). Solve j(f) = 0.
-4, 1
Suppose 112 - 27 = 89*z - 93. Factor -8/7*t + 60/7 - 4/7*t**z.
-4*(t - 3)*(t + 5)/7
Let j be (-27)/(12555/(-248))*3/2. Let f = -52/85 + 24/17. Determine p, given that 0*p + f*p**2 - 4/5*p**4 - j*p**5 + 4/5*p**3 + 0 = 0.
-1, 0, 1
Let n(d) be the first derivative of 8*d**2 + 16 + 1/450*d**5 - 1/90*d**4 + 0*d + 1/45*d**3. Let s(i) be the second derivative of n(i). Factor s(u).
2*(u - 1)**2/15
Let t be 15/(-3) - (-5 + (-738)/(-2964)). Let x = 1/988 - t. Suppose x*m**2 - 3/2*m + 9/4 = 0. Calculate m.
3
Let q = 82746371/408288 + -1/136096. Factor -q*b + 8/3 - 3750*b**3 + 3950*b**2.
-2*(b - 1)*(75*b - 2)**2/3
Let r(x) be the first derivative of -3*x**5/50 - 2*x**4/5 - x**3/5 + 18*x**2/5 + 13*x - 83. Let o(c) be the first derivative of r(c). Factor o(w).
-6*(w - 1)*(w + 2)*(w + 3)/5
Factor -88/5*o + 2/15*o**3 - 272/15 - 4*o**2.
2*(o - 34)*(o + 2)**2/15
Let y(d) = -9*d**2 + 111*d + 144. Suppose 28 = -2*o + 38. Let l be 4 - -3*o/15. Let x(r) = 2*r**2 - 22*r - 29. Let i(t) = l*y(t) + 24*x(t). Factor i(n).
3*(n + 1)*(n + 8)
Let a(f) be the first derivative of 3*f**4/4 + 79*f**3 + 231*f**2 + 4307. Solve a(r) = 0.
-77, -2, 0
Suppose 9 = i + 2*i. Let x be 40/12 + (-4)/i. Solve -8*j - 9 - 2 + 15 + 4*j**x = 0 for j.
1
Suppose 8*h - r - 25 = 3*h, -3*r - 23 = -2*h. Factor 2*p**3 + 1122*p + 3*p**3 + 5*p**h - 15*p**2 + 10 - 1127*p.
5*(p - 1)**2*(p + 1)*(p + 2)
Factor -68*o**2 + 8/3*o**3 + 104/3 - 36*o.
4*(o - 26)*(o + 1)*(2*o - 1)/3
Let o(l) = 3*l**2 - 1. Let q(p) = 57*p**2 + 54*p + 117. Let c(d) = 18*o(d) - q(d). Factor c(z).
-3*(z + 3)*(z + 15)
Factor -1796*u + 858*u + 1613*u - 3*u**2.
-3*u*(u - 225)
Let b(h) be the third derivative of h**7/8820 - h**6/2520 - h**4/8 + 2*h**2. Let x(c) be the second derivative of b(c). Factor x(d).
2*d*(d - 1)/7
Let j(y) = 17*y**4 + 154*y**3 + 1193*y**2 + 3092*y + 2640. Let b(w) = 4*w**4 + w**2 + 2*w + 3. Let u(g) = -4*b(g) + j(g). Determine l, given that u(l) = 0.
-146, -3, -2
Let y(k) be the first derivative of 0*k + 18/5*k**5 + 3/2*k**2 - 162 + 39/4*k**4 + 8*k**3. Solve y(w) = 0.
-1, -1/6, 0
Let y(h) be the first derivative of -2*h**5/25 + 259*h**4/10 - 11266*h**3/5 + 16641*h**2/5 - 1913. Suppose y(t) = 0. What is t?
0, 1, 129
Let t be 21 + -24 + (11 - -19)/6. Determine p, given that 0*p - 3/2*p**3 + 3/2*p**t + 0 = 0.
0, 1
Let m(l) be the third derivative of -l**8/5040 + l**7/360 + l**6/90 - l**5/60 - 17*l**3/3 - 122*l**2. Let q(g) be the third derivative of m(g). Solve q(y) = 0.
-1/2, 4
Let l(r) = 26*r - 412. Let u be l(16). Let k be (11 + (-1575)/144)*u. Factor -1/2 - 3/8*g**2 + 1/8*g**4 - k*g**3 + g.
(g - 2)*(g - 1)**2*(g + 2)/8
Let o(f) = -f**3 + 5*f**2 + 29*f - 8. Let x be o(8). Let -40 + 38*l - 36*l + x*l - 12*l**2 + 34*l = 0. Calculate l.
2/3, 5
Solve 53/2*o - 6 + 7*o**4 - 4*o**3 + 3/2*o**5 - 25*o**2 = 0.
-4, -3, 1/3, 1
Let b(j) be the first derivative of 95 + 1/3*j**3 + 0*j + 11*j**2. Factor b(k).
k*(k + 22)
Let p(w) = 8*w**2 + 5*w**3 + 0*w**2 + 8*w - 2 + 4*w**2 - 25*w. Let t(b) = 15*b**3 + 37*b**2 - 52*b - 7. Let s(d) = 7*p(d) - 2*t(d). Solve s(r) = 0 for r.
-3, 0, 1
Factor 1/3*j**2 + 4/3*j - 207.
(j - 23)*(j + 27)/3
Let t(v) = -273*v - 1360. Let m be t(-5). Let a(i) be the first derivative of 15*i - 5/2*i**4 + 1/4*i**m + 115/12*i**3 - 35/2*i**2 - 17. Solve a(h) = 0.
1, 2, 3
Let w = 87 + -66. Suppose -181*v + w*v + 5*v**2 + 551 + 729 + 0*v**2 = 0. Calculate v.
16
Let a(b) be the third derivative of 27*b**8/28 - 9*b**7/2 + 21*b**6/5 + 26*b**5/5 - 12*b**4 + 8*b**3 - 317*b**2. Solve a(q) = 0 for q.
-2/3, 1/4, 2/3, 2
Let i be 12*(200/32 + -6). Find h such that -80 + 35*h**4 + 40*h**2 + 0*h**4 + 480*h**3 - 400*h**i - 80*h + 5*h**5 = 0.
-2, 1
Let k be (-3)/(-4) - 1/((-24)/54). Factor -n**5 - 3*n**5 + 2*n**2 - 2*n**4 + k*n**4 - 6*n**3 + 5*n**5 + 5*n - 3.
(n - 1)**3*(n + 1)*(n + 3)
Let r(a) be the third derivative of a**6/120 + 59*a**5/240 + 47*a**4/48 + 13*a**3/8 - 1511*a**2 - 1. Factor r(m).
(m + 1)*(m + 13)*(4*m + 3)/4
Let w be (-6)/153 + 14/357. Let f(g) be the first derivative of w*g + 0*g**2 + 1/12*g**3 + 1/20*g**5 - 1/8*g**4 - 19. Factor f(z).
z**2*(z - 1)**2/4
Factor -2/11*c**5 - 514/11*c**4 - 5927040/11*c + 0 - 44856/11*c**3 - 127008*c**2.
-2*c*(c + 5)*(c + 84)**3/11
Find v, given that -54040 - 80960 - v**5 - 10138*v**3 - 283500*v - 460*v**4 + 0*v**5 - 4*v**5 - 4267*v**3 - 162450*v**2 = 0.
-30, -1
Let u be ((-97545)/(-4785) - 19) + 26/377. Find c, given that 50/11*c**3 + 60/11*c**2 - 72/11*c + u = 0.
-2, 2/5
Let h(x) be the first derivative of 2*x**3/39 + 17*x**2/13 - 36*x/13 + 248. Factor h(y).
2*(y - 1)*(y + 18)/13
Let g(y) = 6*y + 32. Let f be g(-5). Factor 20*u**2 + u - 16*u**f - 9*u**4 - 3*u + 5*u**4 + 2*u**5.
2*u*(u - 1)**3*(u + 1)
Let y(d) = -d**3 - 28*d**2 - 52*d - 16. Let u be y(-26). Let v be (429/(-102) + 4)*u/28. Find s such that -2/17*s - 6/17*s**2 + 6/17 + v*s**3 = 0.
-1, 1, 3
Find h, given that -9*h**2 + 5/2*h**3 - 8 - 1/4*h**4 + 14*h = 0.
2, 4
Let z(r) be the third derivative of r**7/12600 - 7*r**6/1800 + r**4/12 + 4*r**3/3 - 11*r**2 + 2. Let f(y) be the second derivative of z(y). Factor f(m).
m*(m - 14)/5
Le