te n.
-15, 1
Let z(r) = 65*r**2 - 263*r + 220. Let o(j) = -12*j**2 + 52*j - 44. Let p(x) = 11*o(x) + 2*z(x). Determine y so that p(y) = 0.
1, 22
Let l = 672443/3 + -224147. What is h in -l*h + 0 + 7/3*h**2 = 0?
0, 2/7
Let x(y) = y**2 + y - 1. Let t(h) = 132*h**3 + 142*h**2 + 10*h - 1. Let r(n) = t(n) - x(n). Factor r(l).
3*l*(l + 1)*(44*l + 3)
Let b(s) be the second derivative of s**4/4 + 83*s**3/2 + 2428*s. Factor b(c).
3*c*(c + 83)
Let c be 20/130 + 9200/(-177372)*3. Let x = c + 6832/5685. Suppose 3/5*q - x*q**4 + 0 + 6/5*q**2 - 3/5*q**3 = 0. What is q?
-1, -1/2, 0, 1
Suppose -34*u = 15 + 461. Let a be 2/1*((-924)/u)/11. Find q, given that a*q**2 + 38/9*q**3 + 64/9*q - 64/9 + 4/9*q**4 = 0.
-4, -2, 1/2
Let h(n) be the second derivative of -2 + 8/5*n**4 - 11/10*n**3 - 30*n + 1/70*n**7 + 0*n**2 + 4/25*n**6 - 9/10*n**5. Factor h(z).
3*z*(z - 1)**3*(z + 11)/5
Factor 0 - 54*f - 17480/3*f**3 + 2712*f**2 + 3200*f**4.
2*f*(10*f - 9)**2*(48*f - 1)/3
Let u(g) be the first derivative of -3/28*g**4 + 0*g - 118 - 62/7*g**3 + 0*g**2. Factor u(z).
-3*z**2*(z + 62)/7
Let c be (-20 - 6240/(-375))/((-1)/(10/6)). Suppose 4/5 - c*h + 13/5*h**2 = 0. Calculate h.
2/13, 2
Let w(i) be the third derivative of -i**7/315 - i**6/45 + 16*i**5/45 - 4175*i**2. Factor w(x).
-2*x**2*(x - 4)*(x + 8)/3
Let g(l) be the second derivative of 12167*l**6/45 + 2645*l**5/2 + 1633*l**4/3 + 836*l**3/9 + 8*l**2 + l + 119. Factor g(r).
2*(r + 3)*(23*r + 2)**3/3
Suppose 2*p = -4*n - 2*p - 4, -5*p - 9 = 3*n. Factor 204*d**n - 236 + 121 + 115 - 8*d.
4*d*(51*d - 2)
Let k(r) be the second derivative of 3*r**5/20 - 147*r**3/2 - 1029*r**2 - 20*r + 2. Let k(v) = 0. What is v?
-7, 14
Suppose 8*h + 98 = 314. Factor 24*i**3 + 2*i**2 - h*i**3 + i**2.
-3*i**2*(i - 1)
Let x(d) be the third derivative of d**6/840 + 33*d**5/280 + 4*d**4/7 - 103*d**3/2 - 19*d**2. Let o(s) be the first derivative of x(s). Solve o(k) = 0 for k.
-32, -1
Let v = 2850 - 2847. Let q(h) be the first derivative of 4/5*h**5 + 0*h**2 + 2/3*h**6 + 0*h + 0*h**v + 0*h**4 - 1. Find m such that q(m) = 0.
-1, 0
Let u be (-26)/39 - -3 - (-1 - (-20)/6). Let i be (4 + (-21)/14)*16/10. Factor 2/3*j**i - 2/3*j**2 + u - 4/3*j**3 + 4/3*j.
2*j*(j - 2)*(j - 1)*(j + 1)/3
Determine u so that 89640*u + 5855098880*u**3 - 135/2 - 39680640*u**2 = 0.
3/1328
Suppose -5795*p**2 - 562*p**2 + 6875*p**3 - 625*p**4 + 1159 + 12220*p - 1912 - 1487 - 12843*p**2 = 0. What is p?
2/5, 16/5, 7
Let a(d) = d**3 - 2*d**2 + 2. Let n(q) = -6*q**3 + 9*q**2 - 11. Let y(l) = l**2 + 14*l + 37. Let h be y(-8). Let k(t) = h*a(t) - 2*n(t). Factor k(j).
j**2*(j + 4)
Let i be (-32)/(1024/18768) - 3/2. Let j be -37*2/72 - 735/i. Determine y, given that -2/9*y + j*y**2 + 0 = 0.
0, 1
Let p = 5838 - 5833. Let y(v) be the third derivative of 0*v**3 - 1/72*v**4 + 0 - v**2 - 1/180*v**p + 0*v. Determine z, given that y(z) = 0.
-1, 0
Let q(p) = -2*p**3 + 8*p**2 - 7*p + 3. Let x = -271 + 274. Let u be q(x). Factor 0*s + 2/5*s**3 + 4/5*s**5 - 6/5*s**4 + 0 + u*s**2.
2*s**3*(s - 1)*(2*s - 1)/5
Let o(r) = 7*r**2 + 32*r + 128. Let u be 1/(-1)*(-3 - -5). Let g(y) = -3*y**2 - 16*y - 64. Let l(z) = u*o(z) - 5*g(z). Solve l(f) = 0.
-8
Let s be (-340)/(-22) + (-66)/(-121). Suppose s*r = 48 - 16. What is p in -4/9*p - 4/9 - 1/9*p**r = 0?
-2
Let y = -526 - -12625/24. Let f(p) be the second derivative of -y*p**4 + 11*p + 0 - 1/6*p**3 + 0*p**2. Factor f(a).
-a*(a + 2)/2
Let h(w) = -w**2 - 5190*w + 114666. Let q be h(22). Solve -2 - 1/6*n + 1/6*n**q = 0.
-3, 4
Suppose 0 = -4*t + 4 + 8. Suppose -2*n - 4*f = -2 - 2, 3*f - 9 = -t*n. Factor -8*p**5 - 19*p**3 + 4*p**2 + 4*p**3 + 0*p**n + 20*p**4 - p**3.
-4*p**2*(p - 1)**2*(2*p - 1)
Let g(a) = 15*a**3 - 45*a**2 - 142*a + 8. Let x(h) = -4*h**3 - h**2 + h - 2. Let p(k) = 5*g(k) + 20*x(k). Factor p(r).
-5*r*(r + 3)*(r + 46)
Suppose -24*s - 15913 + 15523 = -154*s. Solve 2/3*r**s - 4/3 - 31/6*r - 14/3*r**2 = 0.
-1/2, 8
Factor 5/2*b**3 + 0 - 30*b**2 - 665/2*b.
5*b*(b - 19)*(b + 7)/2
Suppose 0 = -9*b + 17*b - 24. Factor -4*q**2 + 9387*q - 2025 - 9477*q + b*q**2.
-(q + 45)**2
Let v(t) be the first derivative of -5/22*t**4 - 6/55*t**5 + 4/11*t**2 - 131 - 24/11*t + 10/11*t**3 + 1/33*t**6. Let v(j) = 0. What is j?
-2, -1, 1, 2, 3
Suppose 0 = 5*g + 43 - 168. Let k = 28 - g. Factor z**2 + 2*z**k + 3*z**2 - 3*z - 2*z**2 + z - 2*z**4.
-2*z*(z - 1)**2*(z + 1)
Let h = -791623/49740 - 6/4145. Let x = 97/6 + h. Determine c, given that x*c**2 + c + 1 = 0.
-2
Let w = -210 + 208. Let s(y) = y**3 + y**2 - y. Let j(o) = o**4 + o**3 + 5*o**2 + 11*o - 16. Let f(c) = w*j(c) + 10*s(c). Factor f(a).
-2*(a - 2)**3*(a + 2)
Let k = 271649/9 + -30183. Factor -k*l**2 - 2/3*l + 8/9.
-2*(l - 1)*(l + 4)/9
Let d(v) be the first derivative of 2*v**6/3 - 8*v**5 - 38*v**4 - 64*v**3/3 + 74*v**2 + 104*v - 832. Let d(o) = 0. What is o?
-2, -1, 1, 13
Let r(n) be the first derivative of -3*n**4/4 - n**3 + 48*n**2 + 180*n + 236. Suppose r(q) = 0. What is q?
-5, -2, 6
Let v be ((-15)/(-27)*6 - 64/20)*6. Let y be (-5)/100 - 1/(-4). Solve 2/5*a**3 + y*a**4 - 2/5*a + 3/5 - v*a**2 = 0 for a.
-3, -1, 1
Let p(v) be the second derivative of -67 + 0*v**2 - 13/2*v**3 + 1/4*v**4 - v. Suppose p(d) = 0. What is d?
0, 13
Let v(d) be the first derivative of -2*d**5/15 - d**4/2 + 34*d**3/9 + 13*d**2 + 40*d/3 + 2209. Let v(u) = 0. What is u?
-5, -1, 4
Suppose 4*u - 9 - 1 = -g, 20 = 4*u - 4*g. Determine v, given that -2*v**3 - 3 - 8*v**2 - 3*v**3 - 15*v + 26*v + v**u = 0.
-3, 1/2
Let i(x) be the second derivative of 2*x**7/21 + 2192*x**6/15 + 299206*x**5/5 - 200568*x**4 + 200934*x**3 + 422*x - 6. Factor i(n).
4*n*(n - 1)**2*(n + 549)**2
Let u(l) be the third derivative of -7*l**2 + 1/9*l**4 - 2/3*l**3 - 4 - 1/135*l**5 + 0*l. Factor u(i).
-4*(i - 3)**2/9
Let d(x) = -x**3 + 12*x**2 + 17*x + 27. Let g be d(13). Suppose 157*c**2 + 119*c**3 + 2*c**5 + 5*c**2 + g*c**3 + 38*c**4 = 0. Calculate c.
-9, -1, 0
Let w be (300/(-84) - -5 - 0)/((-4)/(-14)). Let y(c) be the third derivative of 1/6*c**w - 3*c**3 + 0 + 1/4*c**4 + 1/60*c**6 - 53*c**2 + 0*c. Factor y(f).
2*(f - 1)*(f + 3)**2
Let p = 5095932/7 + -727944. Factor -468/7*n - 169/7*n**2 - p.
-(13*n + 18)**2/7
Let w(x) be the first derivative of 5*x**7/84 + x**6/2 + 9*x**5/8 - 38*x - 140. Let i(g) be the first derivative of w(g). Solve i(j) = 0.
-3, 0
Let b(s) be the third derivative of -s**7/42 - 25*s**6/24 + 13*s**5/6 + s**2 - 259*s + 1. Solve b(f) = 0 for f.
-26, 0, 1
Factor 24800*k**2 + 410*k**3 + 5/3*k**4 + 0 - 153760/3*k.
5*k*(k - 2)*(k + 124)**2/3
Let h = 717645/263197 - -15/23927. Factor 58/11*z - 4/11*z**2 + h.
-2*(z - 15)*(2*z + 1)/11
Let l(q) be the first derivative of 10*q + 15/4*q**4 + 50/3*q**3 + 45/2*q**2 + 65. Factor l(h).
5*(h + 1)*(h + 2)*(3*h + 1)
Let b = 1319390/247389 - -6/82463. Suppose 3*w = 12, 0*l = -4*l + w + 4. Find c such that 185/6*c**3 - b*c**4 - 21/2*c**5 + 4/3 + 38/3*c + 37*c**l = 0.
-1, -2/7, -2/9, 2
Let q(f) = -4*f**3 - 4*f**2 + 8*f + 24. Let g(d) = 33*d**3 + 31*d**2 - 64*d - 192. Let z(s) = 2*g(s) + 17*q(s). Factor z(b).
-2*(b - 2)*(b + 2)*(b + 3)
Suppose -21 + 45 = 6*g. Solve -g*v**2 - 4*v - 2*v**2 + 7*v**2 + 4*v**2 - 11*v - 90 = 0 for v.
-3, 6
Let a(t) = 4*t**3 - 1250*t**2 + 96090*t + 197200. Let o(j) = 16*j**3 - 5001*j**2 + 384363*j + 788804. Let z(b) = 9*a(b) - 2*o(b). Factor z(k).
4*(k - 157)**2*(k + 2)
Factor 42*g**2 + 508/3*g + 16/3.
2*(g + 4)*(63*g + 2)/3
Let m(p) be the first derivative of p**3/6 - 113*p**2/4 - 57*p - 2348. Factor m(u).
(u - 114)*(u + 1)/2
Let b(s) = s**5 - 3*s**4 - 30*s**3 + 112*s**2 - 96*s - 9. Let h(o) = -32*o**3 + 112*o**2 - 96*o - 12. Let m(y) = 4*b(y) - 3*h(y). Let m(j) = 0. Calculate j.
-3, 0, 2
Let j(p) be the third derivative of 3*p**2 + 1/240*p**6 - 10*p - 1/48*p**4 + 0 - 7/600*p**5 + 1/2100*p**7 + 1/10*p**3. Determine l so that j(l) = 0.
-6, -1, 1
Let v(x) be the second derivative of -3*x**5/4 + 83*x**3/6 - 45*x**2 + 2*x + 50. Let o(z) = -3*z**3 + 17*z - 18. Let t(k) = 11*o(k) - 2*v(k). Factor t(u).
-3*(u - 2)*(u - 1)*(u + 3)
Solve -33*v**3 + 2957*v**4 - 447*v**2 - 2906*v**4 - 17*v**2 - 43*v**2 + 3*v**5 + 0*v**5 - 408 + 894*v = 0 for v.
-17, -4, 1, 2
Suppose -906*s = 6*s. Factor -8/5*o**3 + s + 0*o**2 + 0*o - 2/15*o**4.
-2*o**3*(o + 12)/15
Let l(w) be the first derivative of -w**7/210 + w**5/10 + w**4/3 + 