8*n**2 + 15/4*n + 9 = 0. Calculate n.
-2, -1, 1, 12
Let n = 1572062/13 + -120926. Factor 12/13*k**3 + n*k - 2/13*k**4 - 2*k**2 - 8/13.
-2*(k - 2)**2*(k - 1)**2/13
Let u(k) be the second derivative of 6/7*k**2 + 76*k + 0 - 1/28*k**4 - 2/21*k**3 + 1/140*k**5. Solve u(y) = 0 for y.
-2, 2, 3
Let a(b) = b**3 + 12*b**2 + 4. Let p be a(-12). Suppose -2*d + p*u + 23 = -d, 2*u + 79 = 5*d. Factor 3*m - 5*m**2 - 3*m - 2*m + d + 12*m.
-5*(m - 3)*(m + 1)
Let b(a) be the third derivative of -a**8/1008 + a**7/15 - 19*a**6/10 + 30*a**5 - 288*a**4 + 1728*a**3 - 8638*a**2. Factor b(j).
-(j - 12)**2*(j - 6)**3/3
Suppose 4*b + 3 = 3*f, 0 = -7*f + 11*f - 2*b - 14. Suppose -3*p - 4*x = -13, 4*x - 7 = -3*p + 6*x. Factor -7*m + f*m + p*m + 3*m - 4*m**2.
-4*m*(m - 1)
Let w(k) = 25*k**2 - 737*k. Let a(n) = 11*n**2 - 369*n. Let x(m) = 7*a(m) - 3*w(m). Determine i, given that x(i) = 0.
0, 186
Let p(u) be the second derivative of -u**9/3024 + u**8/560 + u**7/840 - u**6/120 - 14*u**3/3 - 20*u + 3. Let v(i) be the second derivative of p(i). Factor v(h).
-h**2*(h - 3)*(h - 1)*(h + 1)
Suppose 33*v + 229 = -167. Let p be 2 + ((-60)/48 - 15/v). Find f, given that 0*f + 5/3*f**p + 5/3*f**3 + 0 = 0.
-1, 0
Let s = 45528 - 45521. Let k(c) be the third derivative of c**3 - 1/120*c**6 + 0 + 13/24*c**4 - 1/210*c**s + 0*c + 7/60*c**5 + c**2. Solve k(m) = 0.
-2, -1, 3
Let h = 6461 - 71067/11. Let f(p) be the first derivative of -4/55*p**5 + 0*p**3 + 12 + 0*p**2 + 0*p - h*p**4 + 1/33*p**6. Determine b, given that f(b) = 0.
-2, 0, 4
Let s(x) = -x**2 + x + 1. Let w(f) = 3*f**3 + 25*f**2 - 7*f - 25. Let g = 64 + 192. Let m be (g/12)/(-4) + 4/3. Let u(v) = m*s(v) - w(v). Factor u(n).
-3*(n - 1)*(n + 1)*(n + 7)
Let c(j) be the third derivative of 103*j**2 - 85/24*j**4 + 10/3*j**3 + 1/3*j**5 + 0*j + 0. Factor c(k).
5*(k - 4)*(4*k - 1)
Let s(g) be the second derivative of 13*g**4/66 + 3755*g**3/33 - 578*g**2/11 - 3922*g. Suppose s(p) = 0. What is p?
-289, 2/13
Factor 14213*i - 157717*i**4 + 95*i - 3892*i**2 + 236*i**3 + 157721*i**4.
4*i*(i - 7)**2*(i + 73)
Suppose -3*t - 3*b + 6 = 0, -t = -3*b + 16 - 26. Solve -7*r**5 - 10*r**4 - 2*r**4 + 13*r**2 - 12*r + 19*r**3 - 4 - 5*r**4 + 8*r**t = 0 for r.
-2, -1, -2/7, 1
Let o(y) be the first derivative of 15/2*y**2 - 24 + 10/3*y**3 + 5/12*y**4 + 31*y. Let v(a) be the first derivative of o(a). Suppose v(t) = 0. Calculate t.
-3, -1
Let o(m) = 2*m**3 - 12*m + 30. Let l be o(14). Factor 20*z - 5350 + l + 3*z**2 - 5*z.
3*z*(z + 5)
Let o be (-8)/(-14)*((-42)/15)/(1176/(-490)). Suppose 0 + o*k**4 - 118/3*k**3 + 600*k + 560*k**2 = 0. What is k?
-1, 0, 30
Let o(n) = n**3 - n - 1. Let h(k) = 42*k**3 + 38*k**2 - 4*k - 10. Let m be ((-300)/(-90))/((-2)/6). Let d(g) = m*o(g) + h(g). Factor d(r).
2*r*(r + 1)*(16*r + 3)
Let d(w) be the first derivative of -800*w**3/27 + 280*w**2/9 - 98*w/9 + 1207. Suppose d(m) = 0. What is m?
7/20
Let i(l) = 2*l - 16. Let o be i(10). Suppose -2*p - 5*k - 19 = 0, o*k + 24 = 4*p - 8. Factor 15*y**2 - 6*y**3 + 12*y + 12*y + 12 + 9*y**p.
3*(y + 1)*(y + 2)**2
Let r(m) = -6*m**2 + 408*m - 6946. Let l(v) be the first derivative of 7*v**3 - 714*v**2 + 24312*v + 137. Let t(n) = 5*l(n) + 18*r(n). Factor t(g).
-3*(g - 34)**2
Suppose -6*y = -2*b + 34, -3*y - 319 + 306 = b. Let a = -4 + 7. Factor 14*q - 14*q + a*q**3 + 9*q**b + 0*q**3.
3*q**2*(q + 3)
Suppose -5000/3 + 3017/3*l**2 + 1/3*l**5 + 550*l - 15*l**4 + 377/3*l**3 = 0. Calculate l.
-4, -2, 1, 25
Factor 101488*y - 812128*y - 5*y**3 + 714420 - 9675065*y**2 + 9671290*y**2.
-5*(y - 1)*(y + 378)**2
Let a(p) be the first derivative of -7*p**3/3 + 3099*p**2/2 + 886*p - 3864. Factor a(w).
-(w - 443)*(7*w + 2)
Let g(x) = x**3 - 5*x**2 - 29*x + 46. Let k be g(8). Let w(n) be the first derivative of -k*n - 13 - n**3 - 9/2*n**2. Solve w(h) = 0 for h.
-2, -1
Let a be -8 + (205 - 8)/1. Let y be a/49 - -7 - 8. Factor -16/7 - 68/7*c**2 - y*c**3 - 64/7*c.
-4*(c + 1)*(c + 2)*(5*c + 2)/7
Suppose 5*t = -4*g - 20, -3*g - 3 = t + 1. Let r be t*5/(-40)*6. What is x in 23*x**3 + 21*x**3 - 10*x**2 - 49*x**r = 0?
-2, 0
Let v(i) be the third derivative of 0*i + i**2 - i**3 + 1/60*i**5 - 10 - 1/24*i**4. Factor v(m).
(m - 3)*(m + 2)
Let z(s) be the second derivative of 18*s + 1/18*s**4 + 22/3*s**2 - 1 - 23/9*s**3. Factor z(f).
2*(f - 22)*(f - 1)/3
Determine r so that 0 + 40/3*r - 13*r**3 + 14/3*r**2 - 14/3*r**4 - 1/3*r**5 = 0.
-10, -4, -1, 0, 1
Suppose -619*y = 191*y - 1620. Find i such that 2/5*i**5 + 0 + 32/15*i**y + 32/15*i**4 + 52/15*i**3 + 2/5*i = 0.
-3, -1, -1/3, 0
Let s(d) be the third derivative of d**5/140 + 23*d**4/8 + 296*d**2 + 1. Factor s(m).
3*m*(m + 161)/7
Factor -4*c**2 - 24*c + 7*c**2 + 7*c**2 - 25 - 9*c**2.
(c - 25)*(c + 1)
Let w(g) = -6*g**3 - 28*g**2 - 2*g + 12. Let m(s) = -5*s**3 - 28*s**2 - 7*s + 12. Let a(c) = -6*m(c) + 7*w(c). Factor a(v).
-4*(v - 1)*(v + 3)*(3*v + 1)
Let a(g) = 6*g**3 - 273*g**2 + 534*g - 255. Let x(l) = 7*l**3 - 273*l**2 + 533*l - 251. Let y(h) = -4*a(h) + 3*x(h). Let y(b) = 0. What is b?
1, 89
Let x(b) be the first derivative of -9 - 8*b + 1/3*b**3 + b**2. Factor x(f).
(f - 2)*(f + 4)
Let x(y) be the first derivative of y**4 - 12*y**3 + 16*y**2 + 2533. Suppose x(b) = 0. What is b?
0, 1, 8
Let n(w) be the second derivative of -w**4/48 - 5*w**3/3 - 39*w**2/8 + 6584*w. Suppose n(h) = 0. Calculate h.
-39, -1
Let k(w) = w**3 - 2*w**2 + 3*w - 2. Let a be k(2). Factor 3*b**2 + 54*b + 30 - a*b**2 - 41*b.
-(b - 15)*(b + 2)
Let x(o) be the first derivative of -5/9*o**3 - 5/36*o**4 - 13 - 5/6*o**2 + 13*o. Let n(i) be the first derivative of x(i). Factor n(c).
-5*(c + 1)**2/3
Let l(o) = 2*o + 17. Let v be l(-9). Let a be 4/((-4)/(-1)) - (-3 - v). Factor 90 - 57*d + d**a - 6*d**3 + 4*d**2 - 48*d + 36*d**2.
-5*(d - 3)**2*(d - 2)
Let p be -5*((-473)/440)/43. Let a(c) be the second derivative of 0*c**2 - 42*c + 0 + p*c**3 - 3/80*c**5 + 0*c**4. Find g such that a(g) = 0.
-1, 0, 1
Suppose 24*h = 20*h + 2*v + 6, -5*v = -4*h + 21. Let b be (4/4 - 1)/(h + -3). Factor b + 2/5*x**2 - 2/5*x.
2*x*(x - 1)/5
Let x(z) = 7*z**3 - 55*z**2 + 116*z - 77. Let j(s) = 2*s**3 - 5*s**2 + s - 1. Let a(h) = -6*j(h) + 2*x(h). Determine r, given that a(r) = 0.
1, 2, 37
Let d(k) = k**3 - k**2 + 2*k + 155. Let y be d(0). Let v = y + -153. Factor 2/3*u - 2/3*u**3 - 2/3 + 2/3*u**v.
-2*(u - 1)**2*(u + 1)/3
Determine k so that 698/11*k + 2/11*k**3 - 700/11*k**2 + 0 = 0.
0, 1, 349
Let w(g) be the third derivative of 0*g - 1/90*g**5 - 1/108*g**4 + 0 + 1/9*g**3 + 1/540*g**6 - 28*g**2. Factor w(j).
2*(j - 3)*(j - 1)*(j + 1)/9
Suppose 0*h = -r - 3*h - 14, -r - 4*h - 17 = 0. Let t = r - -10. Factor 5*x**2 + 4*x + t*x**2 - 5*x**2 - 29*x.
5*x*(x - 5)
Let z = -1/7597 - 7021/4375872. Let w = 583/4032 + z. Find m, given that w*m**2 - 1/7 + 0*m = 0.
-1, 1
Suppose -m - 2 = 1. Let w(f) = -10*f + 8 + 5*f**2 + 12*f - f. Let u(d) = 2*d**2 + 3. Let g(z) = m*w(z) + 8*u(z). Factor g(p).
p*(p - 3)
Let m(r) be the third derivative of r**7/1050 - 37*r**6/600 + 137*r**5/300 - 167*r**4/120 + 11*r**3/5 - 7*r**2 + 19*r - 4. Factor m(w).
(w - 33)*(w - 2)*(w - 1)**2/5
Suppose 66 = 5*b + 4*v, -1679*v = b - 1674*v - 51. Find u, given that 82/3*u**2 + 94/3*u**4 + 0 - b*u**5 - 146/3*u**3 - 4*u = 0.
0, 2/9, 1, 3
Let g(m) be the third derivative of 0*m**4 + 0*m**5 + m + 0*m**3 - 1/10*m**6 - 2/35*m**7 + 0 + m**2 - 1/112*m**8. Solve g(b) = 0 for b.
-2, 0
Let g(h) be the first derivative of -11*h**3/9 - 20*h**2/3 + 16*h/3 + 1565. Factor g(c).
-(c + 4)*(11*c - 4)/3
Let h(r) be the third derivative of -298*r**2 + 0 + 33/16*r**4 + 17/2*r**3 + 0*r - 1/40*r**5. Factor h(l).
-3*(l - 34)*(l + 1)/2
Let h(k) = -k**3 + 13*k**2 + 4*k - 52. Let c(l) = 2*l**3 - 28*l**2 - 7*l + 105. Let v(g) = -4*c(g) - 9*h(g). Determine d so that v(d) = 0.
-3, 4
Let w(q) be the third derivative of 1/8*q**4 - 1/60*q**6 + 2*q**2 - 1/336*q**8 - 54*q + 0 - 7/30*q**5 + 1/42*q**7 + 3/2*q**3. Factor w(b).
-(b - 3)**2*(b - 1)*(b + 1)**2
Let y(o) be the second derivative of 75*o**5/4 + 185*o**4/3 + 355*o**3/6 - 5*o**2 - 2*o - 272. Factor y(z).
5*(z + 1)**2*(75*z - 2)
Let b = 213 - 197. Factor -4*i**2 + b*i + 73 - 73.
-4*i*(i - 4)
Let c(a) be the second derivative of 568/3*a**3 + 9*a - 64*a**2 - 81/5*a**5 + 4 - 204*a**4. Solve c(n) = 0 for n.
-8, 2/9
Let n(z) be the second derivative of z**5/1