*2 + 70*p**2 - 254*p**3 + 51*p**4 - 436*p**3 + 94*p**4 = 0.
0, 6, 23
Let j(c) be the third derivative of c**7/735 - 13*c**6/420 + 23*c**5/210 - 11*c**4/84 - 3*c**2 + 204. Factor j(r).
2*r*(r - 11)*(r - 1)**2/7
Suppose 18*z = 35*z - 13*z - 28, -g + 2*z - 12 = 0. What is x in -3/2*x**g + 3 + 3/2*x = 0?
-1, 2
Suppose -173*a + 686*a = -239*a + 3008. Determine k, given that -48*k - 72 + 10*k**a + 142/3*k**3 + 62*k**2 + 2/3*k**5 = 0.
-6, -3, -1, 1
Find s, given that 1188 - 801*s - 81/4*s**3 + 195*s**2 + 3/4*s**4 = 0.
4, 6, 11
Let b(y) = 15*y**2 - 177*y - 182. Let d(c) = -335*c**2 + 3895*c + 4005. Let k(j) = -45*b(j) - 2*d(j). Determine h, given that k(h) = 0.
-1, 36
Let w(v) = 2*v**2 + 12*v + 3. Let q be w(-6). Let f be 20/q + 1/3. Let f + 180*h**4 - 4 + 420*h**2 + 2 + 144*h + 11 + 472*h**3 = 0. Calculate h.
-1, -2/5, -2/9
Let y(w) = 5*w + 15. Let v be y(0). Let i be (-2)/((-4)/(-6))*(-15)/v. Solve -i*a - 10*a**3 - 11*a + 0*a**4 + 4 + 15*a**2 + 2*a**4 + 3*a**2 = 0.
1, 2
Let p(l) be the first derivative of l**4/16 + 215*l**3/6 + 11663*l**2/2 + 22898*l - 142. Factor p(h).
(h + 2)*(h + 214)**2/4
Factor 61*p**3 + 5*p**4 + 144*p**3 - 38200 + 204*p**3 + 1081*p**3 + 150700 - 223500*p + 109505*p**2.
5*(p - 1)**2*(p + 150)**2
Let w be (945/(-36))/(2/(-144)). Factor -1905 + 5*y + 0*y + 10*y**2 + w.
5*(y - 1)*(2*y + 3)
Factor 1/11*v**3 + 51/11*v - 54/11 - 14/11*v**2.
(v - 9)*(v - 3)*(v - 2)/11
Let j(l) = -13*l**2 + 6*l + 7. Let t be j(-1). Let s = t - -16. Determine d so that 1/9*d**s - 1/9*d + 1/9*d**3 + 0 - 1/9*d**2 = 0.
-1, 0, 1
Find h such that -86/9*h**2 + 178/9*h - 10 - 2/9*h**3 = 0.
-45, 1
Let x be 4/8 - (9 - (-102)/(-12)). Let z(p) be the first derivative of 3/10*p**4 + x*p**2 + 7 - 4/15*p**3 - 1/15*p**6 + 0*p + 0*p**5. Factor z(o).
-2*o**2*(o - 1)**2*(o + 2)/5
Let q(b) be the first derivative of 32/7*b - 2/21*b**3 + 0*b**2 - 1. Suppose q(a) = 0. Calculate a.
-4, 4
Factor 1861706/3*h + 36500/3*h**3 + 2/3*h**5 + 984676/3*h**2 + 913066/3 + 466/3*h**4.
2*(h + 1)**2*(h + 77)**3/3
Let k be (4 - 190/55)*206/309. Determine w so that 0 + 0*w**2 - 2/11*w**5 - 2/11*w**3 + k*w**4 + 0*w = 0.
0, 1
Let a = 440 - 448. Let w(q) = -4*q - 32. Let t be w(a). Factor t + 3/8*m**3 - 3/8*m**2 + 0*m.
3*m**2*(m - 1)/8
Let y(t) be the first derivative of -t**5/18 - 8*t**4/27 - 4*t**3/27 - 87*t**2/2 - 82. Let c(p) be the second derivative of y(p). Let c(z) = 0. Calculate z.
-2, -2/15
Suppose -18*h = -24*h + 2124. Factor 122*n + 120*n + 122*n + 8*n**2 - h*n + 4 + 2*n**3.
2*(n + 1)**2*(n + 2)
Suppose 4*z - 857*i + 859*i = 14, -i + 7 = -2*z. Let l(g) be the second derivative of g**2 + 0*g**3 + z - 1/6*g**4 - 11*g. Factor l(b).
-2*(b - 1)*(b + 1)
Let w(s) = -2*s**2 - 17*s + 49. Let l(v) = -2*v**2 - 18*v + 48. Let q(b) = 5*l(b) - 6*w(b). Factor q(n).
2*(n - 3)*(n + 9)
Let z = -339 + 341. Let f(r) be the third derivative of 1/180*r**6 + 4/9*r**3 + 2/9*r**4 + 6*r**z + 0*r + 1/18*r**5 + 0. Factor f(o).
2*(o + 1)*(o + 2)**2/3
Suppose 0 = -4*i - 2*x + 325 + 567, 5*i - 1115 = 5*x. Suppose 211*g**4 - 446*g**4 + i*g**4 - 24*g + 8*g**2 + 64*g**3 - 40*g**5 + 4 = 0. What is g?
-1, 1/5, 1/2, 1
Let g(j) = -j**3 + j + 7878 - 7878. Let y(l) = -7*l**3 - 5*l**2 - l - 3. Let u(b) = 6*g(b) - y(b). What is x in u(x) = 0?
-3, -1
Suppose 448 = 8*d - 32. Let a be -7*d/(-42)*18/10. Let -21/2*p**4 - 6 + 33/2*p**2 - 18*p + a*p**3 = 0. What is p?
-1, -2/7, 1, 2
Let y(w) = 32*w**4 + 16*w**3 + 46*w**2 - 52*w - 13. Let t(v) = -15*v**4 - 9*v**3 - 24*v**2 + 24*v + 6. Let a(h) = -13*t(h) - 6*y(h). Solve a(u) = 0.
-4, -3, 0
Suppose 0 = 24*w - 243 - 453. Solve 8 + 217*q**2 - 106 - q - 219*q**2 + w*q = 0 for q.
7
Let n(j) be the first derivative of 0*j - 1/3600*j**6 + 4/3*j**3 + 0*j**2 + 1/60*j**4 - 18 + 0*j**5. Let l(p) be the third derivative of n(p). Factor l(a).
-(a - 2)*(a + 2)/10
Suppose -47*h + 73 - 355 = 0. Let t(j) = 5*j**2 + 43*j - 28. Let y(d) = -d**2 + 2*d + 1. Let k(v) = h*y(v) - 2*t(v). Determine x, given that k(x) = 0.
-25, 1/2
Let q(x) be the first derivative of 27 - 2/9*x**3 + 2*x - 7/270*x**5 - 23/108*x**4 - 2*x**2. Let w(d) be the second derivative of q(d). Factor w(c).
-2*(c + 3)*(7*c + 2)/9
Suppose 5*z + 42380 = 5*w, -4*w - 5*z = -3*z - 33934. Factor 8472*f**3 - w*f**3 - 3*f**4 + 0*f**4.
-3*f**3*(f + 3)
Let x = -12373/1380 + 149/15. Let w = x - 5/23. Factor w*y + 3/4*y**2 - 3/4*y**4 - 3/4*y**3 + 0.
-3*y*(y - 1)*(y + 1)**2/4
Let r be ((-107)/(-7704))/(6/96). What is b in 0 + 2/9*b + 2/9*b**2 - r*b**4 - 2/9*b**3 = 0?
-1, 0, 1
Suppose -39*g + 163*g = -225*g + 698. Factor 4/5 + 2/5*s**g - 6/5*s.
2*(s - 2)*(s - 1)/5
Let o = -254544/7 - -36364. Let 24/7 - 20/7*g - o*g**2 = 0. Calculate g.
-6, 1
Factor -1/12*h**3 - 55/12*h + 29/12*h**2 + 9/4.
-(h - 27)*(h - 1)**2/12
Let x(p) be the third derivative of -p**7/42 + 13*p**6/12 - 9*p**5 - 675*p**4/4 - 1125*p**3/2 + p**2 - 594. Factor x(y).
-5*(y - 15)**2*(y + 1)*(y + 3)
Let b(c) = c**4 - c**3 - 744*c + 1 + 744*c + c**2. Let d(r) = 6*r**4 - 3*r**3 - 6*r**2 + 6*r + 3. Let o(v) = 3*b(v) - d(v). Determine h, given that o(h) = 0.
-2, 0, 1
Let m be -15*6/243*-6. Let t be (-2)/((-6)/(-9)*81/(-108)). Factor -16/3*h**t + 4/3*h - 8/3*h**3 - m*h**5 + 0 + 16/9*h**2.
-4*h*(h + 1)**3*(5*h - 3)/9
Solve 1165*m + 603*m - 194*m**3 - 600*m - 90*m**3 + 216*m**2 - 102*m**4 - 2*m**5 + 768 = 0.
-48, -2, -1, 2
Let k(t) = t**3. Let p(q) = 4*q**4 - 37*q**3 + 12*q**2 + 14*q. Suppose -60 = 17*a + 178. Let w(z) = a*k(z) - 2*p(z). Factor w(c).
-4*c*(c - 7)*(c - 1)*(2*c + 1)
Let b(g) be the second derivative of 5*g**4/12 + 505*g**3/6 + 495*g**2 + 2*g - 1261. Factor b(f).
5*(f + 2)*(f + 99)
Let w be ((6 - 9) + 4)*(4 - 0). Suppose -13*q**4 + 216 + 5*q**w - 9*q**3 + 276*q + 126*q**2 - 576*q + 5*q**4 = 0. What is q?
-9, 2
Suppose -2 - 34 = -12*s. Factor s*t - 3*t + 24*t**2 + 5*t**4 - 29*t**2.
5*t**2*(t - 1)*(t + 1)
Let r(n) = -n**3 + 11*n**2 + 4*n - 6. Let g be r(11). Let w be (-6)/(-10) - g/190. Factor -w*f**3 + 2/5*f + 6/5 - 6/5*f**2.
-2*(f - 1)*(f + 1)*(f + 3)/5
Let w be (142/42 - 3)/(18/27). Let g = 583 - 4077/7. Factor -g*u**3 + 0*u**2 + w*u + 0.
-4*u*(u - 1)*(u + 1)/7
Suppose 82*l = 307*l - 900. Let v(o) be the second derivative of 28*o + 1/48*o**l + 0*o**2 + 0*o**3 + 0 + 0*o**5 - 1/120*o**6. Factor v(d).
-d**2*(d - 1)*(d + 1)/4
Let d(q) = -q**2 - 24*q - 118. Let t be d(-5). Let u be (t - -25)*70304/28. Factor -4/7*j**4 + 208/7*j**3 + u*j - 4056/7*j**2 - 114244/7.
-4*(j - 13)**4/7
Let r(c) be the second derivative of -c**5 + 2695*c**4/12 + 3395*c**3/6 + 340*c**2 - c - 1094. Suppose r(w) = 0. Calculate w.
-1, -1/4, 136
Suppose 44*v + 82 - 12*v - 131 + 4*v**2 + 35 + 62 = 0. What is v?
-6, -2
Determine c, given that 490*c - 487*c + 19*c**2 - 26 + 41*c**2 - 3*c**3 - 10 - 24 = 0.
-1, 1, 20
Let -153*x**2 - 675 - 1206*x - 25654*x**3 - 25651*x**3 + 381*x + 51302*x**3 = 0. Calculate x.
-45, -5, -1
Let w(p) = 8*p**4 + 32*p**3 - 10*p**2 - 5*p + 10. Let d(g) = -g**4 - g**3 + 2*g**2 + g - 2. Let x(u) = 5*d(u) + w(u). Factor x(v).
3*v**3*(v + 9)
Let u = -5348 + 37490/7. Let m(a) be the second derivative of 4/3*a**4 + 78/5*a**6 + 0*a**3 - 22*a + 0 - 8*a**5 + 0*a**2 - u*a**7. Let m(l) = 0. What is l?
0, 2/9, 1
Let t(w) be the second derivative of w**5/20 - w**4/12 - 5*w**3/6 - 3*w**2/2 - 741*w. Suppose t(g) = 0. Calculate g.
-1, 3
Let u(v) be the first derivative of 3*v**5/5 + 3*v**4 + 5*v**3 + 3*v**2 + 919. Solve u(n) = 0.
-2, -1, 0
Suppose -630 = -238*n + 168 - 84. Let j(r) be the third derivative of 0*r**n + 0*r**5 - 1/6*r**4 - 26*r**2 + 0*r - 1/210*r**7 + 0 + 1/40*r**6. Factor j(w).
-w*(w - 2)**2*(w + 1)
Solve 3*u**5 + 5355*u**2 - 25*u**4 + 25*u**3 - 2*u**5 - 5330*u**2 - 30*u + 4*u**5 = 0 for u.
-1, 0, 1, 2, 3
Let l(a) = a**3 + 4*a**2 - 8*a - 20. Let t be l(-4). Let -21*p**2 + 25*p**3 + t + 8*p - 31*p**3 - 20*p = 0. What is p?
-2, 1/2
Determine o so that -15*o**4 + 223/3*o**3 + 8/3 - 350/3*o**2 + 164/3*o = 0.
-2/45, 1, 2
Let t(q) = 2*q**2 - 38*q - 71. Let x be t(21). Suppose -43*j + 142 - x = 0. Find b, given that 48/13*b**j + 0 + 8/13*b**2 - 98/13*b**5 + 42/13*b**4 + 0*b = 0.
-2/7, 0, 1
Factor 144*s**2 + 270 + 411*s - 377*s**3 - 373*s**3 - 379*s**3 + 1132*s**3.
3*(s + 1)*(s + 2)*(s + 45)
Let c be (1809/(-135) + 13)*-2. Let w = 50 + -48. Factor 4/5*y + c + 1/5*y**w.
(y + 2)**2/5
Let x(g) be the 