 12. Let w(c) = -4*c**3 + c**2 - 4. Let g(r) = -3*v(r) - 8*w(r). Let n be g(-2). Factor -2*j + 0*j**2 + 2*j**n + j**2 - 4*j**2.
-j*(j + 2)
Let q(s) be the first derivative of -7*s**6/270 + 4*s**5/45 + 2*s**4/27 - 23*s**2/2 + s - 15. Let x(m) be the second derivative of q(m). Factor x(t).
-4*t*(t - 2)*(7*t + 2)/9
What is f in 11/3*f**3 - 292/3*f**2 + 2015/3*f - 338 = 0?
6/11, 13
Let i(d) = 5*d**2 + 108*d - 60. Let p(q) = -2*q**2 - 38*q + 20. Let l(s) = 4*i(s) + 11*p(s). Factor l(t).
-2*(t - 5)*(t - 2)
Let m(f) be the second derivative of -f**5/10 + f**4/3 + 29*f**3/3 - 30*f**2 - 343*f. What is t in m(t) = 0?
-5, 1, 6
Suppose 5*v = 5*w - 185, -3*w = -9*v + 10*v - 95. Suppose 0 = w*z + 37*z. Determine x, given that z - 16/5*x**2 - 2/5*x - 32/5*x**3 = 0.
-1/4, 0
What is n in 5*n**4 - 94*n**2 + 15*n**3 - 450 - 20*n**2 + 4*n**2 + 24*n**2 - 435*n - 9*n**2 = 0?
-3, -2, 5
Let r(x) be the second derivative of -14/3*x**7 + 0 - 11680/3*x**3 - 488*x**5 + 1600*x**2 + 11408/3*x**4 + 76*x - 1708/15*x**6. Solve r(b) = 0.
-10, 2/7, 2
Let p(k) be the third derivative of -2*k**7/735 - 307*k**6/420 + 31*k**5/42 + 11*k**4/6 + 29*k**2 - 4*k + 15. Let p(o) = 0. What is o?
-154, -1/2, 0, 1
Solve -209*g + 210 - 130*g - 8*g + 5*g**4 - 4*g - 184*g - 125*g**3 + 445*g**2 = 0.
1, 2, 21
Factor -1/2*a**4 + 5*a + a**3 + 13/2*a**2 + 0.
-a*(a - 5)*(a + 1)*(a + 2)/2
Suppose 20*d - 4*o = 17*d - 14, 2*d - 5*o = 0. Let g be (-7)/(d + -4)*(-20)/(-5). What is z in 1/7*z**g + 100/7 - 20/7*z = 0?
10
Let z(q) be the first derivative of 3/4*q**3 + 15/8*q**2 - 1/8*q**6 + 85 - 3/4*q**4 - 27/40*q**5 + 9/8*q. Suppose z(d) = 0. Calculate d.
-3, -1, -1/2, 1
Let d = -45 + 51. Suppose i - r - 14 = 0, -r = i - d + 2. Find b, given that -8 + 32*b - i*b**2 - 3*b**2 - 2*b**2 = 0.
2/7, 2
Suppose 23 - 35 = -4*w. Let i(u) be the first derivative of -24/5*u**2 - 8/5*u**3 - 1/5*u**4 - 32/5*u + w. Let i(q) = 0. Calculate q.
-2
Suppose 8*h - 255 = -5*s + 3*h, -s + 5*h + 63 = 0. Suppose 0 = -3*o + 2*z + 3*z + s, -57 = -3*o + 3*z. Find r, given that 4*r**2 + 7 + 14 - o = 0.
0
Let n be (-3)/(51/(-35)) - -1 - 0. Let x = -53/34 + n. Factor 0*g - 3/2*g**3 - x*g**4 + 0 + 3*g**2.
-3*g**2*(g - 1)*(g + 2)/2
Let c(j) be the second derivative of -j**7/1680 + j**6/40 + 3*j**4 + 9*j - 1. Let h(k) be the third derivative of c(k). Factor h(f).
-3*f*(f - 12)/2
Suppose -2*d - 1 = 5*t, 5*t + 3*d - 61 = -70. What is v in -3/11*v**4 - v**t + 16/11 + 36/11*v + 12/11*v**2 = 0?
-4, -1, -2/3, 2
Let u(s) be the third derivative of 15*s**8/448 + 39*s**7/56 + 395*s**6/96 + 275*s**5/48 - 55*s**4/24 - 20*s**3/3 + 519*s**2 + 5. Let u(z) = 0. What is z?
-8, -4, -1, -1/3, 1/3
Suppose 3 = 5*k - 17. Suppose -4*b + k = 4*o, b = 2*b - 5*o - 13. Factor 18/5*m + 4/5 - 224/5*m**b - 48/5*m**2.
-2*(4*m + 1)**2*(7*m - 2)/5
Let g = -748855/3 - -249619. Solve g*p**2 + 172/3*p + 3698/3 = 0 for p.
-43
Suppose 4*h + 24*h - 15*h = 52. Let 22*i**2 - h*i**3 - 41/4*i + 5/4 = 0. What is i?
1/4, 5
Let j be 190/8 - (-9)/(-12). Suppose 15 - j = -4*a. Let h(t) = 24*t**2 - 98*t + 128. Let s(o) = o**3 - o. Let v(p) = a*s(p) - h(p). What is r in v(r) = 0?
4
Factor -32*n**2 + 1254*n - 1251 - 40*n**2 - 38*n**2 + 158*n**2 - 51*n**2.
-3*(n - 417)*(n - 1)
Let i(h) be the second derivative of h**7/63 + h**6/9 - 7*h**5/30 - 41*h**4/18 - 10*h**3/3 + 137*h + 2. Let i(d) = 0. Calculate d.
-5, -2, -1, 0, 3
Solve 5/2*k - 1/6*k**3 - 1/3*k**2 + 0 = 0.
-5, 0, 3
Let c = -121130 - -121133. What is l in -1/5*l - 1/10*l**2 + 0 + 1/10*l**4 + 1/5*l**c = 0?
-2, -1, 0, 1
Let n = 108/155 + 127/930. Let c(d) be the second derivative of 0 - 21*d + 0*d**2 + n*d**3 + 1/12*d**4. Factor c(w).
w*(w + 5)
Let g = -200458 + 200460. Factor 2/7*q**g - 68/7 + 66/7*q.
2*(q - 1)*(q + 34)/7
Suppose -7*t - 196 = 3*f - 326, -2*f = -t - 47. Factor f*q**2 - 83/3*q + 2/3.
(q - 1)*(81*q - 2)/3
Let v(f) = -4*f**2 - 171*f. Let j(c) = 17*c**2 + 681*c. Let x(u) = -9*j(u) - 39*v(u). Factor x(q).
3*q*(q + 180)
Let h(o) be the second derivative of 3*o**7/28 - 11*o**6/10 + 51*o**5/40 + 41*o**4/4 + 10*o**3 - o + 328. Suppose h(v) = 0. Calculate v.
-1, -2/3, 0, 4, 5
Let k(v) be the second derivative of -v**5/4 - 605*v**4/12 + 5*v**3/6 + 605*v**2/2 - 1954*v. Find g, given that k(g) = 0.
-121, -1, 1
Let v(i) = 5*i**4 + 10*i**3 + 25*i**2 - 162*i + 167. Let f(y) = 3*y**4 + 5*y**3 + 13*y**2 - 81*y + 80. Let w(a) = -14*f(a) + 8*v(a). Let w(x) = 0. Calculate x.
-4, 3
Let z(h) = 8*h**2 - 2213*h + 156773. Let g(j) = -2*j**2 + 554*j - 39194. Let l(x) = -18*g(x) - 4*z(x). Factor l(p).
4*(p - 140)**2
Suppose 5*j - 4*y = -29, 5*y - 1077 = -j - 1019. Factor -12 - j*a + 15/2*a**2 - 3/2*a**3.
-3*(a - 4)*(a - 2)*(a + 1)/2
Let o be 5 + (-3)/(5 - 1510/305). Let z be ((-16)/12)/(-3 - o/21). Find w, given that -1226/7*w**2 - 8/7 - 126*w**z - 184/7*w - 276*w**3 = 0.
-1, -2/21
Solve -61/2*b**2 - 1800 - 1/4*b**3 - 960*b = 0 for b.
-60, -2
Let d = 8155/43536 + 1/5442. Let v(l) be the first derivative of 1/16*l**6 + 3/16*l**2 - 3/8*l - 3/40*l**5 + 1/4*l**3 - d*l**4 - 11. Factor v(m).
3*(m - 1)**3*(m + 1)**2/8
Let f(y) = -4*y**2 + 49*y - 8. Let w be f(12). Find k, given that -k**5 + 10*k**4 + 29*k**4 - 35*k**4 + 8 - k**3 + w*k - 10*k**2 = 0.
-1, 2
Suppose 5*c = 2*a + 46718 - 46742, 216 = 18*a. Factor 2/11*f**2 + c - 14/11*f.
2*f*(f - 7)/11
Let j(u) be the third derivative of -u**8/20160 - u**7/60 - 49*u**6/20 - 4*u**5/15 - 10*u**2 + 4. Let i(d) be the third derivative of j(d). Factor i(p).
-(p + 42)**2
Let s(p) be the third derivative of 0*p + 1/120*p**5 + 182*p**2 + 0 + 0*p**3 - 1/720*p**6 + 5/72*p**4. Find m such that s(m) = 0.
-2, 0, 5
Let l be ((-72)/(-18))/(2 - 0*13/(-182)). Factor -32/9 + 32/9*v + 2/9*v**l - 2/9*v**3.
-2*(v - 4)*(v - 1)*(v + 4)/9
Let v(u) be the first derivative of 2*u**5/95 - 2*u**4/19 + 2*u**3/19 - 1536. What is c in v(c) = 0?
0, 1, 3
Let h(p) be the first derivative of -p**6/660 + p**5/165 - p**4/132 - 13*p**2/2 + 41. Let j(r) be the second derivative of h(r). Factor j(x).
-2*x*(x - 1)**2/11
Let a be 3 + (266 - 7) + -6. Suppose -4*z**2 + 7*z - 2*z + z - a + 58*z = 0. What is z?
8
Factor -2 - 61345*o**4 + 2 + 61461*o**4 - 4*o**5 - 780*o**3 - 900*o**2.
-4*o**2*(o - 15)**2*(o + 1)
Let c be ((-125)/(-10) - 14)/(-60). Let x(p) be the third derivative of -c*p**5 + 0*p**3 - 1/8*p**4 + 0 + 1/140*p**7 + 1/40*p**6 + 0*p - 19*p**2. Factor x(u).
3*u*(u - 1)*(u + 1)*(u + 2)/2
Let z(p) be the second derivative of 95*p**4/4 + 101*p**3/2 + 9*p**2 - 3990*p. Determine l so that z(l) = 0.
-1, -6/95
Let j(c) be the second derivative of -11*c**5/10 + 2311*c**4/3 - 161980*c**3 + 88200*c**2 + 7672*c. Factor j(k).
-2*(k - 210)**2*(11*k - 2)
Let b = 64 - 68. Let m be 5 + 4 + b + -2. Find k such that -30*k**3 - 9*k**2 + 11*k**m + 36*k + 4*k**3 - 12 = 0.
-2, 2/5, 1
Suppose 2/3*a**2 + 68450/3 - 740/3*a = 0. What is a?
185
Let y(t) be the third derivative of t**6/24 + 107*t**5/12 + 14575*t**4/24 + 14045*t**3/6 - 698*t**2. Solve y(r) = 0 for r.
-53, -1
Factor -2*p - 8/3 + 2/3*p**2.
2*(p - 4)*(p + 1)/3
Let z be 72 - (-126)/(-6) - 9. Suppose z*p - 1/2*p**2 - 882 = 0. Calculate p.
42
Let v(u) be the third derivative of u**6/60 + u**5/60 + u**4/24 + 8*u**2 + 1. Let q(t) = 3*t**3 + 114*t**2 - 601*t. Let i(l) = q(l) - 4*v(l). Factor i(g).
-5*g*(g - 11)**2
Let a be (-2150)/13640 - 4/(-22). Let b = a - -107/62. Solve -g**3 + b*g + 5/4*g**2 - 1/2 = 0 for g.
-1, 1/4, 2
Suppose 0 = -5*f + 3*j + 113, -2*f + 104 = 2*f + j. Suppose -3*k - 2*k = f, -2*h + 3*k = -21. Factor 3*r**2 - 12 + 16*r**2 - 34*r**2 + 3*r**h + 24*r.
3*(r - 2)**2*(r - 1)
Factor -4/3*s**2 + 0 + s**4 + 0*s**3 + 0*s - 1/3*s**5.
-s**2*(s - 2)**2*(s + 1)/3
Factor 0 + 48/7*q**2 + 0*q - 22/7*q**3 + 2/7*q**4.
2*q**2*(q - 8)*(q - 3)/7
Let d(g) = g**3 - 7*g**2 - 8*g + 4. Let u be d(8). Suppose 0 = u*s + a - 0*a - 13134, 2*s + 3*a - 6572 = 0. Factor 3283*p + 3*p**2 - s*p.
3*p**2
Let k(o) be the first derivative of -5*o**4/4 - 245*o**3/3 - 350*o**2 - 460*o - 303. Factor k(s).
-5*(s + 1)*(s + 2)*(s + 46)
Let g = -371200 + 371206. What is s in 0 + 9/5*s**3 - 24/5*s + 12/5*s**4 - g*s**2 - 3/5*s**5 = 0?
-1, 0, 2, 4
Let x(d) be the second derivative of 32*d**6/105 - 58*d**5/7 + 887*d**4/14 - 90*d**3/7 - 243*d**2/7 + 472*d. Determine u, given that x(u) = 0.
-1/4, 3/8, 9
Let v(o) = 2*o**4 - 74*o**3 - 149*o**2