 6*k**2.
3*(k + 1)**2
Let p(h) = -h**3 - 13*h**2 + 11*h - 6. Let j(s) = -s**3 - s**2 - s. Let l(c) = c**2 + 15*c - 28. Let r be l(-17). Let g(w) = r*j(w) - 2*p(w). Factor g(o).
-4*(o - 3)*(o - 1)**2
Let p be (-171)/(-630) + 1 + 8/(-14). Let t = p + 1/20. Factor -1/4*j + 1/2 - t*j**2 + 1/4*j**3 + 1/4*j**4.
(j - 1)**2*(j + 1)*(j + 2)/4
Suppose 0 = 15*t - 10*t - 20. Let p(u) be the first derivative of 9/5*u + 7/15*u**3 + 1/20*u**t + 1 + 3/2*u**2. Let p(c) = 0. What is c?
-3, -1
Let f(j) be the third derivative of -j**8/8400 + j**7/4200 + 31*j**3/6 - 16*j**2. Let a(q) be the first derivative of f(q). Factor a(d).
-d**3*(d - 1)/5
Let w(x) be the second derivative of x**5/70 - 2*x**4/7 - 13*x**3/21 - 182*x - 2. Find i, given that w(i) = 0.
-1, 0, 13
Suppose 0 = -5*f - 5*f - 2180. Let j = 879/4 + f. Factor 3/4*p**2 + 1/2 + j*p.
(p + 2)*(3*p + 1)/4
Let q(w) = w**2 + 51*w + 11. Let a(o) = o**2 + 26*o + 6. Let j(i) = -11*a(i) + 6*q(i). What is p in j(p) = 0?
0, 4
Let k(z) = -z**2 - z + 1. Let u(p) = -2*p**4 + 30*p**3 - 151*p**2 + 249*p + 1. Let r(a) = -2*k(a) + 2*u(a). Solve r(c) = 0.
0, 5
Let s = 969 - 966. Let u(p) be the first derivative of -8 - 1/16*p**4 - 1/4*p**2 + 0*p + 1/4*p**s. Factor u(f).
-f*(f - 2)*(f - 1)/4
Let f(m) be the third derivative of 0 + 0*m + 3*m**2 - 1/420*m**6 + 1/84*m**4 + 1/21*m**3 - 1/210*m**5. Factor f(h).
-2*(h - 1)*(h + 1)**2/7
Suppose -z = 0, 4*r + 5*z - 12 = -140. Let k = -24 - r. Suppose -1 + 17*j**3 - 1/2*j + k*j**2 + 7/2*j**5 + 13*j**4 = 0. What is j?
-1, 2/7
Let r(a) be the first derivative of -a**3/3 - 18*a**2 + 325. Factor r(j).
-j*(j + 36)
Let h be (9/6 + (-2)/1)*-10. Solve h*i**2 - 76*i**4 + 3*i**5 - 3*i + 70*i**4 + i**2 = 0 for i.
-1, 0, 1
Factor -27*v - 1/6*v**2 - 161/6.
-(v + 1)*(v + 161)/6
Let z be 16 - 2 - (8 + -10). Let m be z/(-6) + -4 + 1 + 6. Solve 0 - 2/3*g - m*g**2 = 0.
-2, 0
Let h be 117/52*(-5)/(1*-300). Let d(w) be the second derivative of 0*w**2 + 1/120*w**6 + 7*w - h*w**5 + 0*w**4 + 1/6*w**3 + 0. Find f, given that d(f) = 0.
-1, 0, 2
Let m(b) be the first derivative of 9/2*b + 21/4*b**3 + 3/20*b**5 + 27/16*b**4 - 14 + 57/8*b**2. Determine q, given that m(q) = 0.
-6, -1
Let t = 269 + -263. Let l(u) be the first derivative of -1/3*u**3 + 0*u - 1 - 1/6*u**t + 1/4*u**4 + 0*u**2 + 1/5*u**5. Solve l(o) = 0 for o.
-1, 0, 1
Let 2542 + 216*m - 121 + 495 + 4*m**2 = 0. Calculate m.
-27
Let p(v) be the second derivative of -v**7/560 - 7*v**6/240 - 3*v**5/16 - 9*v**4/16 - 47*v**3/6 + 21*v. Let u(y) be the second derivative of p(y). Factor u(g).
-3*(g + 1)*(g + 3)**2/2
Let l(a) be the first derivative of 2*a**6/3 - 8*a**4 + 8*a**3 + 14*a**2 - 24*a - 6. What is h in l(h) = 0?
-3, -1, 1, 2
Let p(q) be the first derivative of -4*q**3/15 - 148*q**2/5 - 5476*q/5 + 50. Factor p(i).
-4*(i + 37)**2/5
What is l in -13/3*l - 8/3*l**2 - 2 - 1/3*l**3 = 0?
-6, -1
Let d(w) = 15*w**2 - 5*w - 25. Let r(k) = 7*k**2 - 3*k - 12. Let g(c) = 2*d(c) - 5*r(c). Find j, given that g(j) = 0.
-1, 2
Suppose -f - 17 = -4*o, 19 = -4*o - 143*f + 140*f. Factor -14/5*i**3 + 24*i + 24/5*i**o + 32/5.
-2*(i - 4)*(i + 2)*(7*i + 2)/5
Factor 3*m**3 - 9*m**2 + 8*m**2 + 55*m**2 - 6*m**3 - 15*m - 36*m.
-3*m*(m - 17)*(m - 1)
Let p = -5 + 7. Let h be 7/p + 3/(-2). Factor 2 + 2 + 2*i + 2*i + h*i**2 - 2.
2*(i + 1)**2
Let d(q) be the second derivative of -q**6/20 + 81*q**5/80 + q**4 - 27*q**3/8 - 21*q**2/4 - 2*q. Suppose d(a) = 0. What is a?
-1, -1/2, 1, 14
Let k(j) be the second derivative of -8/3*j**3 - 1/84*j**7 - 22*j + 0 + 2*j**2 + 11/6*j**4 + 17/120*j**6 - 7/10*j**5. Suppose k(o) = 0. Calculate o.
1/2, 2
Let b(v) be the third derivative of -v**7/1365 - v**6/130 - 2*v**5/65 - 2*v**4/39 - 75*v**2. Factor b(l).
-2*l*(l + 2)**3/13
Factor 10*f**3 + 93*f**2 - 29*f**3 + 42*f - 13*f**2 + f**4 + 58*f.
f*(f - 10)**2*(f + 1)
Let f(v) be the second derivative of -v**4/27 - 8*v**3/3 - 72*v**2 + 5*v. Factor f(g).
-4*(g + 18)**2/9
Let p be 7089/(-556) - (-2 - 11). Let m(w) be the first derivative of -1/12*w**3 - p*w - 1/4*w**2 - 13. Factor m(n).
-(n + 1)**2/4
Let l(a) be the third derivative of -a**8/1344 + a**6/60 - a**4/6 + a**2 + 67. Factor l(h).
-h*(h - 2)**2*(h + 2)**2/4
Let 361 + 4*y**4 - 361 - 50*y**3 - 38*y**3 = 0. Calculate y.
0, 22
Factor 24/5*y + 0 + 4/5*y**3 + 28/5*y**2.
4*y*(y + 1)*(y + 6)/5
Let h = 8 - 37/5. Suppose -25 = 23*r - 19*r - 9*r. Factor -h*v**2 - 3/5*v**r - 9/5*v**4 + 0*v + 0 - 9/5*v**3.
-3*v**2*(v + 1)**3/5
Let y(x) be the second derivative of -31*x + 0*x**2 + 0 - 1/51*x**4 - 1/255*x**6 + 3/170*x**5 + 0*x**3. Suppose y(z) = 0. Calculate z.
0, 1, 2
Let o be (4/32*3)/(75/10). Let t(p) be the first derivative of -1/16*p**4 - o*p**5 + 1/12*p**3 + 0*p + 7 + 1/8*p**2. Factor t(l).
-l*(l - 1)*(l + 1)**2/4
Suppose 5*h - 11 + 11 = 0. Let g(c) be the third derivative of -2*c**2 + 0*c**4 + 1/240*c**5 + 0 + h*c - 1/480*c**6 + 0*c**3. Factor g(l).
-l**2*(l - 1)/4
Let v(t) = 2*t**4 + 8*t**3 - 30*t**2 - 66*t - 18. Let i(s) = 5*s**4 + 25*s**3 - 90*s**2 - 199*s - 51. Let n(f) = 2*i(f) - 7*v(f). Solve n(y) = 0 for y.
-2, -1/2, 3
Let v(y) be the second derivative of y**5/60 - y**3/2 + 9*y + 2. Determine n so that v(n) = 0.
-3, 0, 3
Suppose -6*d + 82 = -38. Suppose 4*j + 6*j = d. Find k, given that 1/3*k**4 - 4/3*k**3 - 2/3*k**j + 3 + 4*k = 0.
-1, 3
Let d(k) be the second derivative of 0 + 12*k + 0*k**2 + 0*k**3 + 1/72*k**4 + 1/90*k**6 + 1/40*k**5. Factor d(b).
b**2*(b + 1)*(2*b + 1)/6
Let f(w) be the first derivative of -w**5/10 + 11*w**4/8 - 6*w**3 + 4*w**2 + 32*w - 131. Solve f(q) = 0.
-1, 4
Suppose 8*q + 1 = -9*q + 35. Solve -2/3*c + 4/3 - 2/3*c**q = 0 for c.
-2, 1
Let u be ((-74)/5)/(-1) + 1300/(-130). Find q such that 3/5*q**2 + u + 18/5*q = 0.
-4, -2
Let m(x) = 2*x**3 + 8*x**2 - 13*x - 55. Let a be m(-3). Factor -1/4*i**a + 0*i + 1/4*i**3 + 0.
i**2*(i - 1)/4
Let t(a) = 5*a**4 + 33*a**3 - 17*a**2 - 117*a - 74. Let f(q) = 135*q**4 + 890*q**3 - 460*q**2 - 3160*q - 2000. Let p(c) = 2*f(c) - 55*t(c). Factor p(d).
-5*(d - 2)*(d + 1)**2*(d + 7)
Let w(q) = 16*q**4 + 16*q**3 + 8*q**2 - 40*q. Let y(o) = -o**4 + o**3 - o**2 + o. Let f(v) = w(v) + 12*y(v). Let f(m) = 0. Calculate m.
-7, -1, 0, 1
Let z(t) = -10*t - 7. Let w be z(-1). Suppose 4 = -3*v - h, 3 + 5 = -w*v - 2*h. Factor -2/3*u**2 + 1/3*u**5 + v*u + 2/3*u**4 + 0 - 1/3*u**3.
u**2*(u - 1)*(u + 1)*(u + 2)/3
Let t(f) be the second derivative of -2*f**6/15 + 4*f**4/3 - f + 59. Determine h, given that t(h) = 0.
-2, 0, 2
Suppose 14*d - 104 = -34. Let c(p) be the second derivative of 23/60*p**d + 0 + 5/9*p**4 + 0*p**2 + 7/90*p**6 + 6*p + 2/9*p**3. Factor c(z).
z*(z + 1)*(z + 2)*(7*z + 2)/3
Let m(f) = 8*f**2 + 7*f + 8. Let a(g) = g**2 + g + 1. Let k = 1 - 3. Let w(o) = k*m(o) + 18*a(o). Suppose w(z) = 0. What is z?
-1
Let f be 3/(-3)*(0 + -2). Let w = 0 + f. Find o, given that 0*o**w + 0*o - 6*o**2 + 3*o**2 - 3*o = 0.
-1, 0
Let u be 1*(2 - -9) + -9. Factor 0 - 8/13*t**3 + 2/13*t - 6/13*t**u.
-2*t*(t + 1)*(4*t - 1)/13
Let m(r) be the third derivative of -r**8/336 + 3*r**7/14 - 109*r**6/40 - 3961*r**5/60 - 403*r**4 - 1014*r**3 + r**2 - 26*r. Suppose m(d) = 0. What is d?
-3, -1, 26
Determine t so that -26*t - 28*t**2 - 14*t - 8*t**3 + 4*t**4 + 24*t**3 = 0.
-5, -1, 0, 2
Let f(b) be the third derivative of b**7/6300 - b**6/225 + 4*b**5/75 + b**4 - 10*b**2. Let h(y) be the second derivative of f(y). Factor h(z).
2*(z - 4)**2/5
Let f be (9 - (-27)/(-3))*-1. What is b in -6/5*b + f + 3*b**2 = 0?
0, 2/5
Let d = 351/34 - 2355/238. Find h such that 2/7*h**2 + 1/7*h**4 + 0 + d*h**3 + 0*h = 0.
-2, -1, 0
Let i(a) be the third derivative of 1/8*a**6 + 0 + 0*a + a**3 + 7/8*a**4 + 1/70*a**7 - 24*a**2 + 9/20*a**5. Factor i(r).
3*(r + 1)**3*(r + 2)
Let g(r) = 2*r**2 - 25*r - 23. Let y be g(13). Let s be (8/y)/(32/(-80)). Factor 0*o - 1/3*o**s + 1/3.
-(o - 1)*(o + 1)/3
Suppose 2*x + 15 = 7*x. Determine y, given that -13*y**2 + 3*y**x + 8*y - 23*y**3 + y**2 = 0.
-1, 0, 2/5
Let l(k) = k**3 - 1. Let y(u) = -15*u + 15. Suppose 9*n + 1 = 8*n. Let x(v) = n*y(v) - 5*l(v). What is g in x(g) = 0?
-2, 1
Let b be 2*(6 + 30/(-6)). Determine u, given that -b*u**5 - 4*u**4 + u**5 + 4*u**3 - u**5 + 2*u**3 = 0.
-3, 0, 1
Let n(m) = 4*m**5 + 5*m**4 + 12*m**3 - 5*m**2 - 16*m - 6. Let p(j) = j**5 - j**4 - j**2 - j. Let h(a) = 5*n(a) - 15*p(a). Fact