be the third derivative of h**6/120 - h**5/15 + h**4/12 - 5*h**3/6 - 5*h**2. Let v be g(4). Factor 6*j**5 - 6*j**4 - 2*j**3 + 0*j**v + 3*j**4 - j**4.
2*j**3*(j - 1)*(3*j + 1)
Factor -1/3*x**4 - 2/3*x**3 + 2/3*x + 0 + 1/3*x**2.
-x*(x - 1)*(x + 1)*(x + 2)/3
Let x(q) = q**4 + q**3 - 2*q**2. Let l(f) = 62*f**4 + 94*f**3 - 344*f**2 - 188*f - 24. Let u(c) = l(c) + 2*x(c). Factor u(d).
4*(d - 2)*(d + 3)*(4*d + 1)**2
Suppose -11*l - 6*l + 151 = 117. Determine y so that 8*y**3 - 4 + 3/2*y**4 + 15/2*y**l - 3*y = 0.
-4, -1, 2/3
Let u(p) be the first derivative of 15*p**3 + 185*p**2/2 + 20*p + 119. Factor u(y).
5*(y + 4)*(9*y + 1)
Suppose s + 11*s = 48. Let o(x) be the second derivative of -1/20*x**s + 1/100*x**5 + 1/15*x**3 + 0 + 3*x + 0*x**2. Suppose o(y) = 0. Calculate y.
0, 1, 2
Let a(l) be the third derivative of 0 - 4/105*l**5 + 16*l**2 - 2/21*l**3 - 1/140*l**6 - 1/12*l**4 + 0*l. Let a(k) = 0. What is k?
-1, -2/3
Let w(m) be the first derivative of -3*m**5 + 10*m**4 - 10*m**3 + 5*m - 137. Factor w(i).
-5*(i - 1)**3*(3*i + 1)
Let h(k) be the first derivative of 3/10*k**4 + 7/5*k**2 + 4/5*k + 16/15*k**3 - 3. Determine g so that h(g) = 0.
-1, -2/3
Let l(h) be the first derivative of 2*h**5/5 - 20*h**4 + 800*h**3/3 - 92. Suppose l(t) = 0. Calculate t.
0, 20
Suppose 36 + 456 = 123*k. Let v = -82 - -331/4. Factor 0*u**2 + 3/2*u**3 - 3/4*u + 0 - v*u**5 + 0*u**k.
-3*u*(u - 1)**2*(u + 1)**2/4
Let x(p) = -3*p**3 + 9*p**2 - 12*p + 9. Let u = -4 + 2. Let g(n) = 3*n**3 - 18*n + 4*n + 27*n - 8 - 10*n**2. Let w(b) = u*x(b) - 3*g(b). Factor w(v).
-3*(v - 2)*(v - 1)**2
Let t(f) be the first derivative of f**4/2 - 2*f**3 + 2*f**2 + 87. Let t(m) = 0. Calculate m.
0, 1, 2
Let p(y) be the second derivative of 5/12*y**4 + 45/2*y**2 + 0 - 39*y + 5*y**3. Find z such that p(z) = 0.
-3
Let b(w) be the first derivative of -w**7/280 - w**6/32 - 7*w**5/80 - 3*w**4/32 - 4*w**2 - 18. Let c(v) be the second derivative of b(v). Factor c(m).
-3*m*(m + 1)**2*(m + 3)/4
Let w be 459/15 - (36/(-15) - -3). Solve -4*h**2 - 28*h + 50*h - w*h + 4*h**3 = 0 for h.
-1, 0, 2
Let c = 359 - 1076/3. Let x(d) be the second derivative of -3/5*d**5 - 6*d - 4*d**2 + 2/15*d**6 + 0 + 2*d**3 + c*d**4. Factor x(h).
4*(h - 2)*(h - 1)**2*(h + 1)
Let j = 4357/5 - 870. Factor 0*w - 4/5*w**5 + j*w**4 + 0*w**2 + 2/5*w**3 + 0.
-w**3*(w - 2)*(4*w + 1)/5
Let h(j) be the third derivative of -1/40*j**6 - 1/8*j**4 + 0 - 3*j**2 + 0*j + 1/10*j**5 + 0*j**3. Suppose h(f) = 0. What is f?
0, 1
Let g(t) = -5*t**2 + 19*t + 14. Let z(p) = -27*p**2 + 96*p + 69. Let o(i) = 21*g(i) - 4*z(i). Find n such that o(n) = 0.
-3, -2
Let d(v) = v**4 - 3*v**3 - 7*v - 3. Let g(r) = -r**4 + r**3 + 2*r**2 + r + 1. Let t(m) = 2*d(m) + 6*g(m). Factor t(c).
-4*c*(c - 1)**2*(c + 2)
Let b(z) be the third derivative of -z**5/60 - z**4/12 + 145*z**2. Factor b(n).
-n*(n + 2)
Let c(z) be the third derivative of -6859*z**6/360 - 361*z**5/30 - 19*z**4/6 - 4*z**3/9 - 12*z**2. Factor c(f).
-(19*f + 2)**3/3
What is v in -6*v**3 - 103 - 62 - 171*v**2 + 333*v + 9*v**3 = 0?
1, 55
Factor 933*b + 4256 + 5*b**3 - 13*b - 3356 + 245*b**2.
5*(b + 2)**2*(b + 45)
Factor 13 - 2*i + 11 + 18*i + 6*i**2 - 4*i**2.
2*(i + 2)*(i + 6)
Let v(k) be the second derivative of -k**7/3360 + k**6/480 - k**5/240 + k**3/2 - 11*k. Let s(r) be the second derivative of v(r). Factor s(m).
-m*(m - 2)*(m - 1)/4
Suppose 5*g - 3 = 32. Factor 3 + g + 160*h**2 + 64*h**3 - 5 + 7 - 92*h.
4*(h + 3)*(4*h - 1)**2
Let m(v) = 7*v**3 - 74*v**2 + 576*v - 860. Let a(u) = -u**3 - u**2 - 1. Let h(r) = 4*a(r) + m(r). What is w in h(w) = 0?
2, 12
Let n = 162 + -158. Let w(f) be the second derivative of 9/20*f**5 + 1/2*f**3 + 1/10*f**6 + 0*f**2 + 9*f + 3/4*f**n + 0. Factor w(l).
3*l*(l + 1)**3
Let z be 391/(-345) - (-2)/15. Let g be 2*(z + 8/4). What is a in -5/4*a**3 + 1/4*a**4 + 3/2*a**g - 2 + a = 0?
-1, 2
Factor 0 - 5*x**3 - 20/3*x + 10*x**2 + 5/6*x**4.
5*x*(x - 2)**3/6
Suppose 31 = -9*p - 32. Let o(g) = -2*g**3 - 2*g + 2. Let k(i) = -i**4 - 6*i**3 - 7*i + 7. Let u(n) = p*o(n) + 2*k(n). Suppose u(x) = 0. Calculate x.
0, 1
Let x(g) be the first derivative of 7*g**3/12 + 12*g**2 - 7*g + 60. Factor x(i).
(i + 14)*(7*i - 2)/4
Let h(v) = -7*v - 1. Let s(a) = -a - 1. Let w(f) = h(f) - 4*s(f). Let m be w(0). Factor 0 - 1/7*t**m + 1/7*t**2 + 0*t.
-t**2*(t - 1)/7
Find m such that -46*m**4 + 12*m**2 + 21*m**4 + 10*m - 2*m**5 - 8*m**3 + 13*m**4 = 0.
-5, -1, 0, 1
Suppose -l = 4*p - 10, 0 = -l + 8*p - 11*p + 8. Let x(s) be the first derivative of -s**4 + 7 + 16/3*s**3 + 8*s - 10*s**l. Factor x(v).
-4*(v - 2)*(v - 1)**2
What is h in -1/4*h**2 - 1/4 - 1/8*h**5 + 1/2*h**4 + 5/8*h - 1/2*h**3 = 0?
-1, 1, 2
Let r be (5/(-30))/(3/(-6)). Let k = 1 + r. Factor 0 + k*j**3 - 2/3*j**4 - 2/3*j**2 + 0*j.
-2*j**2*(j - 1)**2/3
Suppose -23 + 35 = 6*t. Find v such that 10*v**3 + 216*v + 15*v**t + 0 - 211*v + 0 = 0.
-1, -1/2, 0
Suppose 0*a - 9 = -2*b + a, -b - 6 = 3*a. Let f(z) be the second derivative of -1/135*z**6 + 1/54*z**4 + 0 - 1/27*z**b + 0*z**2 + 1/90*z**5 + 4*z. Factor f(d).
-2*d*(d - 1)**2*(d + 1)/9
Let o = 1980 + -7919/4. Let l(b) be the first derivative of -3/4*b - 1/16*b**4 + 1/8*b**2 + o*b**3 - 15. Determine u, given that l(u) = 0.
-1, 1, 3
Let t(q) be the third derivative of q**7/1785 + q**6/510 - q**5/170 + 22*q**2 - 2. Factor t(y).
2*y**2*(y - 1)*(y + 3)/17
Factor 0*q - 2/21*q**5 - 2/7*q**4 + 0*q**2 + 8/21*q**3 + 0.
-2*q**3*(q - 1)*(q + 4)/21
Let k(q) be the second derivative of q**5/4 + 5*q**4/12 - 5*q**3 + 40*q + 1. Factor k(l).
5*l*(l - 2)*(l + 3)
Let i(g) be the first derivative of -1/4*g**4 + 5*g**3 + 14 - 75/2*g**2 + 125*g. Determine k, given that i(k) = 0.
5
Let i(d) be the first derivative of -d**3/4 - 9*d**2/4 + 111. Suppose i(t) = 0. Calculate t.
-6, 0
Let n be (-13)/(-13) - (-18)/(-72). Factor 3/4*f**2 + n*f + 0.
3*f*(f + 1)/4
Determine s so that 3*s - 3/4*s**4 - 3*s**3 + 0 + 3/4*s**2 = 0.
-4, -1, 0, 1
Let s(d) = d**2 - 7*d + 10. Let u be s(6). Let y(k) be the second derivative of -1/24*k**u + 1/2*k**2 + 0 + k + 1/12*k**3. Find p, given that y(p) = 0.
-1, 2
Suppose 2*h + 1 = -5*y + 24, -3*h + y = -9. Let i = -11222 - -11222. Factor i*b + 0 + 1/5*b**h - 1/5*b**2 + 1/5*b**3 - 1/5*b**5.
-b**2*(b - 1)**2*(b + 1)/5
Let w(o) be the second derivative of o**8/1680 - o**6/360 - o**3/2 + 7*o. Let z(s) be the second derivative of w(s). Factor z(h).
h**2*(h - 1)*(h + 1)
Suppose -2*o + 125 = 3*o + 5*w, 0 = -4*o - 3*w + 95. Determine y, given that o*y**5 + y - 5*y + 24*y**2 + 16*y**5 - 24*y**4 - 32*y**3 = 0.
-1, 0, 1/3, 1
Let n(g) be the second derivative of 1/15*g**3 + 0 + 10*g + 0*g**2 - 1/30*g**4. Factor n(f).
-2*f*(f - 1)/5
Let z(b) = -6*b**3 - 222*b**2 + 220*b + 406. Let p(h) = 2*h**3 + 73*h**2 - 73*h - 135. Let v(x) = 20*p(x) + 6*z(x). Let v(i) = 0. What is i?
-33, -1, 2
Factor 60*j**2 + 800/3 + 5/3*j**3 - 260*j.
5*(j - 2)**2*(j + 40)/3
Let y(k) be the second derivative of k**4/6 - 88*k**3/3 + 1936*k**2 + 4*k + 7. Solve y(o) = 0 for o.
44
Let h = 113 + -121. Let g(q) = -4*q**3 - 4*q**2 + 9*q + 4. Let f(a) = -6*a**3 - 6*a**2 + 14*a + 6. Let z(i) = h*g(i) + 5*f(i). Find r such that z(r) = 0.
-1, 1
Let t(u) be the third derivative of -u**7/210 - u**6/40 + u**5/60 + u**4/8 + 6*u**2 - 14*u. Factor t(w).
-w*(w - 1)*(w + 1)*(w + 3)
Let v(q) be the third derivative of -9/4*q**4 + 81/2*q**3 + 0 + 0*q + 1/20*q**5 + 31*q**2. Factor v(d).
3*(d - 9)**2
Let g(m) be the third derivative of m**10/30240 + m**9/15120 - m**8/3360 + 3*m**4/8 - 10*m**2. Let x(t) be the second derivative of g(t). What is i in x(i) = 0?
-2, 0, 1
Let u(k) be the third derivative of k**6/1200 - k**5/150 - k**4/240 + k**3/15 + k**2 + 46*k. Factor u(x).
(x - 4)*(x - 1)*(x + 1)/10
Let w be (-154)/(-110) - (-3)/(-5). Let 2*l + 2/5*l**3 + w + 8/5*l**2 = 0. What is l?
-2, -1
Let m(o) be the second derivative of 1/60*o**5 - 21*o + 2 + 0*o**4 + 1/3*o**2 - 1/6*o**3. Solve m(z) = 0 for z.
-2, 1
Let y(z) be the second derivative of 11*z + 1/5*z**3 - 1/50*z**5 - 2/5*z**2 + 0*z**4 + 0. Factor y(o).
-2*(o - 1)**2*(o + 2)/5
Let v = 1478 - 1476. What is l in -4/7*l - 6/7*l**4 + 0 - 16/7*l**3 - 2*l**v = 0?
-1, -2/3, 0
Let z(q) be the second derivative of q**8/26880 + q**7/10080 - q**6/1440 - 7*q**4/12 + 8*q. Let j(d) be the third derivative of z(d). Solve j(x) = 0 for 