9/2 + -1559. Let n(t) = t**3 - 3*t**2 + 3*t. Let m be n(2). Factor 0 - 2*o**4 + 1/2*o**5 + r*o + 3*o**3 - m*o**2.
o*(o - 1)**4/2
Let s(u) be the second derivative of -u**7/420 - u**6/90 + u**5/20 + u**3/6 + 9*u. Let m(k) be the second derivative of s(k). Solve m(a) = 0.
-3, 0, 1
Let d(h) = -h**3 + 7*h**2 - 4*h - 8. Let m be d(6). Factor -6*z**2 + 8*z**3 + 11*z**2 + m*z**5 - 5*z**2 + 12*z**4.
4*z**3*(z + 1)*(z + 2)
Let c(y) = -y**3 - 11*y**2 - 24*y - 429. Let v be c(-12). Factor 3/2*b**v + 5/2*b**2 - 6 - 8*b.
(b - 2)*(b + 3)*(3*b + 2)/2
Suppose 0 = 7*h - 5*h - 10. Solve -10*c**h + 8*c**4 - 14*c**5 - 4*c**2 + 23*c**3 + 6*c**4 - 9*c**3 = 0 for c.
-2/3, 0, 1/4, 1
Let m(n) be the second derivative of -n**4/24 + 7*n**3/12 - 3*n**2/2 - 7*n + 17. Let m(r) = 0. Calculate r.
1, 6
Let t(p) be the second derivative of 0 - 1/6*p**4 + p**3 + 6*p - 2*p**2. Factor t(c).
-2*(c - 2)*(c - 1)
Let n(k) = k + 2. Let u = -27 + 29. Let f be n(u). Find b such that -b + b**f + 23*b**2 - 5*b**3 - 20*b**2 + 2*b**3 = 0.
0, 1
Solve -1 + 7/10*o - 1/10*o**2 = 0.
2, 5
Let u be ((-6)/(-15))/(29/290). Let a(h) be the second derivative of 1/2*h**2 + 0 - 1/4*h**3 + 1/24*h**u - 7*h. Suppose a(s) = 0. What is s?
1, 2
Let s(a) = 6*a + 38. Let k(y) = 2*y. Let t(u) = -6*k(u) + 3*s(u). Let p be t(-19). What is v in 2*v**3 - 1/2*v**4 + v + p - 5/2*v**2 = 0?
0, 1, 2
Suppose 2 + 208 = 39*w + 15. Suppose 2/3*g + 7/3*g**4 - g**w + 0 - g**2 - g**3 = 0. Calculate g.
-2/3, 0, 1
Let s be 80/12*(-32)/(-240). Solve -8/9*w**3 - 2/9*w**2 + 2/9 + s*w = 0 for w.
-1, -1/4, 1
Let c(h) = -2*h**2 - 23*h - 18. Let l be c(-9). Let n be 2*(4 + l/(-7)). Factor 4/7*s - n*s**2 + 6/7.
-2*(s - 3)*(s + 1)/7
Let t be (0 - 0) + (1 - 0). Suppose 5 = 3*u - t. Factor 3*c**5 + u*c**2 - 6*c**4 + 0*c**5 - 3*c**3 + 4*c**2.
3*c**2*(c - 2)*(c - 1)*(c + 1)
Factor 96/5*t - 36/5 - 3*t**2.
-3*(t - 6)*(5*t - 2)/5
Let q(c) = -11*c**4 + 6*c**3 + 9*c**2 - 4*c. Let d(r) = 24*r**4 - 12*r**3 - 19*r**2 + 7*r. Let i(f) = 6*d(f) + 13*q(f). Factor i(s).
s*(s - 1)*(s + 2)*(s + 5)
Let x(p) be the first derivative of 2/35*p**5 - 2/7*p**4 - 4/7*p**2 + 4/7*p**3 - 11 + 2/7*p. Factor x(c).
2*(c - 1)**4/7
Let r(x) be the second derivative of -x**6/20 - 33*x**5/40 - 45*x**4/8 - 81*x**3/4 - 81*x**2/2 - 282*x. Factor r(g).
-3*(g + 2)*(g + 3)**3/2
Let y(s) be the first derivative of 27 - 16*s + 8*s**2 - 2*s**4 - 4/5*s**5 + 4*s**3. Solve y(n) = 0 for n.
-2, 1
Let d = -4457693/270 - -16510. Let w(k) be the third derivative of -d*k**5 + 5/108*k**4 + 0*k + 1/180*k**6 - 4*k**2 + 0 - 1/27*k**3. Solve w(y) = 0.
1/3, 1
Let 3/4*k**3 - 3*k + 6 - 3/2*k**2 = 0. What is k?
-2, 2
Let h(r) = -75*r**2 + 40*r + 5. Let s(f) = -5*f + 1. Let w be s(1). Let n(t) = -19*t**2 + 10*t + 1. Let i(j) = w*h(j) + 15*n(j). Factor i(k).
5*(k - 1)*(3*k + 1)
Find m, given that 5*m**2 + 205 - 1740*m + 20 + 1510*m = 0.
1, 45
Let d(n) be the first derivative of 0*n + 2/33*n**3 + 3 + 3/11*n**2. Suppose d(o) = 0. What is o?
-3, 0
Let z(o) be the second derivative of o**5/15 + o**4/6 + 4*o**2 - 2*o. Let u(r) be the first derivative of z(r). Factor u(k).
4*k*(k + 1)
Let t(j) = -j**4 - 9*j**3 - 30*j**2 - 12*j + 5. Let g(z) = z**4 + 5*z**3 + 16*z**2 + 6*z - 3. Let p(y) = -5*g(y) - 3*t(y). Determine h, given that p(h) = 0.
-1, 0, 3
Let o = -23966/3 - -8002. Solve 200/3 - o*p + 2/3*p**2 = 0.
10
Let g = -45 + 44. Let r(k) = 7*k**5 - 4*k**4 + 7*k**3. Let f(a) = -a**5 + a**4 - a**3. Let d(x) = g*r(x) - 6*f(x). Factor d(l).
-l**3*(l + 1)**2
Let z = 39 - 37. Let -28 - 8*j - 127*j**z - 2*j**4 + 2*j**3 - 20 + 147*j**2 = 0. Calculate j.
-2, 2, 3
Let q(k) be the second derivative of k**5/10 - 2*k**4/3 - 16*k**3/3 + 64*k**2 - 9*k - 1. Determine h, given that q(h) = 0.
-4, 4
Let n(f) be the first derivative of -f**5/20 + f**4/8 + 11*f**3/12 - 3*f**2/2 + 223. Let n(y) = 0. Calculate y.
-3, 0, 1, 4
Let i(m) = -32*m**3 + 280*m**2 - 1656*m + 2250. Let l(z) = -9*z**3 + 80*z**2 - 473*z + 643. Let k(j) = -5*i(j) + 18*l(j). Factor k(u).
-2*(u - 9)**2*(u - 2)
Let t(a) = 21*a**2 + 36*a. Let k(v) = -60*v**2 - 107*v. Let b(x) = -6*k(x) - 17*t(x). Let b(i) = 0. What is i?
-10, 0
Let h = -39 + 42. Let h*z + 993*z**3 + 3*z - 996*z**3 - 3*z**2 = 0. Calculate z.
-2, 0, 1
Suppose -d - 3 = -0. Let t(o) = o**3 + 3*o**2 - o + 2. Let i be t(d). Determine g, given that 4*g**2 - 2*g**5 + 9*g**i - g**5 - 3*g**4 - 5*g**5 = 0.
-1, 0, 2
Let f be (-3 + (-12)/(-8))/((-6)/16). Factor y**4 + 55*y - 2 - 4*y**2 + 5*y**4 + f*y**3 + 2*y**5 - 61*y.
2*(y - 1)*(y + 1)**4
Let o(j) be the first derivative of -j**5/10 + j**4 - 2*j**3 - 63. Factor o(h).
-h**2*(h - 6)*(h - 2)/2
Let v(s) = -8*s**3 + 21*s**2 - 63*s + 57. Let m(h) = -10*h**3 + 22*h**2 - 66*h + 58. Let y(p) = -3*m(p) + 4*v(p). Solve y(u) = 0 for u.
3
Let z = -15 + 39. Determine f so that -24 + 11*f + 25*f - z*f**2 + 12*f - 8 + 4*f**3 = 0.
2
Let g(w) = -16*w**2 + 13*w + 85. Let d(t) = -7*t**2 + 7*t + 42. Let y(q) = 14*d(q) - 6*g(q). Factor y(s).
-2*(s - 13)*(s + 3)
Suppose 5*o = 3*c, -7*o + 8*o = 3*c. Let i = 148/1335 + 2/89. Factor i*l - 2/15*l**2 + o.
-2*l*(l - 1)/15
Suppose 3 - 11 = -x + 4*c, x = 2*c + 4. Factor -2/11*a**3 + 2/11*a**2 + 4/11*a + x.
-2*a*(a - 2)*(a + 1)/11
Solve 2/9*y**4 - 8/3*y**2 - 2/9*y**3 + 0*y + 0 = 0 for y.
-3, 0, 4
Let k(y) be the second derivative of -y**6/75 + 3*y**5/25 + y**4/10 - 4*y**3/3 + 12*y**2/5 + y - 1. Find s, given that k(s) = 0.
-2, 1, 6
Suppose 176/7*g**4 + 65536/7 - 2752/7*g**3 + 18688/7*g**2 - 4/7*g**5 - 8192*g = 0. What is g?
4, 16
Suppose -g = -p - 0*g - 14, -3*g = 4*p + 77. Let u = -14 - p. Factor -75*a**2 + u*a**5 - 20 + 8 - 14*a**4 + 57*a**3 + 29*a - 7*a**4 + 19*a.
3*(a - 2)**2*(a - 1)**3
Suppose 10*m - 32 - 56 = -68. Factor 2/5*g + 0 + 2/3*g**m - 4/15*g**3.
-2*g*(g - 3)*(2*g + 1)/15
Let n(f) be the third derivative of 8/525*f**7 + 0*f - 3/10*f**4 + 23/150*f**6 + 13*f**2 + 0 + 2/5*f**5 + 0*f**3. Let n(v) = 0. Calculate v.
-3, 0, 1/4
Let u(t) be the first derivative of 2*t**3 - 1/2*t**4 + 0*t**2 + 28 - 8*t. Factor u(v).
-2*(v - 2)**2*(v + 1)
Let 23/9*d - 14/9 - 1/3*d**2 = 0. Calculate d.
2/3, 7
Let y be (-2)/(-38) - 10251/(-26163). Determine o so that 20/3*o**2 + 100/3*o**3 + 500/9*o**4 + y*o + 0 = 0.
-1/5, 0
Let c(r) be the second derivative of 0*r**3 - 1/30*r**5 - 1/18*r**4 + 0 - 7*r + 0*r**2. Factor c(f).
-2*f**2*(f + 1)/3
Factor -87 - 116*k + 4*k**2 + 388 + 114 + 67 + 70.
4*(k - 23)*(k - 6)
Let f(d) = 5*d**4 - 3*d**3 + 3*d**2 - d. Let q(w) = 11*w**4 - 6*w**3 + 7*w**2 - 2*w. Let y(z) = -13*f(z) + 6*q(z). Let y(o) = 0. Calculate o.
-1, 0
Let d(n) = 4*n**2 - 2*n - 3. Let m be d(-1). Solve 46*g - g**5 - 6 + 48*g**m + 5 - 16*g**4 + 3*g**5 - 11 - 68*g**2 = 0 for g.
1, 2, 3
Let q(n) = 51*n**2 - 253*n - 8. Let l be q(5). Solve -3/2 - 3/4*h**l + 9/4*h = 0.
1, 2
Suppose -3*p + 1 = -x - 12, 3*p = 2*x + 11. Factor -5*n**5 + 10*n**2 + 15*n - 15*n**4 + p + 20*n**3 - 13*n**3 - 17*n**3.
-5*(n - 1)*(n + 1)**4
Let w = 2309/99 - 205/9. Factor -2/11*g**2 + 0 + w*g**3 - 4/11*g.
2*g*(g - 1)*(3*g + 2)/11
Factor 25/3 - 1/3*g**2 + 8*g.
-(g - 25)*(g + 1)/3
Suppose -60*z + 3 - 3 - 90*z**3 - 67*z**3 - 140*z**2 - 40*z**4 - 5*z**5 + 42*z**3 = 0. What is z?
-3, -2, -1, 0
Suppose -10*r + 22 + 588 = 0. Factor 180 + 408*v - r*v + 257*v + 56*v + 605*v**2.
5*(11*v + 6)**2
Let s be (168/(-8))/21*(1 + (2 - 4)). Factor -1/6*c**2 + 5/6*c + s.
-(c - 6)*(c + 1)/6
Suppose 0 = -2*d + 2 - 8. Let i be d - -1*(-35)/(-5). Let 0*w + 0 - 3/2*w**5 - 9/2*w**i - 3/2*w**2 - 9/2*w**3 = 0. What is w?
-1, 0
Let h(r) be the second derivative of r**6/120 + r**5/100 + 7*r**3/6 - 7*r. Let m(y) be the second derivative of h(y). Solve m(u) = 0 for u.
-2/5, 0
Let o(q) be the third derivative of -q**6/60 + 13*q**5/10 + 10*q**4/3 - 90*q**2. Factor o(i).
-2*i*(i - 40)*(i + 1)
Let r = 45 + -34. Factor -4*t - 6 - 36*t**2 - 76*t + r*t**2 - 9.
-5*(t + 3)*(5*t + 1)
Determine c so that 120 + 45*c**2 - 5*c**3 - 93*c + 11*c + 252*c = 0.
-2, -1, 12
Suppose -5*p = -0 - 20. Suppose -5*r - 4*q + 3*q = 2, 0 = 3*r + 4*q + 8. Determine j so that p*j**4 + 4*j**5 + j**3 - 2*j**5 + r*j**3 + j**3 = 0.
-1, 0
Suppose 0*g = 2*g - 18. Let i be (-65)/(-9) + (-2)/g. Solve -z + z**3 + i*z**4 - z**2 - 6*z**4 + 0*z**4 = 0.
-1, 0, 1
Let b(c) be the first derivative of 0*c**2 + 8*c - 2/3*c**3 - 23. Solve b(g) = 0.
-2, 2
Let v(p