**5/80 - 11*v**4/96 - v**3/6 + 102*v**2. Factor p(r).
(r - 4)*(r + 1)**3/4
Suppose 2*j + y + 54 = 51, 15 = -5*y. Find c such that -1/4*c**4 - 1/2*c**3 + j*c**2 + 1/4 + 1/2*c = 0.
-1, 1
Let q(z) = -14*z - 10. Let u be q(-1). Let m(o) be the first derivative of 1 - 1/2*o**6 - 3/2*o**u + 3*o + 9/2*o**2 - 9/5*o**5 + 2*o**3. Factor m(y).
-3*(y - 1)*(y + 1)**4
Let m(c) be the second derivative of -1/2*c**3 + 37*c + 1/16*c**4 + 0 - 15/8*c**2. Factor m(o).
3*(o - 5)*(o + 1)/4
Let s = 65 + -63. Suppose -l = 3*l - 4, 0 = 4*b - 2*l + s. Factor -4/7*r + b + 6/7*r**2 - 2/7*r**3.
-2*r*(r - 2)*(r - 1)/7
Let y(f) be the first derivative of -5 + 1/120*f**6 + 0*f**2 + 2/3*f**3 + 1/4*f**4 + 0*f - 3/40*f**5. Let u(j) be the third derivative of y(j). Factor u(x).
3*(x - 2)*(x - 1)
Let y(d) be the third derivative of d**8/1512 + d**7/945 - d**6/270 - d**5/135 + d**4/108 + d**3/27 + 61*d**2. Factor y(u).
2*(u - 1)**2*(u + 1)**3/9
Let d(s) be the first derivative of s**6/1260 + s**5/70 + 3*s**4/28 - 8*s**3/3 - 5. Let z(o) be the third derivative of d(o). Factor z(g).
2*(g + 3)**2/7
Let i be 15*2/12*72/480. Determine u, given that 9/8*u**3 + 0 + i*u**4 + 3/4*u**2 + 0*u = 0.
-2, -1, 0
Suppose -5*k - 60 = 5*v, -k - 5*v - 9 - 15 = 0. Let d = -6 - k. Let -n**2 - 4*n**3 + 2*n**d - 2*n**3 + 2*n + 3*n**3 = 0. What is n?
-2, 0, 1
Let h(l) = -26*l**3 + 423*l**2 + 144*l - 285. Let a(z) = -4*z**3 + z**2 - 1. Let g(m) = -5*a(m) + h(m). Factor g(y).
-2*(y - 70)*(y + 1)*(3*y - 2)
Let 2821*l - 6220*l - 15821*l + 12871*l**2 + 16682*l**2 - 9713*l**2 - 625*l**3 + 5*l**4 = 0. What is l?
0, 1, 62
Let w(l) be the second derivative of l**6/720 - l**5/180 + 19*l**2/2 + 8*l. Let x(u) be the first derivative of w(u). Factor x(r).
r**2*(r - 2)/6
Let g(y) = 7*y**2 - 15*y - 22. Let w(k) = -49*k**2 - 405*k + 239*k**2 - 419 - 176. Let b(j) = 55*g(j) - 2*w(j). Factor b(z).
5*(z - 4)*(z + 1)
Let i = 0 + -2. Let c be 0 - (1 + -1 + i). Factor c*d**2 - 5 - 6 - 3*d**3 + 3*d + 10 - 1.
-(d - 1)*(d + 1)*(3*d - 2)
Let p(n) be the second derivative of -n**5/420 - n**4/56 + 2*n**3/21 + 21*n**2 + 13*n + 3. Let w(g) be the first derivative of p(g). Factor w(q).
-(q - 1)*(q + 4)/7
Suppose 6 = 10*v + 6. Let u(b) be the second derivative of 0*b**3 - 1/170*b**5 - 7*b + 1/51*b**4 + 0 + v*b**2. Determine h, given that u(h) = 0.
0, 2
Let n be 39/6 + ((-15)/6)/(-5). Solve 8 + g**5 + n - 15 - g**4 = 0.
0, 1
Let w(n) be the second derivative of -n**7/504 - n**6/144 - 7*n**4/4 - 4*n. Let x(q) be the third derivative of w(q). Factor x(s).
-5*s*(s + 1)
Let d be ((-2)/10*-3)/((-3512)/(-4390)). Factor 3/4*h**3 + d*h**2 + 0*h + 0.
3*h**2*(h + 1)/4
Let a be (5 + -1 + -3)/((-4)/12). Let g be a - ((1 - (-30)/(-4)) + -1). Factor -g*w + 27/4 + 3/4*w**2.
3*(w - 3)**2/4
Determine k, given that 3750 + 1/6*k**2 + 50*k = 0.
-150
Let w(m) be the third derivative of -m**8/2016 - m**7/630 + m**6/90 - m**5/180 - 7*m**4/144 + m**3/9 + 8*m**2 + 2*m. Factor w(t).
-(t - 1)**3*(t + 1)*(t + 4)/6
Factor 85*l**3 - 114 - 150 + 12*l - 32*l + 210*l**2 - 16 + 5*l**4.
5*(l - 1)*(l + 2)**2*(l + 14)
Let m = -8 + 17/2. Let r(j) be the first derivative of -1 - m*j**2 + 2*j - 1/3*j**3. Solve r(k) = 0.
-2, 1
Let d(p) be the second derivative of p**7/399 + 2*p**6/57 - 27*p**5/190 - 16*p**4/57 + 52*p**3/57 + 48*p**2/19 - 503*p. What is b in d(b) = 0?
-12, -1, 2
Factor 8/9*f + 16/9*f**2 + 2/9*f**4 + 10/9*f**3 + 0.
2*f*(f + 1)*(f + 2)**2/9
Let a be (-6 + 3 - (2 - 5))*(1 + 0). Determine f, given that 39/8*f**4 + a + 51/8*f**2 + 3/4*f + 21/2*f**3 = 0.
-1, -2/13, 0
Let a(m) be the first derivative of 5*m**6/3 + 94*m**5/5 + 93*m**4/2 - 190*m**3/3 - 50*m**2 - 314. What is x in a(x) = 0?
-5, -2/5, 0, 1
Let i = -17864/15 + 1193. Let n = i - 11/15. Factor 8/3 - 4/3*v + n*v**3 - 8/3*v**2.
4*(v - 2)*(v - 1)*(v + 1)/3
Let m(i) be the second derivative of -2*i**7/21 + 32*i**6/15 - 28*i**5/5 - 2*i**4/3 + 58*i**3/3 - 28*i**2 + 458*i. Factor m(b).
-4*(b - 14)*(b - 1)**3*(b + 1)
Suppose -12*w + 13*w = 108. Let u be 360/w - (3 - 1). Factor -4/3*r**3 + 8/3*r - u*r**2 + 0.
-4*r*(r - 1)*(r + 2)/3
Solve -12*x**2 - 44*x - 14*x**2 - 8 + 4*x**3 + 16*x**4 + x**2 - 15*x**2 - 8*x**2 = 0.
-1, -1/4, 2
Let y be (-24)/84 - 6*24/(-63). Factor 0*s + 0 + 1/3*s**y.
s**2/3
Let w be 3/12*10*(-8 + 10). Let b be (-2)/12 + (-3)/((-18)/w). Find q such that 1/3*q + 1/3*q**3 + b*q**2 + 0 = 0.
-1, 0
Let l(s) = s**3 - 3*s**2 + 3. Let o be l(3). Suppose -7*w - o = -17. Let 18*u**2 + 3*u**2 - 16*u**3 - 48*u + 23*u**2 + w*u**4 + 18 = 0. What is u?
1, 3
Find m, given that -10*m**4 - 8/7*m - 8/7 + 8/7*m**3 + 78/7*m**2 = 0.
-1, -2/7, 2/5, 1
Let v(g) = g**2 + 2*g - 9. Let d be v(4). Find n, given that 349*n**5 + 864*n**3 + 3456*n**2 + 81*n**4 - 345*n**5 + 5184*n + d*n**4 = 0.
-6, 0
Let o = 1539 - 1535. Let q(v) be the first derivative of -15/4*v**o + v**5 - 5/2*v**2 + 0*v + 5*v**3 + 5. Factor q(h).
5*h*(h - 1)**3
Let y(f) = 59*f**2 - 29. Suppose 4*h - 1 = -17. Let i be 8 + 3/3 + h. Let j(d) = -147*d**2 + 72. Let r(b) = i*j(b) + 12*y(b). Let r(w) = 0. What is w?
-2/3, 2/3
Let a(n) be the second derivative of 0*n**2 + n**4 - 1/2*n**3 + 0 + 15/56*n**7 - n - 2/5*n**6 - 33/80*n**5. Suppose a(s) = 0. Calculate s.
-1, 0, 2/5, 2/3, 1
Let w be 12/(-8)*-2*(-3)/18. Let i = 3/4 + w. Solve 1/4*l**3 + i*l - 1/2*l**2 + 0 = 0.
0, 1
Let m be (-24)/(-36)*(-9)/(-2). Factor -27 - 31*t**m - 225*t**2 + 8*t**3 - 159*t + 50*t**3.
3*(t - 9)*(3*t + 1)**2
Let a(j) be the third derivative of j**7/23940 + j**6/1368 + j**5/285 - 7*j**4/24 - 13*j**2. Let p(u) be the second derivative of a(u). Factor p(d).
2*(d + 1)*(d + 4)/19
Let v(z) be the third derivative of 0 - 85/12*z**4 + 31*z**2 + 1/12*z**5 + 1445/6*z**3 + 0*z. Let v(y) = 0. Calculate y.
17
Let p(f) be the first derivative of 9 - 110*f**3 - 121/2*f**4 - 8*f - 48*f**2. Suppose p(i) = 0. Calculate i.
-1, -2/11
Let b(c) = -4*c + 12. Let h(o) = -9*o + 24. Let y(l) = -5*b(l) + 2*h(l). Let d be y(14). Solve -4*x**4 + 12*x**3 + 14*x**2 + d*x**2 - 30*x**2 = 0.
0, 3
Let k(g) be the first derivative of 8*g - 5/2*g**4 - 10/3*g**3 + 1/3*g**6 + 4*g**2 - 13 + 2/5*g**5. Suppose k(v) = 0. What is v?
-2, -1, 1, 2
Let f(o) be the first derivative of o**6/45 - 92*o**5/25 + 172*o**4 - 55456*o**3/45 + 17776*o**2/5 - 23232*o/5 + 317. Solve f(t) = 0 for t.
2, 66
Solve -6/5*x**3 + 16/5*x**2 + 0 + 0*x = 0 for x.
0, 8/3
Let k(t) be the second derivative of -1/147*t**7 + 0*t**4 + 0 + 0*t**5 + 1/105*t**6 + 23*t + 0*t**2 + 0*t**3. Find u, given that k(u) = 0.
0, 1
Let z(x) be the first derivative of 1/6*x**4 + 40 + 0*x**2 + 0*x + 2*x**3. Factor z(v).
2*v**2*(v + 9)/3
Let q be -186 + 185 + 4 + 1. Suppose -42*c**3 + 69*c**2 + 135/2*c**5 + 3 - 72*c**q - 51/2*c = 0. Calculate c.
-1, 1/3, 2/5, 1
Let s(n) = n**2 - 4*n + 9. Let o be s(4). Suppose o*l - 11*l = -8. Factor l*y**3 - 4*y + 39 - 39.
4*y*(y - 1)*(y + 1)
Let t = -77/4930 + -2/145. Let v = 49/68 - t. Factor -v + 3/4*d**2 + 0*d.
3*(d - 1)*(d + 1)/4
Suppose -6*w = -4*w - 8. Suppose 5*s - 2*x = -7 + 32, 0 = s - w*x + 13. Factor m**2 + 6*m + m**3 - 25*m + 10*m + s*m.
m*(m - 1)*(m + 2)
Let i(u) be the third derivative of u**7/630 - u**6/90 + 25*u**4/24 + 26*u**2. Let g(t) be the second derivative of i(t). Find y, given that g(y) = 0.
0, 2
Factor -1/5*k**2 - 125 - 10*k.
-(k + 25)**2/5
Suppose -11*a + 45 = -2*a. Let x(f) be the second derivative of -1/4*f**4 - 1/20*f**a - 1/3*f**3 + 0*f**2 - f + 0. Solve x(p) = 0 for p.
-2, -1, 0
Let b = -3208 - -28876/9. Factor 4/9*r + 2/9*r**4 + 0*r**2 - 2/9 - b*r**3.
2*(r - 1)**3*(r + 1)/9
Let w(u) be the first derivative of -u**5/5 - u**4 + 8*u**2 - 4*u - 15. Let a(j) be the first derivative of w(j). Factor a(f).
-4*(f - 1)*(f + 2)**2
Let d = -95 + 143. Let n = -45 + d. Suppose -3/2*j**2 + 3/2*j**n - 3/2*j + 3/2 = 0. Calculate j.
-1, 1
Let m(v) be the second derivative of -v**6/30 - v**5/20 + 126*v. Factor m(y).
-y**3*(y + 1)
Let s(j) = 2*j - 17. Let m be s(12). Factor -m*p + 0*p + 3*p**2 + p - 15*p.
3*p*(p - 7)
Let z be (1 - 28/20) + 532/280. Let v(d) be the first derivative of -1/3*d**3 - z*d**2 + 0*d - 8. What is y in v(y) = 0?
-3, 0
Suppose 7 = 3*z + 137*l - 142*l, 5*l + 15 = 5*z. Factor -2/5*d**z - 2/5*d**3 + 0 + 2/5*d + 2/5*d**2.
-2*d*(d - 1)*(d + 1)**2/5
Let r = -2411 + 2415. Let v(a) be the second derivative of -1/72*a**r