6. Suppose b = -2*v - 57 + 63. Factor -5/2*f**3 + 2*f + 1/2*f**4 - 4 + v*f**2.
(f - 2)**3*(f + 1)/2
What is t in 84/5*t + 82/5 + 2/5*t**2 = 0?
-41, -1
Let b(v) be the third derivative of v**7/1575 - v**6/75 + v**5/45 + v**4/15 - 11*v**3/45 + 28*v**2 + 8*v. Find o, given that b(o) = 0.
-1, 1, 11
Let u(c) = c**2 - 20*c + 19. Let m be u(19). Suppose -5 + 1 + 2*w**2 - 2*w + m + 0*w**2 = 0. Calculate w.
-1, 2
Factor -q**3 - 191 - 147 - 3*q**3 - 63*q + 6*q**3 + 50*q**2 + 349*q.
2*(q - 1)*(q + 13)**2
Let h(v) be the first derivative of v**5 - 15*v**4/2 + 55*v**3/3 - 15*v**2 + 299. Factor h(a).
5*a*(a - 3)*(a - 2)*(a - 1)
Let -b**2 + 360*b - 1329 - 16619 - 7129 - 7323 = 0. What is b?
180
Let i(b) = 24*b**5 - 54*b**4 + 50*b**3 - 10*b**2 + 6*b. Let h(d) = -d**5 + d**4 - d**3 - d. Let l(q) = 8*h(q) + i(q). What is w in l(w) = 0?
-1/8, 0, 1
Let a(m) = -5*m**3 + 2*m**2 - m. Let k = -51 + 47. Let r(t) = 11*t**3 - 4*t**2 + 3*t. Let x(c) = k*r(c) - 9*a(c). Factor x(n).
n*(n - 3)*(n + 1)
Let r(s) = -s**3 - 47*s**2 - 343*s - 5. Let f be r(-9). Factor 1/4*o**f + 0 + 9/4*o**3 - 25/4*o + 15/4*o**2.
o*(o - 1)*(o + 5)**2/4
Let x(g) be the first derivative of 2*g**5/105 + g**4/7 + 8*g**3/21 + 8*g**2/21 - 217. Suppose x(j) = 0. Calculate j.
-2, 0
Let w(z) be the first derivative of -3/2*z**2 - 6 - 1/3*z**3 - 2*z. Solve w(h) = 0.
-2, -1
Factor -8/7*o - o**3 - 4/7 + 19/7*o**2.
-(o - 2)*(o - 1)*(7*o + 2)/7
Let p(g) be the second derivative of -1/2*g**2 - 5/6*g**6 - 23/6*g**4 + 2*g**3 + 22*g + 3*g**5 + 0. Determine s so that p(s) = 0.
1/5, 1
Let t(r) be the third derivative of -1/360*r**6 + 0*r**3 - 1/45*r**5 - r**2 + 1/18*r**4 + 1/630*r**7 - 13*r + 0. Factor t(g).
g*(g - 2)*(g - 1)*(g + 2)/3
Suppose 0 = -2*q + 5*l + 30, -3*l + 9 + 4 = 5*q. Let s(i) be the first derivative of q + 1/6*i**2 + 1/9*i**3 - 2/3*i. Solve s(c) = 0.
-2, 1
Let y be 3/(-3) + 2 - 27. Let c = -14 - y. Solve -7*j**2 + 18*j**2 + 32*j + 33*j**2 + c*j**3 - 16 = 0 for j.
-2, 1/3
Let q be -2 - ((-4)/(-8) + -3). Let l = -4339 + 4341. Factor -1/2*z**l - q*z + 1/2*z**3 + 1/2.
(z - 1)**2*(z + 1)/2
Let f(v) be the second derivative of v**4/12 + v**3/2 + v**2 - 4*v. Let t be f(-3). Factor -6*y**t + 6*y**3 - y**4 + 1 - 5 - 7*y**2 + 12*y.
-(y - 2)**2*(y - 1)**2
Let u(a) be the first derivative of 15*a - 3/5*a**5 + 3/2*a**4 + 12*a**3 - 23 + 21*a**2. What is t in u(t) = 0?
-1, 5
Let n(j) = j**3 - 2*j - 4. Let s be n(3). Suppose 3*k - 14 = -2*u, -3*u + 6*u = 5*k - s. Factor -2*y**k - 3*y**2 + 13 - 13 + 5*y**2.
-2*y**2*(y - 1)*(y + 1)
Let j(t) = -5*t**4 + 24*t**3 - 66*t**2 - 308*t + 371. Let v(q) = 14*q**4 - 71*q**3 + 200*q**2 + 924*q - 1111. Let i(b) = -11*j(b) - 4*v(b). Factor i(g).
-(g - 11)**2*(g - 1)*(g + 3)
Let m be (-5 - 1/(-1)) + (7 - 2). Let h(x) = -x + 1. Let t(s) = 4*s**2 + 12*s - 16. Let i(w) = m*t(w) + 4*h(w). Solve i(q) = 0.
-3, 1
Let s = -44 + 49. Let a(m) = 25*m**5 - 5*m**4 + 5*m**3 + 5*m**2 - 5*m. Let q(r) = -r**5 + r**3 + r**2 - r. Let z(v) = s*q(v) - a(v). Solve z(d) = 0.
0, 1/6
Let n(q) be the first derivative of q**5/40 + 21*q**4/32 + 19*q**3/8 + 55*q**2/16 + 9*q/4 + 11. Determine h so that n(h) = 0.
-18, -1
Let x be 10/(-12) + 6*(-1)/(-4). Let t(y) be the third derivative of -1/12*y**4 + 0 - 1/30*y**5 + x*y**3 + 0*y - 4*y**2. Suppose t(a) = 0. Calculate a.
-2, 1
Let c(u) be the first derivative of -7*u**6/18 - 8*u**5/3 + 61*u**4/12 - 14*u**3/9 + 73. Find d such that c(d) = 0.
-7, 0, 2/7, 1
Suppose 5*f = 4*r + 12, -3*r - f + 2 = -8. Let g(c) be the third derivative of 0*c + 0*c**3 + 1/60*c**5 - 1/12*c**4 + 0 + 4*c**r. Solve g(z) = 0 for z.
0, 2
Let v(z) be the third derivative of -z**6/420 + 11*z**5/210 - 3*z**2 + 2. Factor v(l).
-2*l**2*(l - 11)/7
Let f(m) be the third derivative of -39*m**6/80 - 61*m**5/20 - 25*m**4/4 - 6*m**3 + 238*m**2. Determine t so that f(t) = 0.
-2, -2/3, -6/13
Suppose 4*j = -3*z - 11, -3*j + 35 = 5*z - 7*j. Let m = 34 + -34. Factor 2/7*c**2 - 2/7*c**z + m + 4/7*c.
-2*c*(c - 2)*(c + 1)/7
Let y = 1103/60 + -91/20. Let u = y + -901/66. Factor u*j**2 + 0*j + 0.
2*j**2/11
Suppose -19 = -5*n - 4, -2*n - 66 = -2*j. Let m = 36 - j. Determine q, given that -4/9*q + 2/9*q**2 + m - 2/9*q**5 - 2/9*q**4 + 2/3*q**3 = 0.
-2, -1, 0, 1
Let -19068 - 2*n**5 + 18*n**3 + 14*n**4 - 14*n**2 - 16*n + 19068 = 0. Calculate n.
-1, 0, 1, 8
Let f(d) be the first derivative of d**3 - 18*d**2 + 33*d - 109. Factor f(b).
3*(b - 11)*(b - 1)
Let x(g) be the first derivative of 272/5*g**2 - 868/15*g**3 - 49/5*g**4 - 16*g - 7. Factor x(m).
-4*(m + 5)*(7*m - 2)**2/5
Factor -14/3*s**2 + 0 - 2/3*s**3 + 0*s.
-2*s**2*(s + 7)/3
Determine p, given that -2*p - 1/4*p**2 + 0 = 0.
-8, 0
Let u(t) = 31*t**2 + 291*t + 556. Let p(c) = 9*c**2 + 97*c + 186. Let w(s) = 7*p(s) - 2*u(s). Suppose w(k) = 0. Calculate k.
-95, -2
Let g(u) be the first derivative of -u**3/9 - 5*u**2/3 - 16*u/3 - 141. Factor g(d).
-(d + 2)*(d + 8)/3
Let l(c) be the first derivative of c**4/60 - c**3/6 - 3*c**2/5 + 20*c + 12. Let x(k) be the first derivative of l(k). Factor x(s).
(s - 6)*(s + 1)/5
Let w(n) = -6*n**2 + 18*n. Let l be w(3). Let d = 4 + -2. Let 1/5*c**d - 2/5*c**3 + 0 + l*c + 1/5*c**4 = 0. Calculate c.
0, 1
Let p(o) be the third derivative of o**8/1176 + 2*o**7/105 - o**6/210 - 2*o**5/15 + o**4/84 + 2*o**3/3 + 450*o**2 + 2*o. Determine f so that p(f) = 0.
-14, -1, 1
Suppose 0 = 18*f + 2*f - 6*f. Let t(o) be the third derivative of 3*o**2 + 1/3*o**3 + 1/60*o**5 - 1/8*o**4 + f + 0*o. Factor t(w).
(w - 2)*(w - 1)
Let p(u) be the second derivative of -1/15*u**6 + 1/3*u**4 + 0*u**3 + 0 - u**2 + 0*u**5 - 22*u. Factor p(y).
-2*(y - 1)**2*(y + 1)**2
Let g(d) be the first derivative of 10*d**4 - 20*d - 18 + 10*d**2 + 3*d**3 - 15*d**4 + d**5 + 2*d**3 + 3. Determine r, given that g(r) = 0.
-1, 1, 2
Let i = -33 + 44. Factor -6*m**2 - 3*m**3 + 5*m**2 - 6 - 15*m - i*m**2.
-3*(m + 1)**2*(m + 2)
Let v(s) = s**3 - 11*s**2 - 11*s - 8. Let i be v(12). Solve 14*m - 9*m**3 - 3*m**i + 0*m**2 + 3*m**2 - 5*m = 0 for m.
-3, -1, 0, 1
Factor -2/5*r**3 + 24/5*r + 0*r**2 + 32/5.
-2*(r - 4)*(r + 2)**2/5
Let n(r) be the third derivative of 4/39*r**3 + 1/780*r**6 + 0 - 1/130*r**5 + 0*r**4 - 11*r**2 + 0*r. Solve n(d) = 0.
-1, 2
Factor -12 + 11*x + 10*x**2 + 3/4*x**3.
(x + 2)*(x + 12)*(3*x - 2)/4
Let q(t) be the first derivative of -4*t**6/9 + 44*t**5/15 - 6*t**4 + 16*t**3/9 + 16*t**2/3 - 223. Factor q(i).
-4*i*(i - 2)**3*(2*i + 1)/3
Let y = -2531 - -2533. Solve 2 - 1/2*c**3 - 9/2*c + 3*c**y = 0 for c.
1, 4
Let m(p) be the third derivative of -2*p**7/105 - 3*p**6/8 - 151*p**5/60 - 45*p**4/8 - 25*p**3/6 + 2*p**2 + 42*p. Factor m(v).
-(v + 1)*(v + 5)**2*(4*v + 1)
Let a(u) be the second derivative of -u**5/15 + 2*u**2 + 10*u. Let y(d) be the first derivative of a(d). Let y(x) = 0. Calculate x.
0
Let h(x) be the first derivative of x**5/60 + x**4/18 + 12*x - 11. Let p(y) be the first derivative of h(y). Let p(g) = 0. What is g?
-2, 0
Let m(t) be the third derivative of -2/105*t**7 + 31*t**2 + 1/45*t**5 - 2/45*t**6 + 4/9*t**3 + 0*t + 0 + 1/4*t**4 - 1/504*t**8. What is h in m(h) = 0?
-4, -1, 1
Let v(a) = -6*a**2 - 12*a + 3. Let s(k) = 8*k**2 + 27*k - 2. Let h(p) = p**2 - p - 1. Let x(r) = 3*h(r) + s(r). Let j(c) = -5*v(c) - 3*x(c). Factor j(z).
-3*z*(z + 4)
Let f = 24143 - 72409/3. Factor 10/3 + 5*n + 5/3*n**5 - 10/3*n**2 + 0*n**4 - f*n**3.
5*(n - 2)*(n - 1)*(n + 1)**3/3
Suppose -d + 5 = -g, -d - 5*g = 2*d + 17. Let q be (-1)/3 - d*-1. Find r such that 0 - q*r**2 + 4/3*r = 0.
0, 2
Let o = 1/125 - -18/875. Let m(y) be the third derivative of 2*y**2 + 3/40*y**6 + 1/336*y**8 + 0*y**3 + 0*y - o*y**7 + 0*y**4 + 0*y**5 + 0. Factor m(j).
j**3*(j - 3)**2
Let u(k) be the second derivative of -14*k + 0 + 15/4*k**4 - 40/3*k**3 - 10*k**2. Determine c, given that u(c) = 0.
-2/9, 2
Let b = -22641 + 158489/7. Find q, given that -b*q - 4/7*q**2 + 4/7 + 2/7*q**3 = 0.
-1, 1, 2
Suppose -w = -3*y - 161 + 147, -20 = 5*y. Let w*t - 13/6*t**2 + t**3 - 1/6*t**4 - 2/3 = 0. What is t?
1, 2
Let o(i) be the third derivative of 0 + 0*i + 41*i**2 + 7/60*i**5 + 17/360*i**6 - 1/8*i**4 + 1/210*i**7 + 0*i**3. Solve o(y) = 0 for y.
-3, 0, 1/3
What is s in -57 + 7*s**3 - 63*s**2 + 117*s - 3*s**3 + 5*s**3 - 2*s**3 - 4*s**3 = 0?
1, 19
Let g(p) = 21*p**3 - 520*p**2 + 91870*p - 5359380. Let w(h) = -4*h**3 - h**2