2 - 53*i - 174. Let w(k) = 20*k**3 - 65*k**2 + 35*k + 115. Let v(n) = -5*d(n) - 8*w(n). Determine r so that v(r) = 0.
-1, 2, 5
Let f(l) = -l**2 + 6*l - 3. Let k be f(5). Suppose -k*m - n = -6, -3*m + 5*n + 5 = -17. Factor -j + 5*j**m + j - j**4.
4*j**4
Let b = -6 + 10. Suppose -b*f - 2 + 6 = 4*o, 0 = -5*o + f + 11. Factor 9*m**2 + m**3 + o*m**3 + 0*m**3 + 9*m + 3.
3*(m + 1)**3
Let x(n) be the first derivative of -n**3/18 + 3*n**2/2 + 19*n/6 + 183. Factor x(u).
-(u - 19)*(u + 1)/6
Let s(t) be the third derivative of -35*t**8/144 - 157*t**7/90 - 379*t**6/72 - 1537*t**5/180 - 70*t**4/9 - 32*t**3/9 - 243*t**2. Let s(l) = 0. Calculate l.
-8/7, -1, -1/5
Determine b so that 2*b**2 - 2/5*b**4 + 0 - 12/5*b + 4/5*b**3 = 0.
-2, 0, 1, 3
Let l(z) = -36*z**3 - 52*z**2 + 4*z - 4. Let p(o) = -o**4 + o**3 + o**2 - o + 1. Let i(s) = l(s) + 4*p(s). Factor i(j).
-4*j**2*(j + 2)*(j + 6)
Let a(w) = -w**3 - 21*w**2 - 25*w + 21. Suppose -10*u = -13*u + 18. Let v(s) = -10*s**2 - 12*s + 10. Let j(l) = u*a(l) - 13*v(l). Factor j(q).
-2*(q - 1)*(q + 1)*(3*q - 2)
Let l(d) be the third derivative of d**7/525 + d**6/50 + 13*d**5/150 + d**4/5 + 4*d**3/15 + 10*d**2 - 14*d. Factor l(w).
2*(w + 1)**2*(w + 2)**2/5
Let g(p) be the second derivative of 15/2*p**2 + 5/36*p**4 + 0 + 5/3*p**3 + 5*p. Factor g(j).
5*(j + 3)**2/3
Let t(q) be the first derivative of 2/3*q**3 - 8*q + 27 + 6*q**2 + 1/6*q**6 + 0*q**5 - 7/4*q**4. Determine b, given that t(b) = 0.
-2, 1, 2
Let f(a) be the first derivative of a**3/18 - 5*a**2/12 + 74. Let f(w) = 0. Calculate w.
0, 5
Let n = 20 + -24. Let v(h) = -4*h**3 - 8*h**2 + 12*h - 4. Let z(t) = -t**4 + 9*t**3 + 15*t**2 - 23*t + 7. Let o(d) = n*z(d) - 7*v(d). Factor o(k).
4*k*(k - 2)*(k - 1)*(k + 1)
Let z = -415 + 1253/3. What is c in -4/3*c**3 - z*c + 4*c**2 + 0 = 0?
0, 1, 2
Suppose -1/4*s**4 + 19/4*s - 21/2 + 43/4*s**2 - 19/4*s**3 = 0. What is s?
-21, -1, 1, 2
Let p = -248 - -248. Let u(w) be the second derivative of -w - 1/36*w**4 + 0*w**3 + 0*w**2 + p. Factor u(o).
-o**2/3
Let g(v) = 5*v**4 - 15*v**3 + 85*v**2 - 125*v + 50. Let w(j) = j**4 - j**3 + j**2 - j. Let c(n) = g(n) - 10*w(n). Determine a, given that c(a) = 0.
-5, 1, 2
Factor 256/3 - 28/3*l**2 + 2/3*l**3 + 64/3*l.
2*(l - 8)**2*(l + 2)/3
Let n(h) be the third derivative of -h**5/90 + h**4/12 - 4*h**2 + 3*h. Suppose n(m) = 0. Calculate m.
0, 3
Determine i, given that -25*i**3 + 17*i**5 - 18*i**5 + 352*i**2 - 512*i - 87*i**3 + 17*i**4 + 256 = 0.
1, 4
Let i(z) be the first derivative of z**7/3780 + z**6/540 - z**4/27 + 4*z**3 - 12. Let v(r) be the third derivative of i(r). Factor v(y).
2*(y - 1)*(y + 2)**2/9
Factor -11740*o**2 + 12*o**3 - 1 - 30*o + 1 + 11761*o**2 - 3*o**4.
-3*o*(o - 5)*(o - 1)*(o + 2)
Let l be 1212/720 - ((-57)/36)/(-19). Factor -2/5*g**2 + 8/5*g - l.
-2*(g - 2)**2/5
Factor 5*j**5 + 21*j + 25*j**4 - 38*j**2 - 15*j**3 + 29*j - 27*j**2.
5*j*(j - 1)**2*(j + 2)*(j + 5)
Factor 8/11 - 8/11*h + 2/11*h**2.
2*(h - 2)**2/11
Let r(m) = 2*m**3 - 2*m**2 - 3*m. Suppose 0 = -w - 1 + 3. Let l(d) = 0*d - 7*d - d + 0*d**2 - 6*d**w + 6*d**3. Let b(g) = 3*l(g) - 8*r(g). Factor b(i).
2*i**2*(i - 1)
Let w = 7/18 + -1/6. Suppose -6 - 3 = -3*j. Find d, given that 2/9*d**2 - w*d**j + 10/9*d + 2/3 = 0.
-1, 3
Let v(x) = -x**3 - 34*x**2 - 87*x + 23. Let s be v(-3). Determine p so that -9*p**2 - 8/5*p**s + 58/5*p**3 + 108/5 - 108/5*p + 4/5*p**4 = 0.
-2, 3/2
Let j(c) = 5*c**3 + 123*c**2 + 2667*c + 18519. Let r(s) = -6*s**3 - 122*s**2 - 2674*s - 18518. Let l(d) = -4*j(d) - 3*r(d). Factor l(g).
-2*(g + 21)**3
Suppose -2*o + o - 2*q - 2 = 0, 5*o + q = -1. Let f = 5138 + -5135. Factor 4/3*i**4 - i**5 + 0*i - 2/3*i**2 + o + 1/3*i**f.
-i**2*(i - 1)**2*(3*i + 2)/3
Let i(s) = 7*s**2 + 1. Let o be i(-1). Let n be o/(-4) + 1 + 1. Let -1/2*k**3 + 0*k**2 + 0*k**4 + 1/4*k + n + 1/4*k**5 = 0. Calculate k.
-1, 0, 1
Let q(d) = -3*d + 12. Let m be q(-3). Let s = -62/3 + m. Factor -s*p**2 - 2/3 + p.
-(p - 2)*(p - 1)/3
Let z(q) be the third derivative of 0 - 2*q**2 + 0*q**4 + 0*q**3 + 0*q - 1/525*q**7 - 1/300*q**6 - 1/450*q**5 - 1/2520*q**8. Factor z(s).
-2*s**2*(s + 1)**3/15
Suppose 3*l - 2*b - 26 + 6 = 0, 2*l + 4*b = -8. Let n(c) be the third derivative of 1/2*c**3 + 0 + 0*c + 1/10*c**5 + 7*c**2 - 3/8*c**l. Factor n(s).
3*(s - 1)*(2*s - 1)
Let t(f) = f**3 - 38*f**2 - 9*f + 30. Let l(a) = 10*a**3 - 420*a**2 - 100*a + 330. Let w(h) = 4*l(h) - 45*t(h). Factor w(j).
-5*(j - 6)*(j - 1)*(j + 1)
Let f(i) be the first derivative of -3*i**4/20 - 13*i**3/5 - 24*i**2/5 + 576*i/5 - 95. Solve f(m) = 0.
-8, 3
Suppose -2 = 2*z + 37*t - 40*t, 0 = -5*t + 10. Let -4*o + 10 + 2/5*o**z = 0. Calculate o.
5
Suppose 63/5*a + 0 - 3/5*a**2 = 0. What is a?
0, 21
Let g(x) = -10*x**3 + 24*x + 16. Let f(c) = -c**2 + c. Let p(y) = y**3 - 3*y**2 + 4*y. Let m(h) = 4*f(h) - p(h). Let s(j) = -g(j) + 12*m(j). Solve s(v) = 0.
-2
Let r(v) = 8*v**3 - 27*v**2 + 45*v - 16. Let f(x) = -4*x**3 + 14*x**2 - 22*x + 8. Let k = -11 + 13. Let p(o) = k*r(o) + 5*f(o). Let p(w) = 0. What is w?
1, 2
Let m(t) be the third derivative of -2/21*t**4 + 40*t**2 - 1/210*t**5 + 0*t - 16/21*t**3 + 0. Factor m(s).
-2*(s + 4)**2/7
Suppose 0 = 4*v - 15 + 3. Factor -17*n**2 - v*n**3 + 9*n**2 + 5*n**2.
-3*n**2*(n + 1)
Let f = 1353/4 - 675/2. Let w(a) be the first derivative of 4*a + 3 + 16/3*a**3 - f*a**4 - 17/2*a**2. Factor w(j).
-(j - 4)*(j - 1)*(3*j - 1)
Let k(n) be the second derivative of n**7/14 - 7*n**6/10 + 12*n**5/5 - 2*n**4 - 8*n**3 + 24*n**2 + 6*n. Solve k(u) = 0.
-1, 2
Suppose 0 = 8*f - 54*f. Let c(l) be the second derivative of f - 1/2*l**4 - l**2 + l**3 + 5*l + 1/10*l**5. Factor c(k).
2*(k - 1)**3
Suppose 6 + 4 = 5*f. Suppose -21*s**2 - 6*s**2 + 2*s**f + s**3 - 30*s - 6*s**3 = 0. What is s?
-3, -2, 0
Let d(b) be the second derivative of b**5/160 + 7*b**4/96 - b**3/48 - 7*b**2/16 - 68*b. Factor d(w).
(w - 1)*(w + 1)*(w + 7)/8
Let a = -31 - -37. Let d(h) be the second derivative of 0 + 1/30*h**a - 1/4*h**4 - 1/6*h**3 + 1/20*h**5 + h**2 - 4*h. Factor d(c).
(c - 1)**2*(c + 1)*(c + 2)
Let g(l) be the third derivative of -l**6/60 - 3*l**5/10 - 7*l**2 - 6. Let g(v) = 0. Calculate v.
-9, 0
Suppose 3*i = -12, -4*q - q = i - 46. Suppose -q*y + 38 = 8. Factor 2/13*p**y + 2/13*p**2 - 2/13*p - 2/13.
2*(p - 1)*(p + 1)**2/13
Let f(a) be the third derivative of -11*a**2 + 1/240*a**6 + 0*a + 1/60*a**5 + 0 - 1/6*a**3 - 1/48*a**4. Factor f(d).
(d - 1)*(d + 1)*(d + 2)/2
Let p(f) be the first derivative of -15 + 2*f**5 + 3/4*f**6 + 1/2*f**4 - 13/4*f**2 - 3*f**3 - f. Factor p(c).
(c - 1)*(c + 1)**3*(9*c + 2)/2
Let j(n) be the first derivative of n**4/4 + 4*n**3/3 - 15*n**2/2 - 18*n - 204. Determine q, given that j(q) = 0.
-6, -1, 3
Let s(n) be the second derivative of n**8/560 + 3*n**7/280 + n**6/40 + n**5/40 + 2*n**3/3 + 12*n. Let i(q) be the second derivative of s(q). Factor i(p).
3*p*(p + 1)**3
Let m(k) = k**3 - 5*k**2 + 6*k - 2. Let v be m(3). Let q be 2/10 - (-69)/(-210)*v. Solve 15/7*c - 9/7*c**2 - q = 0.
2/3, 1
Let z(f) = f**2 - 5*f + 4. Let d be z(0). Suppose -d*g**3 + 0*g**3 + 8*g**2 + 0*g**3 = 0. Calculate g.
0, 2
Suppose 14*y - 169 = y. Factor y*t - 25*t**2 - 16 - 64 + 197*t.
-5*(t - 8)*(5*t - 2)
Let d(x) be the first derivative of -11*x**6/3 - 92*x**5/5 + 29*x**4 + 112*x**3/3 - 47*x**2 - 20*x + 342. Suppose d(m) = 0. What is m?
-5, -1, -2/11, 1
Find k, given that 30*k**2 - 21*k + 113*k - 13*k**2 + 4*k**3 + 44 + 35*k**2 = 0.
-11, -1
Let o be 17/(-9) - (-2)/1. Let n = 184/2385 + 9/265. Suppose -2/9*r + o*r**3 + 0 + n*r**2 = 0. What is r?
-2, 0, 1
Let f(q) be the second derivative of -q**5/100 + q**4/10 - 11*q**3/30 + 3*q**2/5 + 3*q - 18. Factor f(w).
-(w - 3)*(w - 2)*(w - 1)/5
Let x(r) be the second derivative of -1/24*r**4 + 1/100*r**5 + 0 - 1/15*r**3 + 5*r**2 + 12*r. Let q(j) be the first derivative of x(j). Factor q(c).
(c - 2)*(3*c + 1)/5
Determine a so that 4/5*a**5 + 68/5*a**4 + 0*a + 0 + 64/5*a**3 + 0*a**2 = 0.
-16, -1, 0
Suppose 5*d = -2*x + 14, -5*d + 20 = -11*x + 16*x. Suppose -3*z - 21/2*z**x + 0 = 0. What is z?
-2/7, 0
Suppose 3*i - 31 = 30*n - 25*n, i - 4*n = 22. Determine g so that 0*g + 4/3*g**i + 10/3*g**3 + 0 = 0.
-2/5, 0
Let v be 2/(-2) + 2 + 4/1. Factor -a - 4*a**2 + 9*a**2 + a - v.
5*(a - 1)*(a + 1)
Let c(g) be the first derivative of -48 - 35*g - 20*g**2 - 5/3*g**