) = 3*p**4 - 3*p**3 - 6*p**2 + 6*p + 3. Let g(h) = l(h) - 3*u(h). Determine o, given that g(o) = 0.
-1, 0, 1
Let d(b) = -b + 1. Let h(n) = n - 5. Let y be h(7). Let r(w) = -14*w**2 + 2*w + 2. Let k(p) = y*d(p) - r(p). Factor k(c).
2*c*(7*c - 2)
Let z = -4 + 9. Factor -3 - 1 + 5*f - 4*f**3 + 4*f**2 + z*f**3 + 6.
(f + 1)**2*(f + 2)
Let p(b) = 12*b**4 + 30*b**3 + 33*b**2 + 6. Let s(k) = -36*k**4 - 91*k**3 - 98*k**2 - 17. Let z(l) = -17*p(l) - 6*s(l). Solve z(m) = 0 for m.
-3/2, 0
Let w = -19 + 21. Factor 4*r + 11*r**3 + w*r**3 - 2*r**4 + 3*r**3 - 20*r**3 + 2.
-2*(r - 1)*(r + 1)**3
Let m(b) = 4*b**3 + b**2 - 16*b - 19. Let w(o) = -4*o**3 + 16*o + 20. Let n(k) = -4*m(k) - 3*w(k). Factor n(y).
-4*(y - 2)*(y + 1)*(y + 2)
Let x = 28/25 - 18/25. Factor 0 + 0*c**2 - 2/5*c**3 + x*c.
-2*c*(c - 1)*(c + 1)/5
Let x = 970/3 + -323. Find j such that -2/3*j**2 - x*j**3 + 0 - 1/3*j = 0.
-1, 0
Let r(z) be the first derivative of -z**7/14 + 3*z**5/20 + 2*z + 2. Let t(u) be the first derivative of r(u). What is x in t(x) = 0?
-1, 0, 1
Let w(d) = d**3 + d. Let z(n) = -3*n**4 - 9*n**3 + 6*n**2 - 12*n. Let p(u) = 12*w(u) + z(u). Solve p(l) = 0 for l.
-1, 0, 2
Let l(x) be the first derivative of x**3/12 - 3*x**2/4 + 9*x/4 + 5. Solve l(p) = 0.
3
Find s such that 32/3*s + 16*s**2 + 500/3*s**5 - 280/3*s**3 + 0 - 100*s**4 = 0.
-2/5, 0, 2/5, 1
Let v(r) = r**2 - 3*r - 15. Let f be v(6). Find t such that 0 - 2/9*t - 2/9*t**f - 4/9*t**2 = 0.
-1, 0
Let n(m) be the first derivative of -3*m**4/4 - 4*m**3/3 + 2*m**2 - 1. Factor n(t).
-t*(t + 2)*(3*t - 2)
Let c = 147/5 - 29. Let 2/5*y**5 + 6/5*y**4 + 0*y + 0 + 6/5*y**3 + c*y**2 = 0. What is y?
-1, 0
Let f(z) be the first derivative of -z**4 + 4*z**3/3 + 4*z**2 - 39. Factor f(b).
-4*b*(b - 2)*(b + 1)
Factor -74*l**2 + 5*l + 2*l + 56*l**2 - 3*l.
-2*l*(9*l - 2)
Let h(g) = 4*g**5 - 5*g**4 + g**3 + g**2 - 5*g + 13. Let q(k) = -k**5 + k**4 + k - 3. Let c(p) = -2*h(p) - 9*q(p). Find v, given that c(v) = 0.
-1, 1
Solve 1/3*p**3 - 5/3*p + 1/3*p**2 + 1 = 0 for p.
-3, 1
Let m(w) be the first derivative of -w**6/6 - 4*w**5/5 + w**4/2 + 4*w**3 - 9*w**2/2 + 12. Suppose m(d) = 0. What is d?
-3, 0, 1
Factor 11*i**3 + 0*i**4 + 10*i + 5*i**4 + 4*i**3 + 5*i**3 + 25*i**2.
5*i*(i + 1)**2*(i + 2)
What is n in 32/5*n**3 + 0 - 14/5*n**5 - 2*n**4 + 0*n - 8/5*n**2 = 0?
-2, 0, 2/7, 1
Let l = -3 + 6. Let y(s) be the second derivative of 1/6*s**3 - 1/8*s**2 + 1/40*s**5 + 0 + l*s - 5/48*s**4. Let y(q) = 0. What is q?
1/2, 1
Let i(r) = r**3 - r**2 - 11*r - 2. Let x be i(4). Factor 0 + 0*g**3 - 2/9*g**4 + 2/9*g**5 + 0*g + 0*g**x.
2*g**4*(g - 1)/9
Factor 14*c - 12*c**2 + 24 + 10*c + 4*c.
-4*(c - 3)*(3*c + 2)
Let v = -74 - -76. Factor 2/3*o**3 - 2*o**2 + v*o - 2/3.
2*(o - 1)**3/3
What is x in 6/5*x + 0 - 12/5*x**4 + 39/5*x**3 - 33/5*x**2 = 0?
0, 1/4, 1, 2
Let b = -61 - -66. Let j(y) be the third derivative of -1/20*y**b - 1/12*y**4 + 0*y**3 + 0 + 0*y - 1/120*y**6 - 2*y**2. Determine z, given that j(z) = 0.
-2, -1, 0
Let s = -54 - -86. Factor -s*b - 54*b**2 - 4 + 6*b - 71*b**3 + 25*b**3 - 14*b**4.
-2*(b + 1)**3*(7*b + 2)
Let s(v) = v**2 - 1. Let g(b) = -8*b**2 + 3*b + 11. Let o(z) = -4*g(z) - 36*s(z). Determine i so that o(i) = 0.
-2, -1
Factor 0*c + 5/6*c**2 - 5/6.
5*(c - 1)*(c + 1)/6
Let l(n) be the second derivative of -n**5/20 + n**4/12 + 20*n. Find u such that l(u) = 0.
0, 1
Let o(f) be the second derivative of f**6/720 - f**4/48 + f**3/2 + 3*f. Let l(g) be the second derivative of o(g). Factor l(h).
(h - 1)*(h + 1)/2
Let t = -18 - -20. Let -181*z**t - 17*z - 43*z - 160*z**3 - 1 + 64*z**5 - 7 + 21*z**2 = 0. Calculate z.
-1/2, 2
Let o(k) = k**2. Let v(s) = 2*s**3 + 3*s**2. Let c(x) = 10*o(x) - 2*v(x). Solve c(r) = 0 for r.
0, 1
Let i(y) be the first derivative of y**5/35 - y**3/21 - 10. Determine a so that i(a) = 0.
-1, 0, 1
Let p(i) be the third derivative of -i**10/352800 - i**9/35280 - i**8/11760 - i**5/15 + 6*i**2. Let w(l) be the third derivative of p(l). Factor w(j).
-3*j**2*(j + 2)**2/7
Factor 10*q**2 - q**5 + 5*q - 2*q**5 + 4*q**5 + 1 + 5*q**4 + 10*q**3.
(q + 1)**5
Determine q so that 2*q**5 - 3/2*q**3 + 2*q**4 - 2*q**2 + 0 - 1/2*q = 0.
-1, -1/2, 0, 1
Let r = 17 + -12. Suppose -5*k + 20 = 2*n, 10*n = 7*n - 2*k + 8. Solve 0*g**2 + n*g + 9/4*g**r + 3/4*g**3 + 0 - 3*g**4 = 0.
0, 1/3, 1
Let l(a) be the second derivative of 7/8*a**3 + 0 + 3/16*a**5 + 9/16*a**4 + 3/4*a**2 - 3*a + 1/40*a**6. Find r, given that l(r) = 0.
-2, -1
Let d(z) = z**2 + 3*z + 30. Let g be d(0). Let a = -26 + g. Determine p so that -2/7*p + 0 + 6/7*p**a + 10/7*p**3 + 2/7*p**2 = 0.
-1, 0, 1/3
Let h = -8 + 12. Suppose q + h*t - 2 = 0, 0 = -4*q + 3*t - 4*t + 8. Factor d**3 - 3*d**4 - d**5 - q*d**3 + d**4.
-d**3*(d + 1)**2
Solve -k**2 + 110 + 0*k**2 + 375*k - 5*k**2 - 29*k**2 = 0 for k.
-2/7, 11
Let o(g) = -g**3 + 5*g**2 - 3*g + 1. Let h(k) = 4*k**3 - 21*k**2 + 12*k - 4. Let n be 5/(-15)*27*1. Let p(r) = n*o(r) - 2*h(r). Factor p(c).
(c - 1)**3
Let m = -186983/147 - -1272. Let d(x) be the second derivative of 1/7*x**5 + 0 - 1/21*x**6 + 3*x - 5/21*x**4 + m*x**7 + 5/21*x**3 - 1/7*x**2. Factor d(c).
2*(c - 1)**5/7
Let r(s) be the first derivative of -3 + 2/5*s**2 + 14/15*s**3 + 0*s. Factor r(d).
2*d*(7*d + 2)/5
Factor q**3 - 7*q**2 - 13 + 4 + 7*q + 8*q.
(q - 3)**2*(q - 1)
Suppose 223*j - 18 = 217*j. Let -j*s**2 - 1/2 - 2*s**3 - 1/2*s**4 - 2*s = 0. Calculate s.
-1
Let w(u) be the first derivative of 2*u**3/15 + 8*u**2/5 + 32*u/5 - 3. Factor w(s).
2*(s + 4)**2/5
Let v(f) be the third derivative of 0*f + 0 + 1/210*f**7 - 1/60*f**6 + 1/24*f**4 - 1/30*f**5 + 1/6*f**3 - 5*f**2 + 1/336*f**8. Find q such that v(q) = 0.
-1, 1
Let k(d) = -20*d**4 - 8*d**3 + 140*d**2 - 208*d + 88. Let z(s) = 13*s**4 + 5*s**3 - 93*s**2 + 139*s - 59. Let b(v) = 5*k(v) + 8*z(v). Solve b(a) = 0 for a.
-4, 1, 2
Let p(j) = j**3 - 3*j**2 - 2. Let f(g) = -4 - 4*g**2 + 1 + 2*g - g + 0 + g**3. Let i(h) = 2*f(h) - 3*p(h). Factor i(k).
-k*(k - 2)*(k + 1)
Suppose 14*t = 9*t + 15. Let q(p) be the first derivative of 2 + t*p - 3/2*p**4 - p**3 + 3*p**2. Suppose q(o) = 0. Calculate o.
-1, -1/2, 1
Let s be 6/18 + (-139)/(-6). Let r = s - 23. Solve 0*m**2 + r*m**5 - m**4 + 0*m + 1/2*m**3 + 0 = 0 for m.
0, 1
Find d such that 10/7*d**5 - 6/7*d**4 + 0*d - 34/7*d**3 - 8/7 + 38/7*d**2 = 0.
-2, -2/5, 1
Let m be 3/(-12) - 87/(-12). Suppose 3*r - m*r + 8 = 0. Factor -4/7*w**3 + 4/7*w - 2/7*w**4 + 2/7 + 0*w**r.
-2*(w - 1)*(w + 1)**3/7
Suppose 42 - 33 = 3*c. Let g(q) be the third derivative of 0 + 5/12*q**4 - 2/3*q**3 + 7/30*q**5 - c*q**2 + 0*q. Solve g(j) = 0.
-1, 2/7
Let k = -5 - -5. Suppose 3*f + 2*f = k. Factor f*w**2 + 2/9*w**3 + 0 - 2/9*w.
2*w*(w - 1)*(w + 1)/9
Let x(n) = -n**2 + 7*n - 4. Let p be x(3). Find m such that m + 13*m**2 + p - 25*m - 3*m**2 = 0.
2/5, 2
Let g be -1*1 + (-10)/(-5). Solve 5*q**2 + g - 2*q - 3*q**2 - q**2 = 0.
1
Let r(i) = 11*i**3 + 10*i**2 - 25*i - 30. Let n(m) = 10*m**3 + 10*m**2 - 25*m - 30. Let t(g) = -6*n(g) + 5*r(g). Factor t(z).
-5*(z - 2)*(z + 1)*(z + 3)
Let l(i) be the third derivative of -4*i**7/105 + 7*i**6/30 - i**5/5 - 4*i**4/3 + 8*i**3/3 + 21*i**2. Solve l(f) = 0 for f.
-1, 1/2, 2
Let d(l) be the third derivative of 1/30*l**6 - 2/15*l**5 + 0 + 1/35*l**7 + 1/3*l**3 - 1/6*l**4 + 2*l**2 + 0*l. Let d(m) = 0. Calculate m.
-1, 1/3, 1
Suppose 5*j = 2*o + 1 + 5, 0 = -j - 4*o - 12. Solve -4/5*d**3 + 0 + 0*d**2 - 7/5*d**5 + j*d - 16/5*d**4 = 0 for d.
-2, -2/7, 0
Suppose 1 = -5*c + 6. Suppose -3*v = -5*r - 0*r + c, 5*r = v + 7. Factor -2*a**4 + a**3 - 2*a**3 + r*a**5 + 3*a**4 - a**5 - a**2.
a**2*(a - 1)*(a + 1)**2
Let o = -43 + 46. Let v(p) be the first derivative of p**5 - 1/4*p**4 - 2/3*p**6 - 1 + 0*p**o + 0*p**2 + 0*p. Determine i so that v(i) = 0.
0, 1/4, 1
Suppose -3*n = -3*a - 9, 2*n + 0*a = a + 7. Factor 2/5*o**n + 0 + 0*o + 2/5*o**3 + 0*o**2.
2*o**3*(o + 1)/5
Let d be 1*(3 - (-1 + -2)). Let k = d + -4. Suppose 0*c + 0*c**2 - k*c - 3*c**2 + 4*c**2 = 0. What is c?
0, 2
Let f(j) = j + 4. Let b be f(4). Let d = b + -6. What is n in -3*n**4 + 0*n**4 + n**2 + 2*n**d + 0*n**4 = 0?
-1, 0, 1
Let a(k) be the second derivative of k**7/20160 - k**5/960 + k**4/2 + 2*k. Let o(p) be the third derivative of a(p). Factor o(c).
(c - 1)*(c + 1)/8
Suppose 28*f - 23*f - 6 = -2*p, p + 2*f - 3 = 0. Let l be (-2 + 2)*2/(-2). Fac