17*c**2 - 5*c + 3. Let y(s) = -19*s**3 + 35*s**2 - 11*s + 5. Let q(k) = 5*a(k) - 3*y(k). Factor q(r).
4*r*(r - 1)*(3*r - 2)
Let x(c) be the second derivative of 2/15*c**6 - 2/3*c**3 + 2*c**2 + 2/5*c**5 + 3*c + 0 - 2/3*c**4 - 2/21*c**7. Let x(h) = 0. Calculate h.
-1, 1
Factor 4/7*o - 2/7 - 2/7*o**2.
-2*(o - 1)**2/7
Let r = 27/2 + -737/10. Let c = r - -657/10. Factor -c*l**3 - 8*l**4 - l**2 + 0*l - 7/2*l**5 + 0.
-l**2*(l + 1)**2*(7*l + 2)/2
Factor 0 + 0*b**3 - 1/7*b**2 + 0*b + 1/7*b**4.
b**2*(b - 1)*(b + 1)/7
Let r(d) be the first derivative of 2 + 4*d**2 - 20/3*d**3 + 3/2*d**4 + 16*d. Factor r(u).
2*(u - 2)**2*(3*u + 2)
Suppose 3*r - 9 - 6 = 0. Suppose -6 = 2*v - r*v. Factor -4/9*z**v + 0*z**3 + 4/9*z**4 - 2/9*z + 2/9*z**5 + 0.
2*z*(z - 1)*(z + 1)**3/9
Let z(n) = -975*n**3 - 2775*n**2 - 1760*n - 345. Let y(i) = 122*i**3 + 347*i**2 + 220*i + 43. Let t(b) = 25*y(b) + 3*z(b). Determine u so that t(u) = 0.
-2, -2/5
Let c(m) be the third derivative of m**7/14 - 3*m**6/10 - 4*m**5/5 + 6*m**4 - 8*m**3 + 4*m**2. Suppose c(v) = 0. What is v?
-2, 2/5, 2
Let k(w) be the third derivative of -w**6/10 + 4*w**5/15 - w**4/6 - w**2. Let k(g) = 0. Calculate g.
0, 1/3, 1
Let y(z) = 2*z - 2. Let g(m) = m**2 - 1. Let t(q) = -2*g(q) + 2*y(q). Factor t(w).
-2*(w - 1)**2
Let f(w) = -11*w**5 + 5*w**2 - 5*w - 5. Let c(z) = 6*z**5 - 3*z**2 + 3*z + 3. Let k(i) = -5*c(i) - 3*f(i). Factor k(l).
3*l**5
Let b(k) = -k**5 - k. Let z(t) = -10*t**5 + 5*t**4 + 5*t**3 - 5*t**2 - 5*t. Let m(q) = 5*b(q) - z(q). Solve m(s) = 0 for s.
-1, 0, 1
Let d(i) = -5*i**4 + 13*i**3 - 7*i**2 - 15*i + 8. Let z(s) = -5*s**4 + 12*s**3 - 8*s**2 - 15*s + 7. Let g(t) = 3*d(t) - 2*z(t). Factor g(m).
-5*(m - 2)*(m - 1)**2*(m + 1)
Let b = -126/13 - -391/39. Factor 2/3*o**2 + 0 + b*o**3 + 0*o.
o**2*(o + 2)/3
Let z(g) = -4*g**4 + 5*g**3 - 6*g**2 - 5*g + 7. Let f(k) = 7*k**4 - 10*k**3 + 11*k**2 + 10*k - 13. Let p(q) = 3*f(q) + 5*z(q). What is x in p(x) = 0?
-1, 1, 4
Let i(r) be the third derivative of -r**5/12 + 5*r**3/6 + 37*r**2. What is j in i(j) = 0?
-1, 1
Let y(f) be the first derivative of -2 - 1/6*f**2 - 1/36*f**4 - 1/9*f**3 - 2*f. Let z(n) be the first derivative of y(n). Find q such that z(q) = 0.
-1
Let f = 15 + -15. Suppose 3*k + f*k = 6. Determine n so that -2/3*n**3 - 2/3*n + 0 + 4/3*n**k = 0.
0, 1
Suppose -2*d - 14 = -3*j, 3*j - 4*d - d - 26 = 0. Let x(s) be the third derivative of -2*s**j + 0*s + 0 + 1/5*s**5 + 1/12*s**4 - 1/3*s**3. Factor x(g).
2*(2*g + 1)*(3*g - 1)
Factor -1/2*o + 1 - 1/2*o**2.
-(o - 1)*(o + 2)/2
Let d(q) be the third derivative of 0 + 1/1512*q**8 - 1/270*q**6 + 0*q**3 - q**2 + 0*q**5 + 0*q**7 + 1/108*q**4 + 0*q. Determine h, given that d(h) = 0.
-1, 0, 1
Let s(f) = 2*f**4 - 4*f**3 + 6*f**2 + 8*f. Let z(v) = -v**4 + 4*v**3 - 5*v**2 - 7*v. Let r(m) = -3*s(m) - 4*z(m). Suppose r(l) = 0. What is l?
-2, -1, 0, 1
Let x(t) be the first derivative of -3/4*t**4 + 6*t**3 - 3 + 24*t - 18*t**2. Let x(p) = 0. Calculate p.
2
Let l(m) be the first derivative of -1/4*m**2 - 3/10*m**5 + 0*m + 1/2*m**3 + 1/6*m**6 - 1/8*m**4 + 2. Solve l(n) = 0 for n.
-1, 0, 1/2, 1
Let h(d) be the first derivative of d**9/2268 - d**8/1260 - 2*d**3/3 + 6. Let y(r) be the third derivative of h(r). Factor y(w).
4*w**4*(w - 1)/3
Let k = -143/6 - -24. Let g(b) be the second derivative of 0 - 2/15*b**6 - k*b**3 + 0*b**2 + 1/3*b**4 + b - 1/10*b**5 + 1/14*b**7. Solve g(o) = 0 for o.
-1, 0, 1/3, 1
Let t = 11 - 3. Let n = t + -6. Factor -9*d**n - 3*d + 1 + 3*d**3 + 2 + 6*d**2.
3*(d - 1)**2*(d + 1)
Let m(s) = -2*s - 9. Let f be m(-6). Let -39*i**f + 12*i + 30*i**5 - 24*i**2 - 9*i**5 - 6*i**4 - 24*i**3 = 0. Calculate i.
-1, 0, 2/7, 2
Let w(k) = 11*k**3 - 5*k**2 + 6*k. Let z(i) = 100*i**3 - 45*i**2 + 55*i. Let s(n) = -55*w(n) + 6*z(n). Find c such that s(c) = 0.
0, 1
Let v be (-1 - -1)/(-2)*-1. Let g(x) = 7*x**2 - 2*x + 1. Let j be g(1). Solve -i**2 - j*i**2 - 2 + v*i - 9*i = 0 for i.
-1, -2/7
Let m be 1*6*(-4)/(-6). Suppose -m*o = -4*n - 196, 0 = n + 4*n - 5. Solve -7 + o*v**4 - 4 + 42*v**2 + 3 + 0 + 16*v - 100*v**3 = 0 for v.
-2/5, 2/5, 1
Let t be -2 + 9 + -3 + -3. Let o = 1 - t. Determine l, given that 49/3*l**5 - 8*l**3 - 4/3*l**2 + o*l - 7*l**4 + 0 = 0.
-2/7, 0, 1
Let y(m) be the third derivative of m**6/120 - m**5/10 + m**4/2 - 4*m**3/3 - 4*m**2. Suppose y(u) = 0. Calculate u.
2
Let k be (6 - 4)/(2/3). Suppose k*o + 5*t - 21 = o, 4*t - 6 = 2*o. Solve -i**o + 1/2*i**4 - i**2 + 1/2 + 1/2*i + 1/2*i**5 = 0 for i.
-1, 1
Let j(f) be the second derivative of f**5/210 - f**4/42 + f**3/21 + 3*f**2/2 + 5*f. Let n(c) be the first derivative of j(c). Factor n(y).
2*(y - 1)**2/7
Suppose -11*n + 6*n = 0. Let s(z) be the third derivative of 2/15*z**3 + 0*z + n - 11/60*z**4 + 3/50*z**5 - 3*z**2. Factor s(g).
2*(g - 1)*(9*g - 2)/5
Let c be (-3)/12 - (-36)/16. Let n = 2 - c. Factor n*i**3 - 48*i**3 - 33*i**5 - 17*i**5 - 8*i**2 - 90*i**4.
-2*i**2*(i + 1)*(5*i + 2)**2
Let o(i) be the first derivative of i**6/21 + 4*i**5/35 - 4*i**3/21 - i**2/7 - 13. Factor o(b).
2*b*(b - 1)*(b + 1)**3/7
Let i be (6/(-8))/(42/(-7)). Let d(s) be the second derivative of -1/48*s**4 + 0 - i*s**2 - 1/12*s**3 - 2*s. Determine b so that d(b) = 0.
-1
Suppose -10 = 4*b - 26. Suppose 0 = -w + 4*l - 1 + 5, w + 4*l = b. Factor 2*o**2 + o**5 - 4*o**3 - 2*o**4 + w*o**3 - o.
o*(o - 1)**3*(o + 1)
Let z = -9 - -13. Let -2*k**3 + z*k**2 - 3 - 2*k**2 + 3 = 0. What is k?
0, 1
Suppose 0*o = -2*o - 30. Let v = o + 15. Factor 1/5*a**2 - 1/5*a + v.
a*(a - 1)/5
Let a(s) be the second derivative of s**5/5 + 5*s**4/3 + 11*s**3/2 + 9*s**2 - s. Factor a(t).
(t + 2)*(2*t + 3)**2
Let w(f) be the first derivative of 3*f**5/35 + 6*f**4/7 + 22*f**3/7 + 36*f**2/7 + 27*f/7 - 3. Find z such that w(z) = 0.
-3, -1
Factor -p**4 + 12*p**3 - 5*p**4 + 4*p - 12*p**2 + 2*p**4.
-4*p*(p - 1)**3
Let j(r) be the first derivative of 0*r**3 + 0*r**2 + 2/45*r**5 + 0*r - 1/18*r**4 - 3. Suppose j(q) = 0. Calculate q.
0, 1
Let z(x) be the third derivative of -1/165*x**5 - 1/660*x**6 + 0*x + 0*x**3 - 1/132*x**4 + 0 + 3*x**2. Factor z(r).
-2*r*(r + 1)**2/11
Let y(s) = 2*s**3 - 3*s**2 + 15*s - 4. Suppose -5 = -k + 2*k. Let v(t) = t**3 - 2*t**2 + 7*t - 2. Let p(c) = k*v(c) + 2*y(c). Determine j, given that p(j) = 0.
1, 2
Let f(n) be the first derivative of -n**6/3 + 4*n**5 - 25*n**4/2 + 5. Let f(x) = 0. What is x?
0, 5
Let s(n) = 12*n. Let d be s(1). Let h be (-3)/d + 1/4. Factor -1/3*x + h + 1/3*x**2.
x*(x - 1)/3
Let a(k) be the first derivative of 4 + 0*k**3 + 0*k + 1/14*k**4 - 1/7*k**2. Factor a(b).
2*b*(b - 1)*(b + 1)/7
Let p = 169 - 118. Let s = p + -30. Suppose 2*b**3 - s*b**4 + 15*b**5 - b**3 + 5*b**3 = 0. Calculate b.
0, 2/5, 1
Let r(i) be the first derivative of i**4/18 + 4*i**3/9 + i**2 + 8*i/9 + 33. Solve r(f) = 0 for f.
-4, -1
Let a(g) = 5*g**2 - 11. Let v(c) = -4*c**2 - c + 10. Let z(h) = -2*a(h) - 3*v(h). Let r(l) = 2*l**2 + 2*l - 7. Let p(k) = 6*r(k) - 5*z(k). Factor p(b).
(b - 2)*(2*b + 1)
Factor 0 + 0*t + 2/7*t**3 - 6/7*t**2.
2*t**2*(t - 3)/7
Let i(k) be the third derivative of -k**7/1260 + k**6/360 + k**5/120 + 13*k**2. Factor i(c).
-c**2*(c - 3)*(c + 1)/6
Factor 1/7*x**4 + 2/7*x**3 - 1/7*x**5 - 1/7*x + 1/7 - 2/7*x**2.
-(x - 1)**3*(x + 1)**2/7
Let m = -311 - -311. Suppose -3/5*n**4 + 3/5*n**2 + 3/5*n**3 + m - 3/5*n = 0. Calculate n.
-1, 0, 1
Let h = -8 + 12. Suppose -h*u + 9 = 1. Solve 6*m**3 - m**2 - m**2 - u*m**4 - 2*m**3 = 0.
0, 1
Suppose -1 = -2*n + 1. Let q(z) be the first derivative of 2/3*z - 2/3*z**2 + 2/9*z**3 + n. Factor q(j).
2*(j - 1)**2/3
Let f(w) be the second derivative of 0 - 3*w + 1/50*w**6 + 1/5*w**3 - 1/20*w**4 + 0*w**2 - 3/50*w**5. Suppose f(u) = 0. Calculate u.
-1, 0, 1, 2
Let b be 130/30 + 4/(-3). Suppose 6*k = b*k. Factor -3*o**2 + 3*o + 3/4*o**3 + k.
3*o*(o - 2)**2/4
Let -3*l**2 + 7 - 4 + l + 3*l**3 - 4*l = 0. Calculate l.
-1, 1
Let g(z) be the third derivative of 3*z**2 + 4/105*z**7 + 5/6*z**4 + 0 + 7/30*z**6 + 0*z + 3/5*z**5 + 2/3*z**3. Factor g(r).
4*(r + 1)**3*(2*r + 1)
Let q(l) be the first derivative of -l**5/5 + l**4/4 + l**3/3 + l + 3. Let a(v) = 6*v**4 - 8*v**3 - 2*v**2 - v - 5. Let w(z) = a(z) + 5*q(z). Factor w(m).
m*(m - 1)**3
Suppose -2*z - 26 = 3*k - 7*k, -3*k + 4*z = -17. Factor 3*p**4 + 4*p**3 - k*p**3 - 3*p**2 + 3*p**3.
3*p**2*(p - 1)*(p + 1)
Let 