 77/6*z**4 + 2*z + 32/3*z**3 + 4*z**2. Let w(m) be the first derivative of u(m). Solve w(t) = 0.
-1, -2/7
Suppose -1 = -4*k + 11. Factor -2/11*s**k - 6/11*s + 6/11*s**2 + 2/11.
-2*(s - 1)**3/11
Let g(q) be the first derivative of q**3/3 + 3*q**2 - 7*q + 2. Let g(s) = 0. What is s?
-7, 1
Let t = -326 + 653/2. Suppose d**5 - d**3 + 0 + 0*d - 1/2*d**4 + t*d**2 = 0. Calculate d.
-1, 0, 1/2, 1
Let c(d) be the third derivative of d**5/60 + d**4/12 + 13*d**2. Factor c(k).
k*(k + 2)
Let h(n) be the third derivative of n**9/10584 - n**7/2940 + 2*n**3/3 - n**2. Let i(d) be the first derivative of h(d). Suppose i(k) = 0. Calculate k.
-1, 0, 1
Suppose 9 = 2*v + 9. Let y(o) be the second derivative of -1/12*o**3 - 1/24*o**4 + 1/2*o**2 - 4*o + v. Factor y(c).
-(c - 1)*(c + 2)/2
Suppose -7*l = -3*l. Factor 4*r + 12*r**3 - 13*r**3 - 3*r + l*r**2 - 1 + r**2.
-(r - 1)**2*(r + 1)
Let v(r) = -8*r**3 + 8*r**2 + 6*r. Let s(d) = d**2 + d. Let a be (-2)/6 + 4/(-6). Let k = -2 - -8. Let z(q) = a*v(q) + k*s(q). Factor z(x).
2*x**2*(4*x - 1)
Let v(k) be the first derivative of k**4/8 + k**3/3 + k**2/4 + 8. Factor v(i).
i*(i + 1)**2/2
Let o(f) = f**2 + f. Let y be o(0). Suppose y = g + 4*g. Factor 1/2*p**2 + 0 - 1/2*p**3 + g*p.
-p**2*(p - 1)/2
Let q(r) = -2*r**2 - 11*r + 6. Let k be q(-6). Let d(s) be the third derivative of k + 0*s + 0*s**3 + 0*s**4 + 2*s**2 - 1/30*s**5 + 1/60*s**6. Factor d(i).
2*i**2*(i - 1)
Let a(m) be the first derivative of 2 + 2/3*m**2 + 0*m - 2/9*m**3. Find y such that a(y) = 0.
0, 2
Let z(b) be the first derivative of 3*b**4/4 - 2*b**3 + 3*b**2/2 + 1. Factor z(j).
3*j*(j - 1)**2
Let g = 4/17 - -5/51. What is d in g*d**3 + 0*d**2 + 5/3*d**4 + 4/3*d**5 + 0 + 0*d = 0?
-1, -1/4, 0
Let i(b) be the third derivative of -b**5/30 - 5*b**4/6 - 25*b**3/3 - 3*b**2. Suppose i(s) = 0. What is s?
-5
Let p = 6 - 4. Suppose 0 = f - p. Factor -2/7*y**f - 2/7*y**3 + 0 + 0*y.
-2*y**2*(y + 1)/7
Determine h so that -h**5 - h**5 + 10 - 6*h**4 - 10 = 0.
-3, 0
Let c(a) = -7*a**3 - 5. Let q(x) = -8*x**3 - 6. Suppose 0*f + 2*f - 8 = 4*l, f = 3*l + 7. Let h be 3/(l/8) - -2. Let n(z) = h*c(z) + 5*q(z). Factor n(p).
2*p**3
Suppose 0 = 4*j + r - 14, 5*r + 19 = 3*j + 10*r. Find o such that 2/5*o + 4/5 - 2/5*o**j + 2/5*o**4 - 6/5*o**2 = 0.
-1, 1, 2
Let o be (-15)/(-6) - 1/2. Factor -o*a + 0*a + 4*a**2 - 24*a**4 + 2*a**5 + 20*a**4.
2*a*(a - 1)**3*(a + 1)
Let g be 3909/(-27) + 15/(-5). Let v = 148 + g. Factor -v*k**2 + 4/9 - 2/9*k.
-2*(k - 1)*(k + 2)/9
Suppose -7 = -2*c - 1. Let y = 6 - c. Factor -5/4*n**2 - 1 + 1/4*n**y + 2*n.
(n - 2)**2*(n - 1)/4
Let h(w) = -w**4 - w**3 - w - 1. Let a(r) = -4*r**4 - 7*r**3 - 3*r - 6. Let j(m) = -2*a(m) + 10*h(m). What is f in j(f) = 0?
-1, 1
Let y(w) be the second derivative of -2*w**7/63 - 2*w**6/45 - 12*w. Determine h, given that y(h) = 0.
-1, 0
Let j(f) = 15*f**3 - 25*f**2 - 10*f. Let y(i) = -5*i**3 + 8*i**2 + 3*i. Let v(n) = 3*j(n) + 10*y(n). Factor v(c).
-5*c**2*(c - 1)
Let k = -2 - -6. Factor -l**3 - 4*l**k - 4 + 3*l**3 + 10*l**2 + 4 + 4*l.
-2*l*(l - 2)*(l + 1)*(2*l + 1)
Suppose -5 = 3*i - 5*c, 4*i + 5*c - 40 = -0*i. Let f(m) be the second derivative of 0 + 0*m**3 + 1/21*m**7 + 0*m**6 + m + 0*m**2 + 0*m**i + 0*m**4. Factor f(h).
2*h**5
Let n be -8 + 6 - (-5)/1. Factor 1/2*u**n + 0 + 0*u + u**2.
u**2*(u + 2)/2
Determine a, given that 69*a**3 + 8*a**2 + 8*a - 65*a**3 + 4*a**2 = 0.
-2, -1, 0
Suppose -2/5*l**2 + 34/5*l - 32/5 = 0. Calculate l.
1, 16
Let h(r) be the second derivative of r**4/48 - r**2/8 + 2*r. Factor h(g).
(g - 1)*(g + 1)/4
Let n(w) = -4*w**2 + 2*w + 3. Let j(d) = -3*d**2 + 2*d + 4. Let g(m) = 2*j(m) - 3*n(m). Let q be g(-1). Solve -2*c - c**2 + q*c**2 - c - 2*c**3 - c = 0 for c.
0, 1, 2
Let y be (6/8)/((-6)/(-24)). Suppose 4*a - 1 = y. Factor -r + a + r**4 + 7*r**3 - 5*r**3 + 0*r - r**5 - 2*r**2.
-(r - 1)**3*(r + 1)**2
Let g(a) be the second derivative of 7/10*a**5 + a**3 + 2*a**4 + a - 2*a**2 + 0. Factor g(o).
2*(o + 1)**2*(7*o - 2)
Let c(d) be the first derivative of -3/2*d**2 + 0*d - 3*d**3 - 4. Solve c(p) = 0.
-1/3, 0
Suppose -5*g - 3 = -3*f, -5*g = -0*f - 4*f + 4. Let h(t) = t. Let x(s) = s**2 + 5*s. Let z(j) = f*x(j) - 6*h(j). Let z(o) = 0. Calculate o.
0, 1
Let a = 94/11 + -91/11. Let v = a + 2/33. Factor -v*d**3 + 0*d + 4/3 - d**2.
-(d - 1)*(d + 2)**2/3
Let r = -49 - -75. Suppose -r*f = -23*f - 6. Solve -2/5*x**f + 4/5*x - 2/5 = 0.
1
Let -1/7*y**3 - 1/7*y**2 + 0*y + 0 = 0. What is y?
-1, 0
Let d(t) be the first derivative of -144*t**5/5 - 30*t**4 - 11*t**3 - 3*t**2/2 - 16. Factor d(o).
-3*o*(3*o + 1)*(4*o + 1)**2
Suppose w - 3*b + 15 = 2*w, 4*b - 4 = 4*w. Factor 3*n**2 + 0*n**3 - 4*n**2 + 0*n**3 - n**w.
-n**2*(n + 1)
Suppose 8*h - 5*h = 0. Let t(q) be the second derivative of -q - q**2 + 0*q**3 + h + 0*q**5 + 1/3*q**4 - 1/15*q**6. Factor t(x).
-2*(x - 1)**2*(x + 1)**2
Let j(z) = z**3 + 6*z**2 + 4*z + 1. Let c = -4 + 3. Let k(a) be the first derivative of -a**4/4 + a + 1. Let m(d) = c*j(d) + k(d). Suppose m(s) = 0. What is s?
-2, -1, 0
Let u = -5 - -5. Let a be (u/3)/(1 + -3). Factor a + 0*m + 5 + 2*m**2 + 4*m - 3.
2*(m + 1)**2
Let a be (-750)/(-100)*(-3)/((-9)/2). Let r(s) be the third derivative of 0*s**3 - 1/60*s**a + 2*s**2 + 0 - 1/12*s**4 + 0*s. Factor r(n).
-n*(n + 2)
Suppose 0 = -28*r + 5*r + 46. Factor -3/2*p**r + 0 + 3/2*p.
-3*p*(p - 1)/2
Let j(m) = -m**3 - 7*m**2 - 5*m - 14. Let o be j(-7). Let d = 43/2 - o. Let 1/4*f**2 - 1/2*f**3 + d*f**5 + 0*f + 0 - 1/4*f**4 = 0. Calculate f.
-1, 0, 1/2, 1
Let h(o) be the second derivative of -11*o**4/12 - 7*o**3 + 4*o**2 + 5*o + 2. Factor h(v).
-(v + 4)*(11*v - 2)
Determine m, given that 2/9*m - 4/9 - 2/9*m**3 + 4/9*m**2 = 0.
-1, 1, 2
Factor 0*u - 3/2*u**2 + 8 - 1/4*u**3.
-(u - 2)*(u + 4)**2/4
Let t(p) be the first derivative of -5*p**4/42 + 4*p**3/7 - 4*p**2/7 - 16*p/21 + 1. Factor t(l).
-2*(l - 2)**2*(5*l + 2)/21
Suppose 5*p + j - 14 = 2*p, -2*p + 4*j = 0. Suppose 0*i**3 - 4/9*i**2 + 2/9*i**5 + 4/9*i**p + 0 - 2/9*i = 0. Calculate i.
-1, 0, 1
Let m be 20/18*(-9)/(-45). What is k in 2/9*k**2 + 0*k - m*k**3 + 2/9*k**5 + 0 - 2/9*k**4 = 0?
-1, 0, 1
Let o = -1451/5 - -291. Let -16/5*d**2 + o - 6/5*d - 6/5*d**3 = 0. Calculate d.
-2, -1, 1/3
Let h(a) be the first derivative of 0*a**3 + 0*a + 3/2*a**4 - 2/5*a**5 - 4*a**2 - 1. Factor h(q).
-2*q*(q - 2)**2*(q + 1)
Let l(r) be the second derivative of r**4/54 + r**3/27 - 3*r. Factor l(k).
2*k*(k + 1)/9
Let f(m) = -4*m**3 - 9*m**2 + 3*m + 8. Let z(q) = -q**3 - 2*q**2 + q + 2. Let x(k) = 4*f(k) - 18*z(k). Solve x(i) = 0 for i.
-1, 2
Let h(m) be the third derivative of m**8/112 - m**7/35 - m**6/40 + m**5/10 - m**2. Suppose h(p) = 0. Calculate p.
-1, 0, 1, 2
Let z = 428 - 428. Factor -4/3*q**2 + 0 + 2/3*q**3 + z*q.
2*q**2*(q - 2)/3
Let l = 4 - 4. Suppose l*r - 3*r = -6. Factor 11*k - 4*k**r + 2*k**2 - 3*k - 8.
-2*(k - 2)**2
Solve -6*n - 19*n**2 - 3*n**3 - 99*n + 52*n**2 + 75 = 0 for n.
1, 5
Let p be 48/21 - 4/14. Let o(t) be the third derivative of 0 - t**p - 1/30*t**5 - 1/12*t**4 + 0*t + 0*t**3. Factor o(q).
-2*q*(q + 1)
Determine o so that -2/7*o**3 + 0*o + 2/7*o**2 + 0 = 0.
0, 1
Let f = -8 - 5. Let o be 2/f - 10/(-65). Factor 0 - 2/7*m**4 + 4/7*m**3 - 2/7*m**2 + o*m.
-2*m**2*(m - 1)**2/7
Let p = 29/135 - -5/27. Let a = 38 + -38. Determine h so that -2/5*h**4 + 2/5*h**2 - p*h + a + 2/5*h**3 = 0.
-1, 0, 1
Let v = -156/17 + 1126/119. Solve -1/7*t + 0 - 3/7*t**2 - v*t**3 = 0 for t.
-1, -1/2, 0
Let q = 0 - -13. Let y(j) = -10*j**2 - 19*j + 17. Let k(u) = u + 3. Let i be k(3). Let f(h) = 5*h**2 + 9*h - 8. Let r(l) = i*y(l) + q*f(l). Factor r(v).
(v + 1)*(5*v - 2)
Let p(l) be the third derivative of l**5/330 - l**4/132 + 14*l**2. Solve p(f) = 0 for f.
0, 1
Let i(p) be the first derivative of p**6/30 + 24. Factor i(q).
q**5/5
Factor -16/9*g**3 + 0 + 0*g + 4/3*g**4 + 4/9*g**2.
4*g**2*(g - 1)*(3*g - 1)/9
Suppose 0 = -2*t - 18 - 22. Let v be (-10)/35 - t/21. Find l such that -2/3*l - 2/3 + 2/3*l**2 + v*l**3 = 0.
-1, 1
Let z be ((-105)/(-14) - 7)*2/4. Factor z - 1/2*a + 1/4*a**2.
(a - 1)**2/4
Suppose 2*b - 4 = -0. Factor -11*g**b - g**5 - g**2 + 4*g**5 + 9*g**4.
3*g**2*(g - 1)*(g + 2)**2
Let h(r) = r**2 - 30*r + 81. Let t be h(27). Factor 3/2*q**4 + t + 0*q - 3/2*q**2 - 3/2*q**5 + 3/2*q**3.
-3*q**2*(q - 1)**2*(q + 1)/2
Let o(h) = -21*h**4 