 -1 + 9*c**2 - 10 + 18 - c**3 + 20 - 27*c.
-(c - 3)**3
Let m(f) be the first derivative of -3*f**5/10 + 6. Factor m(q).
-3*q**4/2
Let b(t) be the third derivative of -t**5/160 + t**4/16 + 7*t**2. Factor b(w).
-3*w*(w - 4)/8
Let p(c) be the second derivative of -c**8/11760 + c**7/5880 - 7*c**3/6 - 5*c. Let f(o) be the second derivative of p(o). Suppose f(w) = 0. What is w?
0, 1
Suppose x - 4*q + 13 = -0, 3*x = -3*q + 21. What is k in 2/11*k**x + 2/11*k**5 + 0*k**2 - 4/11*k**4 + 0*k + 0 = 0?
0, 1
Let q(x) be the first derivative of x**4/8 - 23*x**3/6 + 30*x**2 + 72*x - 38. Suppose q(u) = 0. Calculate u.
-1, 12
Let o(x) be the first derivative of -x**6/3 + x**4/2 + 6. Factor o(u).
-2*u**3*(u - 1)*(u + 1)
Determine p, given that 9*p - 1 - 9*p**2 - 8*p**2 - 5 + 14*p**2 = 0.
1, 2
Let 15*p**2 - p - 5*p + 3*p**4 - 68*p**3 + 56*p**3 = 0. What is p?
0, 1, 2
Determine w so that -20 + 2 - 42*w + 9*w - 9*w**2 = 0.
-3, -2/3
Suppose 3 = -3*o + 4*o. Factor -o*k + 10*k**3 - 3*k**3 + 2*k + 5*k**2 + 2*k + 3*k**4.
k*(k + 1)**2*(3*k + 1)
Let v(k) = -k**3 + 18*k**2 + 19*k. Let q be v(19). Determine a so that -2*a**3 + q + 2*a**5 - 4/5*a**2 + 0*a + 4/5*a**4 = 0.
-1, -2/5, 0, 1
Let t(u) be the second derivative of -u**5/40 + 4*u. Suppose t(q) = 0. Calculate q.
0
Let c(k) be the third derivative of k**7/140 - 3*k**5/40 - k**4/8 - 16*k**2. Factor c(t).
3*t*(t - 2)*(t + 1)**2/2
Let g(a) = 3. Suppose v - 8 = -v. Let l(y) = -y**2 - y + 4. Let t(u) = v*g(u) - 3*l(u). Let t(b) = 0. Calculate b.
-1, 0
Factor -3*t + 10*t**2 + 14*t**2 - 20*t**2 - t**3.
-t*(t - 3)*(t - 1)
Let z(i) be the second derivative of 6*i**6/25 - 42*i**5/25 + 13*i**4/15 + 56*i**3/5 + 72*i**2/5 + i. Factor z(p).
4*(p - 3)**2*(3*p + 2)**2/5
Suppose -3*y = 2*c + 18, -y - 1 = -5*c + 4*c. Let v(d) = 2*d + 8. Let r be v(c). Factor 3/4*l - 6*l**r + 12*l**3 + 0.
3*l*(4*l - 1)**2/4
Let n(o) = o**5 - 4*o**4 + 6*o**3 + 4*o**2 - 7*o + 4. Let g(y) = 5*y**5 - 20*y**4 + 31*y**3 + 21*y**2 - 36*y + 21. Let b(d) = -4*g(d) + 22*n(d). Factor b(p).
2*(p - 2)*(p - 1)**3*(p + 1)
Let v(p) be the first derivative of -1/2*p - 1/10*p**5 + 1 - 1/4*p**2 - 1/12*p**6 + 1/4*p**4 + 1/3*p**3. Factor v(o).
-(o - 1)**2*(o + 1)**3/2
Factor 0 - 4/7*q - 4/7*q**2.
-4*q*(q + 1)/7
Suppose t + 8 = 5*t. What is v in v - 3*v - v**2 + v + t = 0?
-2, 1
Let x be 4*(-2)/(-48) - 34/(-84). Factor -3/7 - x*s - 1/7*s**2.
-(s + 1)*(s + 3)/7
Let m(a) be the second derivative of -a**5/20 - a**4/12 + a**3/6 + a**2/2 + 5*a. Let m(r) = 0. What is r?
-1, 1
Let f = -45/4 - -13. Solve 0 - 1/2*d - f*d**2 - 3/4*d**3 = 0.
-2, -1/3, 0
Suppose -3*c - 2*c = -15. Suppose x = 9 - 6. Let -j**c + 0*j**x - j**3 = 0. Calculate j.
0
Determine u, given that -19*u + 344*u**2 + 4*u**3 + 3*u - 336*u**2 - 32 = 0.
-2, 2
Suppose -54*j = -59*j + 15. Let -2/3*t**j - 16/3*t + 10/3*t**2 + 8/3 = 0. What is t?
1, 2
Let q be 8/12 + (-6)/9. Suppose q = -13*c + 9*c + 8. Suppose 0*k - 2/7*k**4 + 2/7*k**c + 0 + 0*k**3 = 0. What is k?
-1, 0, 1
Let f(k) be the second derivative of k**4/4 - 3*k**3/2 + 3*k**2 + k. Find p, given that f(p) = 0.
1, 2
Factor -4/9*p**2 + 13/9*p - 2/3 - 1/3*p**3.
-(p - 1)*(p + 3)*(3*p - 2)/9
What is h in -9/4*h**3 + 9/4*h - 3/4*h**4 + 15/4*h**2 - 3 = 0?
-4, -1, 1
Let f be 0*1/3*1/3. Factor -i + 1/2 + f*i**2 - 1/2*i**4 + i**3.
-(i - 1)**3*(i + 1)/2
Suppose 0 = -4*p - g - 4, -5*p - 26*g = -30*g - 16. Suppose 3/2*z**3 - 1/2*z**4 + p*z - z**2 + 0 = 0. Calculate z.
0, 1, 2
Let i(o) = -2*o. Let q be i(-2). What is z in -q*z + 3*z + 4*z - 2*z**2 + z - 2 = 0?
1
Factor 20*c**2 - 25*c - 11*c - 4*c**3 + 62*c**2 - 42*c**2.
-4*c*(c - 9)*(c - 1)
Let w = 36 + -30. Let u be ((-42)/28)/(w/(-8)). Solve -8/7 - u*d**4 - 2/7*d**5 - 50/7*d**2 - 32/7*d - 38/7*d**3 = 0 for d.
-2, -1
Suppose a + u - 9 = 0, 3*a - 3*u - 9 = -0*u. Suppose a*q = 3*q + 9. Factor -81/4*d**q + 3/4 + 81/4*d**2 - 27/4*d.
-3*(3*d - 1)**3/4
Let k be (12/130)/((-27)/180*-4). Factor 2/13*t**5 - 2/13*t**3 + 0 + 0*t - k*t**2 + 2/13*t**4.
2*t**2*(t - 1)*(t + 1)**2/13
Let p = 4/1741 - -83540/12187. Solve -p - 3/7*t**2 - 24/7*t = 0 for t.
-4
Suppose 3*v = 3, -2 = -3*i - 4*v + 2*v. Factor 2*k**2 + 0 + 2*k**3 + i*k + 1/2*k**4.
k**2*(k + 2)**2/2
Let m(i) = -i**2 + i - 1. Let p(v) = -4*v**2 - 9*v + 44. Let f(u) = -5*m(u) + p(u). Factor f(o).
(o - 7)**2
Let m(h) = -4*h + 21. Let v(g) = g - 1. Let s(a) = m(a) + 5*v(a). Let t be s(-14). Factor 2/3*z**t + z + 1/3 - 2/3*z**3 - z**4 - 1/3*z**5.
-(z - 1)*(z + 1)**4/3
Solve 15*z**3 - 5*z**2 + 24 - 15*z - 9 - 10 = 0 for z.
-1, 1/3, 1
Let q(r) = 3*r**5 - r**4 - 12*r**3 + 14*r**2 + 2*r - 2. Let u(t) = 3*t**5 - 12*t**3 + 15*t**2 + 3*t - 3. Let d(b) = 3*q(b) - 2*u(b). Factor d(m).
3*m**2*(m - 2)*(m - 1)*(m + 2)
Let z(k) be the second derivative of k**7/378 - k**6/270 - k**5/180 + k**4/108 - 7*k. Factor z(h).
h**2*(h - 1)**2*(h + 1)/9
Let g(h) be the second derivative of 1/72*h**4 + 0 + h - 1/120*h**5 - 1/12*h**2 + 1/36*h**3. Factor g(x).
-(x - 1)**2*(x + 1)/6
Let t(u) = -u**4 - 4*u**3 - 2*u**2 + 4*u - 1. Let s(j) = -2*j**4 - 9*j**3 - 5*j**2 + 9*j - 3. Let v(c) = 2*s(c) - 5*t(c). Find o such that v(o) = 0.
-1, 1
Let r(m) = 8*m**3 - m**2 + m. Let f be r(1). Suppose 0 = -7*z + 3*z + f. Suppose -j**z - 4*j + 6*j - 5*j**3 + 4*j**3 = 0. Calculate j.
-2, 0, 1
Let m(f) be the first derivative of 3/2*f**4 - 3*f - 1/2*f**6 - 3/5*f**5 - 3/2*f**2 + 2*f**3 - 3. Factor m(o).
-3*(o - 1)**2*(o + 1)**3
Let h(n) be the first derivative of -n**6/24 + n**5/20 + 3*n**4/8 - 7*n**3/6 + 11*n**2/8 - 3*n/4 - 8. Factor h(z).
-(z - 1)**4*(z + 3)/4
Factor 0 - 8/5*q**4 + 0*q + 4/5*q**2 + 6/5*q**5 - 2/5*q**3.
2*q**2*(q - 1)**2*(3*q + 2)/5
Let s(b) be the first derivative of 2*b**6/3 - b**4 - 6. Factor s(k).
4*k**3*(k - 1)*(k + 1)
Suppose -d - 2*d = 4*t + 2, -8 = 4*t. Factor 2/5*c**d + 2/5*c**3 + 0 - 4/5*c.
2*c*(c - 1)*(c + 2)/5
Factor -o**4 - 5/4*o**3 + 0*o - 1/4*o**2 + 0.
-o**2*(o + 1)*(4*o + 1)/4
Let z(b) be the second derivative of -1/10*b**6 + 0*b**2 - 7/20*b**5 + 5/42*b**7 + 1/4*b**4 + 1/3*b**3 + 0 + 3*b. Factor z(t).
t*(t - 1)**2*(t + 1)*(5*t + 2)
Let k(t) = t**3 - 2*t**2 - 6*t - 7. Let d(l) be the first derivative of l**2/2 + l - 3. Let o(g) = 14*d(g) + 2*k(g). Suppose o(v) = 0. What is v?
0, 1
Let m = -10 + 13. Let h(r) be the first derivative of r**2 + r + 1 + 1/3*r**m. Solve h(i) = 0 for i.
-1
Let z(b) be the third derivative of -b**7/280 + 3*b**5/40 + b**4/4 + 3*b**3/8 + 6*b**2. Factor z(u).
-3*(u - 3)*(u + 1)**3/4
Let h = 13 - 6. Factor -6*m**2 - h + 2*m**2 + 7 + 8*m**3.
4*m**2*(2*m - 1)
Let f = 19/39 + -2/13. Let r = 202/147 - 2/49. Determine y, given that -4/3*y - r*y**3 + 1/3*y**4 + 2*y**2 + f = 0.
1
Let w(y) be the first derivative of y**5/5 + 3*y**4/2 + 13*y**3/3 + 6*y**2 + 4*y + 6. Factor w(p).
(p + 1)**2*(p + 2)**2
Let v = -8/15 - -6/5. Solve v*m**5 + 0 + 0*m**4 - 2/3*m**3 + 0*m + 0*m**2 = 0 for m.
-1, 0, 1
Let f be (101 - 2)/((-12)/(-8)). Let q be 6/(-33) + 56/f. Find o such that 0 - q*o + o**2 + 5/3*o**3 = 0.
-1, 0, 2/5
Suppose 0 = -3*c - 4 + 13. Let s(v) = -v**3 + 4*v**2 - 4*v + 4. Let p be s(c). Determine l so that -1/2*l**2 + 3/2*l - p = 0.
1, 2
Suppose -2 = 3*x - 11. Factor -6*k - 3 - 13*k**2 - 2*k**4 - 9*k**3 + 2 - 3*k**x - 2*k**4.
-(k + 1)**2*(2*k + 1)**2
Solve -2/5*j**2 - 4/5*j - 2/5 = 0 for j.
-1
Let l(h) be the second derivative of 1/10*h**5 - 1/6*h**4 - 3*h + 0 + 0*h**2 - 2/3*h**3. Factor l(d).
2*d*(d - 2)*(d + 1)
Let x(u) be the second derivative of -u**5/5 - 2*u**4/3 - 2*u**3/3 + 50*u. Factor x(q).
-4*q*(q + 1)**2
Let b(n) = -4*n**3 + 5*n**2 + 7*n + 16. Let s(m) = m**3 - m**2 - 2*m - 4. Let a(r) = -4*b(r) - 18*s(r). Suppose a(j) = 0. Calculate j.
-2, -1, 2
Solve 2/3*v - 52/9*v**3 + 4/3*v**2 - 2*v**5 - 2/9 + 6*v**4 = 0 for v.
-1/3, 1/3, 1
Let a(r) be the second derivative of -1/78*r**4 + 1/130*r**5 + 3*r + 0*r**2 + 0*r**3 + 0. Suppose a(m) = 0. Calculate m.
0, 1
Let s(f) be the first derivative of f**3/6 + 5*f**2/2 + 25*f/2 - 7. Factor s(y).
(y + 5)**2/2
Let n(q) be the second derivative of q**7/168 + q**6/60 - q**4/24 - q**3/24 + 4*q. Factor n(m).
m*(m - 1)*(m + 1)**3/4
Suppose 0 = 4*u - 803 + 251. Factor -u*d**2 + 2*d**3 + 138*d**2.
2*d**3
Let g(d) be the first derivative of d**4/4 + 2*d**3/3 - d**2/2 - d + 1. Let y be g(-1). Factor -5*r**2 + y + r**2 + 0*r**2 + 3*r**2.
-(r - 1)*(r + 1)
Su