**2 - 3*v**3 - v**2.
v**2*(v - 2)
Let w(f) be the third derivative of f**9/30240 + f**8/5040 + f**7/2520 + f**5/20 + 2*f**2. Let r(i) be the third derivative of w(i). Solve r(y) = 0 for y.
-1, 0
Let b(z) = 2*z + 18. Let h be b(-8). Let f(m) be the first derivative of 2/3*m**4 + 4/3*m**3 + 2/3*m + 4/3*m**h + 2/15*m**5 - 2. Factor f(p).
2*(p + 1)**4/3
Suppose 0 = 4*g - 27 - 9. Suppose -g + 0 = -3*b. Factor w**b + w**4 + w**3 - w**3.
w**3*(w + 1)
Let j(z) be the first derivative of -z**3/15 - z**2/10 + 2*z/5 - 2. Solve j(c) = 0.
-2, 1
Let p(n) = -n**3 + n**2 - n - 2. Let f(v) = 7*v**3 + 4*v**2 + 6*v + 12. Let y(w) = -5*f(w) - 30*p(w). Factor y(z).
-5*z**2*(z + 10)
Let m(l) be the second derivative of -l + 2/21*l**7 + 0*l**3 - 1/2*l**6 + 1/2*l**2 + l**5 - 5/6*l**4 + 0. Factor m(d).
(d - 1)**4*(4*d + 1)
Let z be ((-27)/(-6))/(-6 - -9). Factor z*d**3 + 3/2*d**2 + 0*d + 0.
3*d**2*(d + 1)/2
Let y = 25 - 18. Let j be (-10)/(-2) + (-1)/1. Suppose 0*p**4 + j*p**2 + 4 - y*p**2 + 4*p + p**4 - 2*p**3 = 0. What is p?
-1, 2
Let l(r) be the second derivative of 0*r**3 + 1/15*r**5 - 3*r + 0*r**2 - 1/45*r**6 + 0 - 1/18*r**4. Factor l(j).
-2*j**2*(j - 1)**2/3
Suppose 7*z - 3*u = 11*z + 12, -z + 4*u = -16. Factor 0*k**2 + 0 + 2/3*k**5 + 2/3*k**3 + z*k - 4/3*k**4.
2*k**3*(k - 1)**2/3
Let t(v) be the first derivative of 0*v**2 + 1/6*v**4 + 0*v + 0*v**3 + 4 + 1/5*v**5. Find o, given that t(o) = 0.
-2/3, 0
Let c(q) be the second derivative of -q**6/60 + q**5/40 + q**4/12 + q. Factor c(r).
-r**2*(r - 2)*(r + 1)/2
Suppose -41 = -14*o + 29. Let u be -3*(0 + 2/(-4)). What is h in 1/2 - 1/2*h**o - h**3 + u*h - 3/2*h**4 + h**2 = 0?
-1, 1
Let t be 1 + 3 + ((-380)/28)/5. Let a(i) be the first derivative of -4/7*i - 8/21*i**3 - t*i**2 + 1. Factor a(v).
-2*(v + 2)*(4*v + 1)/7
Let j(v) be the first derivative of -1/7*v**2 + 1/14*v**4 + 0*v - 3 + 0*v**3. Factor j(y).
2*y*(y - 1)*(y + 1)/7
Let h(n) = 5*n**2 + n + 2. Let u(j) = j**3 + 15*j**2 + 3*j + 5. Suppose 3*p + 11 + 0 = 5*b, 2*p = -3*b + 18. Let a(s) = p*u(s) - 8*h(s). Solve a(y) = 0 for y.
-1, 1/3
Let y(i) = 20*i**4 + 3*i**3 - 17. Let u(r) = -7*r**4 - r**3 + 6. Let s = 1 - -5. Let n(x) = s*y(x) + 17*u(x). Factor n(q).
q**3*(q + 1)
Let f(w) be the second derivative of 3*w**6/50 + 3*w**5/100 - 9*w**4/20 + 3*w**3/10 + 3*w**2/5 + 7*w. Find p, given that f(p) = 0.
-2, -1/3, 1
Let q(v) = -16*v**3 - v**2 + v + 1. Let o be q(-1). Suppose 5*r + 2*a - 10 = 0, 4*r = a + 2*a - o. Factor r*p**5 + 0*p**4 - p**4 + p**5.
p**4*(p - 1)
Let o(y) be the second derivative of 5*y**7/42 + y**6 + 3*y**5 + 25*y**4/6 + 5*y**3/2 + 7*y. Factor o(l).
5*l*(l + 1)**3*(l + 3)
Let q be 1176/288 - (5 + -1). Let m(c) be the second derivative of -q*c**4 - 1/2*c**2 + 3*c + 0 + 1/3*c**3. Factor m(j).
-(j - 1)**2
Let m = -2 - -5. Let d = m + 1. Determine n, given that n**3 - n**d - 2*n**2 + 2*n**2 = 0.
0, 1
Suppose 2*n**4 + 8*n + 8*n + 12*n**3 - 7*n**2 + 31*n**2 = 0. Calculate n.
-2, 0
Solve -1/6*k**4 + 3/2 - 4/3*k**2 - k + k**3 = 0.
-1, 1, 3
Suppose -l = 2*l - 9. Find m such that -3*m - m**2 + m + m**l + 2*m**2 = 0.
-2, 0, 1
Suppose -2*u - 10 = -7*u. Solve 3*x**5 + 4*x**2 - 6*x - 42*x**4 + 3*x**4 - x**u + 27*x**3 + 12*x**5 = 0 for x.
-2/5, 0, 1
Factor 2*r**3 + 4/5*r**2 + 0*r + 0 + 8/5*r**4 + 2/5*r**5.
2*r**2*(r + 1)**2*(r + 2)/5
Suppose -2*i + i + 4*q = 10, 5*i - q - 7 = 0. Find d, given that -8/3*d**3 + 8/3*d - 2/3*d**4 - i*d**2 + 8/3 = 0.
-2, -1, 1
Let y(k) be the first derivative of 2*k**6/3 - 4*k**5 + 8*k**4 - 16*k**3/3 - 23. Determine u so that y(u) = 0.
0, 1, 2
Let d(s) = -4*s**2 + 8*s + 8. Suppose -5*j + 2*j + 18 = 0. Let m(f) = -11 - 4 + 9*f**2 - 8*f - 8*f. Let g(c) = j*m(c) + 11*d(c). Solve g(t) = 0 for t.
-1/5, 1
Let s(q) = q**4 + 9*q**3 + q**2 - 7*q - 7. Let h(x) = -4 - 4*x - 38*x**2 + 4*x**3 + 38*x**2. Let g(m) = 7*h(m) - 4*s(m). What is f in g(f) = 0?
-1, 0
Factor 3/4*s + 1/2 + 1/4*s**2.
(s + 1)*(s + 2)/4
Let o(v) be the first derivative of -2*v**5/5 - v**4 + 2*v**3/3 + 2*v**2 - 3. Suppose o(z) = 0. What is z?
-2, -1, 0, 1
Let i(s) be the third derivative of s**6/900 - 2*s**3/3 - 3*s**2. Let g(l) be the first derivative of i(l). Let g(n) = 0. Calculate n.
0
Suppose 2*v = -3*v + 25. Factor 3*n**2 + 5*n + 0*n - v*n.
3*n**2
Factor -22*c - 8*c - 16*c**2 + 42*c + 72 - 4*c**3.
-4*(c - 2)*(c + 3)**2
Let w(s) be the second derivative of -3*s + 0*s**2 + 2/15*s**6 + 1/3*s**4 - 1/6*s**3 + 0 - 3/10*s**5 - 1/42*s**7. Factor w(i).
-i*(i - 1)**4
Let q = -2/533 - -1116/13325. Let b(a) be the second derivative of q*a**5 + a + 0 - 7/60*a**4 + 0*a**2 - 1/50*a**6 + 1/15*a**3. Factor b(c).
-c*(c - 1)**2*(3*c - 2)/5
Let i(f) = 0*f - 5 + f - 3. Let r be i(11). Solve 3*p**r - 2*p**3 - 9*p**5 - 7*p**3 - 15*p**4 = 0.
-1, -2/3, 0
Let y(l) = -l + 2. Let w be y(8). Let x = w + 9. Suppose -1/2*u**5 + 3/4*u**4 + 0*u - 1/4*u**2 + 0*u**x + 0 = 0. What is u?
-1/2, 0, 1
Let r(u) = 21*u - 123. Let a be r(6). Factor -6/5*k**2 - 8/5 + 1/5*k**a + 12/5*k.
(k - 2)**3/5
Let r be 12/(-15)*(-36 - -6). Suppose -15*s**2 + 2*s**2 + 0 + s**2 + r - 28*s = 0. What is s?
-3, 2/3
Let n be (5/18)/((-45)/(-27)). Let s = 1/3 + n. Factor -1/4*b**2 + 5/4*b - s - 5/4*b**3 + 3/4*b**4.
(b - 1)**2*(b + 1)*(3*b - 2)/4
Let l = -28/5 + 6. Factor l*q**3 + 4/5*q**4 + 0*q + 0 + 0*q**2 + 2/5*q**5.
2*q**3*(q + 1)**2/5
Let n(j) be the second derivative of -2/3*j**2 + 1/3*j**3 + 0 + 5*j + 1/120*j**5 - 1/12*j**4. Factor n(b).
(b - 2)**3/6
Factor 0 + 2/9*i**3 + 0*i + 4/9*i**4 + 0*i**2 + 2/9*i**5.
2*i**3*(i + 1)**2/9
Let b(d) be the second derivative of 0 + 1/6*d**3 - d + 0*d**2 + 1/6*d**4 + 1/20*d**5. Find i such that b(i) = 0.
-1, 0
Let -4/5*h - 2/5*h**2 + 6/5 = 0. What is h?
-3, 1
Let w(j) be the second derivative of j**6/65 + j**5/65 - j**4/78 - 9*j. Let w(c) = 0. Calculate c.
-1, 0, 1/3
Let u(j) = -7*j**4 - 18*j**3 + 49*j**2 - 78*j + 36. Let t(f) = -3*f**4 - 9*f**3 + 25*f**2 - 39*f + 18. Let q(n) = -9*t(n) + 4*u(n). Factor q(y).
-(y - 3)**2*(y - 2)*(y - 1)
Factor 24*n**3 + 4*n**4 + 25*n + 9*n + 48*n**2 + 6*n - 8*n.
4*n*(n + 2)**3
Let b(h) = 6*h**3 - 10*h**2 + 8*h. Let z(o) = 5*o**3 - 9*o**2 + 7*o. Let y(l) = 3*b(l) - 4*z(l). Factor y(j).
-2*j*(j - 2)*(j - 1)
Suppose 2 = 2*z - 4. Let w(u) be the first derivative of 1/2*u**4 - 2 + 0*u - 2/3*u**z + 0*u**2. Factor w(g).
2*g**2*(g - 1)
Let p = 5/131 + 1023/655. Let i be (6/(-10) + 1)*2. Factor -p*c - i - 1/5*c**3 - c**2.
-(c + 1)*(c + 2)**2/5
Let j = -4624/9 - -514. Let -4/9*m + 4/9*m**4 + 0 + 10/9*m**3 + j*m**2 = 0. Calculate m.
-2, -1, 0, 1/2
What is i in 1/4*i**3 - 1/4*i**4 - 1/4*i + 0 + 1/4*i**2 = 0?
-1, 0, 1
Let f(s) = 4*s**2 + 13*s + 4. Let u(i) be the first derivative of 4*i**3/3 + 6*i**2 + 4*i - 8. Let v(h) = -4*f(h) + 5*u(h). Factor v(n).
4*(n + 1)**2
Let o be (-102)/(-42) + (-3 + -1)/(-4). Find c, given that -2*c**3 - 18/7*c**2 + 8/7 + o*c = 0.
-2, -2/7, 1
Let v(c) be the second derivative of c**4/96 + 5*c**3/12 + 25*c**2/4 + 37*c. Determine o so that v(o) = 0.
-10
Find g, given that 0*g**2 - 2/7*g**4 + 0*g - 2/7*g**3 + 0 = 0.
-1, 0
Let i(a) = -2*a**4 + 6*a**3 - 7*a + 4. Let s(n) = -n**4 + n - 1. Let w(d) = -i(d) - s(d). Factor w(q).
3*(q - 1)**3*(q + 1)
Let m = 3 + -3. Suppose 5*j + 4*k - 56 = 0, -5*j - 2*k + 18 + 30 = m. Factor 18*q**4 + 40*q - j*q**2 - 5*q**3 - 16 + 4*q**2 - 37*q**3.
2*(q - 2)*(q + 1)*(3*q - 2)**2
Solve -2*o**3 + 3/2*o + 1/2 + 0*o**2 = 0 for o.
-1/2, 1
Let n = 12 - 3. Suppose -5*a - n*p = -4*p - 20, 0 = -2*p + 8. Let a*y**2 - 2/5*y**3 + 0*y**4 + 0 + 2/5*y**5 + 0*y = 0. Calculate y.
-1, 0, 1
Let o = 223/15 + -44/3. Let w = -3 - -5. Factor -1/5*l**w + 0*l + o*l**3 + 0.
l**2*(l - 1)/5
Let h = -11 - -16. Suppose -r = 2, -h*m = -4*r - r - 35. Let 3*o + m + 2*o**2 - 3 + o = 0. Calculate o.
-1
Let z(p) be the third derivative of -1/10*p**5 + 0*p + 0*p**3 + p**2 + 1/40*p**6 + 0 + 1/8*p**4. Let z(x) = 0. Calculate x.
0, 1
Suppose 5 + 3 = -2*f + 4*g, -4*f - 46 = 2*g. Let u be (-1)/(-5)*f/(-4). Factor 2*a + u*a**2 + 2.
(a + 2)**2/2
Let y(g) be the third derivative of -g**5/30 - g**4/2 - 8*g**3/3 + 39*g**2. Solve y(f) = 0.
-4, -2
Let w = 60 + -56. Determine t, given that 1/6*t**2 + 0*t**3 + 0*t - 1/6*t**w + 0 = 0.
-1, 0, 1
Let p(a) be the first derivative of a**6/300 + a**5/75 + a**4/60 - a**2 - 4. Let l(m) be the second derivative of p(m). Suppose 