Factor w(r).
(r - 1)**2*(r + 4)**2
Let k(v) be the second derivative of -v**5/240 + v**4/24 - v**3/6 - v**2 + 2*v. Let t(b) be the first derivative of k(b). Let t(c) = 0. Calculate c.
2
Factor 1/3*v**3 - 2/3*v**2 + 1/3*v + 0.
v*(v - 1)**2/3
Let c(m) be the third derivative of -1/6*m**3 + m**2 + 0 + 1/1080*m**6 + 1/360*m**5 - 1/36*m**4 + 0*m. Let i(z) be the first derivative of c(z). Factor i(s).
(s - 1)*(s + 2)/3
Let r be (6 - 159/27)/((-3)/(-12)). Factor 0*y**2 - 2/9*y**3 - r + 2/3*y.
-2*(y - 1)**2*(y + 2)/9
Let h(i) be the first derivative of 2/15*i**5 + 0*i - 4 - 2/9*i**3 + 1/3*i**2 - 1/6*i**4. Let h(x) = 0. What is x?
-1, 0, 1
Let z(s) be the third derivative of -1/525*s**7 + 0*s + 1/5*s**4 - 13/150*s**5 - 4/15*s**3 + 1/50*s**6 + 0 - s**2. Suppose z(p) = 0. Calculate p.
1, 2
Let 4/3*c + 2/3*c**2 + 2/3 = 0. Calculate c.
-1
Let s(o) = 4*o**4 - 8*o**3 + 4*o**2 - 8. Let p(r) = r**4 - r**3 - r**2 + r - 1. Let j(w) = -8*p(w) + s(w). What is l in j(l) = 0?
-2, 0, 1
Let z(l) be the first derivative of l**4/24 - 5*l**3/18 + 7*l**2/12 - l/2 - 33. Suppose z(p) = 0. Calculate p.
1, 3
Let m(d) = -9*d**4 - 18*d**3 - 21*d**2. Let t(f) = 9*f**4 + 19*f**3 + 21*f**2 + f. Let w(g) = 5*m(g) + 6*t(g). Factor w(p).
3*p*(p + 1)**2*(3*p + 2)
Let g(h) = 2*h**2 - h + 1. Let d be g(-2). Solve -8*m**4 + d*m**4 - 6*m**4 = 0 for m.
0
Factor -3/4 + 1/2*k + 1/4*k**2.
(k - 1)*(k + 3)/4
Let p be 3 + ((-126)/(-10) - -4). Solve 8/5*n + 18*n**3 - p*n**5 + 0 - 56/5*n**4 + 56/5*n**2 = 0 for n.
-1, -2/7, 0, 1
Let s(t) be the second derivative of t**4/24 + t**3/6 + t**2/4 - 4*t. Determine h, given that s(h) = 0.
-1
Let n(i) be the second derivative of -i**6/165 + i**4/66 - 10*i. Factor n(l).
-2*l**2*(l - 1)*(l + 1)/11
Solve -84/5*n + 156*n**4 - 24/5 + 45*n**5 + 126/5*n**2 + 741/5*n**3 = 0 for n.
-2, -1, -2/5, 1/3
Factor 6*n + 4*n + 127*n**2 - 122*n**2.
5*n*(n + 2)
Let n(l) be the second derivative of l**9/60480 - l**8/13440 + l**7/10080 + l**4/12 + 3*l. Let f(h) be the third derivative of n(h). Let f(m) = 0. What is m?
0, 1
Let i(r) = r - 4. Let z be i(6). Let v = z - 0. Suppose 6*o**3 - 2*o + v*o**2 - 2*o**4 - 5*o**3 + o**3 = 0. Calculate o.
-1, 0, 1
Let t(v) = -22*v**2 + 1. Let g be t(-1). Let m be g/(-12) + (-1)/(-4). Find i such that -1/3*i + 1/3*i**m + 0 = 0.
0, 1
Factor 2/7*i**3 + 0 - 8/7*i + 0*i**2.
2*i*(i - 2)*(i + 2)/7
Let z = -560 + 560. Factor z + 4/7*a + 2/7*a**2 - 2/7*a**3.
-2*a*(a - 2)*(a + 1)/7
Suppose -3*c - 6 = 3*m, -5*c = 3*m - 7*m + 28. Factor 1/3 + 1/3*i**m + 2/3*i.
(i + 1)**2/3
Let n(p) be the first derivative of 5/4*p**4 - 3 - 2/3*p**3 + 0*p + 0*p**2. Solve n(y) = 0 for y.
0, 2/5
Let q(n) be the first derivative of n**5/5 + 3*n**4/4 - 2*n**3/3 - 6*n**2 - 8*n + 10. Factor q(m).
(m - 2)*(m + 1)*(m + 2)**2
Let k(w) be the third derivative of 0 + 0*w**3 + 1/30*w**5 - 1/12*w**4 + 0*w - 3*w**2. Factor k(l).
2*l*(l - 1)
Let h = 5 + -2. What is l in 11*l**5 + 3*l**2 - 16*l**5 + 8*l**5 - 3*l**3 - h*l**4 = 0?
-1, 0, 1
Suppose -4*v = v - 30. Let k(b) be the third derivative of -1/300*b**5 - b**2 + 0*b + 0*b**4 + 0 + 1/1050*b**7 + 1/600*b**v - 1/1680*b**8 + 0*b**3. Factor k(m).
-m**2*(m - 1)**2*(m + 1)/5
Let o = 66 + -35. Let c = -17 + 20. Solve -o*w**4 - 14*w**2 + 21/2*w**5 + 0 + 65/2*w**c + 2*w = 0 for w.
0, 2/7, 2/3, 1
Solve -2/5 + 2/5*t**2 - 1/5*t**3 + 1/5*t = 0 for t.
-1, 1, 2
Let b(z) be the second derivative of z**5/70 - z**4/6 - 17*z**3/21 - 9*z**2/7 + 10*z. Solve b(n) = 0 for n.
-1, 9
Let f be 2 + 1 - 12/5. Factor 0*l**4 - 4/5*l**3 + f*l + 2/5*l**2 - 2/5 + 1/5*l**5.
(l - 1)**3*(l + 1)*(l + 2)/5
Let f(o) be the third derivative of -o**5/60 + 2*o**3/3 + 3*o**2. Factor f(m).
-(m - 2)*(m + 2)
Determine p so that 3*p + 51 + 3*p**3 - 51 - 6*p**2 = 0.
0, 1
Let j(d) be the second derivative of d**6/165 - d**5/55 - d**4/22 - 44*d. Let j(p) = 0. What is p?
-1, 0, 3
Let i(b) be the first derivative of 0*b + 1/12*b**3 + 8 + 0*b**2 + 1/16*b**4. Factor i(a).
a**2*(a + 1)/4
Suppose 2*t + 0*i = -5*i + 24, -14 = -5*t - i. Let 9*v**3 - 3*v**4 + 0*v**2 - 3*v**3 + 0*v**t = 0. Calculate v.
0, 2
Factor 2*u**2 + 0 - 3 - 2*u**3 + 2*u + 0*u**3 + 1.
-2*(u - 1)**2*(u + 1)
Let z be (-15)/4 + 1/(-4). Let g = 7 + z. Let 0*s**g + 1/3*s**4 - 2/3*s**2 + 1/3 + 0*s = 0. Calculate s.
-1, 1
Let q(p) = -4*p**5 + 12*p**4 - 8*p**3 - 8*p - 8. Let k(v) = 3*v**5 - 8*v**4 + 5*v**3 + 5*v + 5. Let u(o) = 8*k(o) + 5*q(o). Solve u(l) = 0.
0, 1
Let z(l) be the third derivative of -l**7/3360 - l**6/1440 + l**3/3 - 3*l**2. Let r(p) be the first derivative of z(p). Factor r(g).
-g**2*(g + 1)/4
Let a(c) = -c. Let u be a(6). Let h be (u - -5) + 3 + 1. Let 0*f**h - 2*f**2 + 4*f - 2*f**3 + f**4 + f**4 + 2*f**5 - 4*f**3 = 0. Calculate f.
-2, -1, 0, 1
Let d(l) = -2*l**2 + 6*l + 4. Let a(p) = p - 1. Let f(r) = 2*a(r) - d(r). Factor f(g).
2*(g - 3)*(g + 1)
Suppose 0 = 2*w - 4*w + 6. Suppose 3 + 0*y**2 + y - 2*y**2 - 3 + y**w = 0. Calculate y.
0, 1
Let a(c) be the third derivative of 2*c**2 + 0 + 1/12*c**3 + 0*c + 0*c**4 - 1/120*c**5. Let a(x) = 0. Calculate x.
-1, 1
Factor -102*c**2 + 53*c**2 + 1 - 6 + 34*c**2 - 5*c**3 - 15*c.
-5*(c + 1)**3
Let s(m) be the second derivative of -m**5/20 - m**4/3 - 2*m**3/3 - 4*m. Factor s(v).
-v*(v + 2)**2
Let j(k) = -k**2 - 5*k + 6. Let m be j(-6). Suppose 2*a + z - 3*z = 0, 4*z = -4*a. Factor a*w**2 + 2/9*w**4 - 2/9*w**3 + 0*w + m.
2*w**3*(w - 1)/9
Let -4*p**4 + 0*p - 1/2*p**2 - 7/2*p**3 + 8*p**5 + 0 = 0. What is p?
-1/4, 0, 1
Suppose -4*v = -4*h - 28, 3*h - 11 = -v + 5*h. Factor -1/2 + 2*k - v*k**2 + 2*k**3 - 1/2*k**4.
-(k - 1)**4/2
Suppose -3*a + 5*f = -2*a - 20, 32 = 4*a - 4*f. Solve -4*t - t**2 + t**4 + 5*t**3 - 2*t**4 + 8 - 10*t**2 + a*t**2 = 0.
-1, 2
Suppose -3/4 + 0*r + 3/4*r**2 = 0. What is r?
-1, 1
Let s(b) be the second derivative of 3*b**5/80 + b**4/12 + b**3/24 + 7*b. Factor s(m).
m*(m + 1)*(3*m + 1)/4
Let z(v) = -2*v**3 - 11*v**2 + 7*v + 8. Let m be z(-6). Suppose 2/5*u - 4/5*u**3 + 2/5*u**m + 0 = 0. Calculate u.
-1/2, 0, 1
Let k(l) be the second derivative of -1/147*l**7 + 0*l**2 + 0*l**6 + 0*l**4 - 4*l - 1/21*l**3 + 0 + 1/35*l**5. Factor k(v).
-2*v*(v - 1)**2*(v + 1)**2/7
Factor 151*b - 65*b**2 + 149*b - 360 + 5*b**3 - 5*b**2.
5*(b - 6)**2*(b - 2)
Let c(w) = -4*w**3 + w**3 + w**2 - 4*w**2 + 1 + 5*w**3. Let i be c(2). Factor -2*g**4 + 4*g**3 - g**2 - 2*g**i + g**2.
-2*g**3*(g - 1)*(g + 2)
Let z(m) be the second derivative of m**4/6 - 3*m. Determine h, given that z(h) = 0.
0
Suppose p + 5*p = -0*p. Solve -1/4*i**3 + 1/4*i**2 + 1/4*i + p - 1/4*i**4 = 0 for i.
-1, 0, 1
Suppose 0*j = -2*j - k + 9, -4 = -4*k. Let w(f) be the third derivative of 0*f**3 + f**2 + 0*f + 0 - 1/48*f**j - 1/120*f**5. Factor w(h).
-h*(h + 1)/2
Let u(g) = -8*g**4 + 6*g + 6. Let a(w) = -w**4 + w + 1. Let m = 7 + -1. Let x(p) = m*a(p) - u(p). Suppose x(l) = 0. Calculate l.
0
Factor 5/4*l - 1/4 - 5/4*l**4 + 1/4*l**5 - 5/2*l**2 + 5/2*l**3.
(l - 1)**5/4
Let -2/3*r**5 - 2*r**4 + 0*r - 2*r**3 + 0 - 2/3*r**2 = 0. What is r?
-1, 0
Suppose p = 6*p + 20. Let g = p + 6. Determine h so that h - g*h - h**3 + 2*h**3 = 0.
-1, 0, 1
Find q, given that 2/3 - 1/3*q - 1/3*q**2 = 0.
-2, 1
Let h be 0 - -2*(0 + (-2)/(-6)). What is q in 0 + 5/3*q**3 + h*q - 7/3*q**2 = 0?
0, 2/5, 1
Let r(n) = n**4 + n**2 - n + 1. Let z(t) = 15*t**3 - 20*t**2 - 30*t + 25. Let s(l) = -5*r(l) - z(l). Factor s(m).
-5*(m - 1)**2*(m + 2)*(m + 3)
Let m = -16 + 29. Factor 2*k - m*k**2 + 4 - 7*k**2 + 2*k**4 - 2*k**3 + 14*k**2.
2*(k - 2)*(k - 1)*(k + 1)**2
Let j(f) = f**2 + 6*f + 2. Let g be j(-6). Suppose 14 = y - 2*n, y + g*n = -3*n - 21. Factor -d**y + 1 + 2 + d**2 - 3.
-d**2*(d - 1)*(d + 1)
Let y(a) = -a**4 + 5*a**3 - 6*a**2 - 4*a + 11. Let w(x) = -2*x**4 + 10*x**3 - 12*x**2 - 8*x + 21. Let r(q) = -3*w(q) + 5*y(q). Solve r(n) = 0.
-1, 2
Let b(z) = -3*z - 73. Let q be b(-25). Factor -1/2*a**q + 1/2*a + 1.
-(a - 2)*(a + 1)/2
Let y(g) = -g**3 + 5*g**2 + g + 1. Let z be y(5). Determine h so that 0 + 25*h**3 - 15*h - 12*h**3 + z + 12*h**2 - 16*h**3 = 0.
1, 2
Let g(a) be the third derivative of a**7/840 - a**6/120 + a**5/40 - a**4/24 + a**3/24 - a**2. Factor g(u).
(u - 1)**4/4
Let q(g) be the third derivative of g**6/540 - g**5/90 + g**4/54 + 6*g**2. Determine c, given that q(c) = 0.
0, 1, 2
Let s = -6/13 + 37/52. Find q, given that 0*q**3 + 0*q - 1/4