. Factor 21/2*b**2 + 0 + 45/2*b**3 + q*b + 6*b**5 + 39/2*b**4.
3*b*(b + 1)**3*(4*b + 1)/2
Let r(s) be the third derivative of -s**8/5880 + s**6/1260 + s**3 + 5*s**2. Let h(a) be the first derivative of r(a). Let h(p) = 0. Calculate p.
-1, 0, 1
Factor -25*q**4 - 10*q**3 + 20*q + 20*q**4 - 11 - 9 + 0 + 15*q**2.
-5*(q - 1)**2*(q + 2)**2
Let b(m) be the third derivative of -m**9/840 + m**7/126 - m**5/60 - 5*m**4/24 + 3*m**2. Let l(x) be the second derivative of b(x). Find c, given that l(c) = 0.
-1, -1/3, 1/3, 1
Let l(y) = 4*y**2 - y**2 + y**3 - 3*y**2. Let c(b) = -4*b**5 - 10*b**4 - 8*b**3 + 8*b**2 + 8*b + 2. Let m(h) = -c(h) - 4*l(h). Find u, given that m(u) = 0.
-1, -1/2, 1
Factor 4*u**5 - 4*u**2 - 12*u**3 + 11*u**2 + u**2.
4*u**2*(u - 1)**2*(u + 2)
Let p(k) = -k + 1. Let j(i) = -2*i - 2. Let f(b) = j(b) - p(b). Let g be f(-5). Factor g*d + 6 - 2*d**3 + 2 - 8.
-2*d*(d - 1)*(d + 1)
Let b(g) be the first derivative of -2/3*g**3 + 1/5*g**5 + 1/2*g**4 - 2 - 1/6*g**6 + g - 1/2*g**2. Factor b(l).
-(l - 1)**3*(l + 1)**2
Let c(z) be the first derivative of 2*z**3/9 + 8*z**2/3 + 32*z/3 + 7. Solve c(i) = 0.
-4
Let k(r) = -2*r**4 + 14*r**2 - 12*r + 12. Let l be (-1*1)/((-2)/24). Let y(b) = -b**2 + b - 1. Suppose 3*x - 3 = -0*x. Let z(q) = l*y(q) + x*k(q). Factor z(j).
-2*j**2*(j - 1)*(j + 1)
Find t, given that 5 - 4*t**2 + 2 - 36 + 24*t - 7 = 0.
3
Let n(t) be the first derivative of -t**3/3 - t**2 + 8. Solve n(b) = 0.
-2, 0
Let k(g) be the third derivative of g**7/280 - g**6/60 + g**5/40 - g**3/24 + 44*g**2. Factor k(b).
(b - 1)**3*(3*b + 1)/4
Factor -2/3*w**2 + 2/3 + 0*w.
-2*(w - 1)*(w + 1)/3
Let i(y) = -1. Let t(v) = 14*v**2 - 18*v + 9. Let a(o) = 5*i(o) + t(o). Solve a(c) = 0.
2/7, 1
Let v(h) be the first derivative of -h**4/2 - 8*h**3/9 + h**2/3 + 4*h/3 - 11. Suppose v(x) = 0. What is x?
-1, 2/3
Let m(q) = 7*q**2 - 13*q - 4. Let g(f) = 6*f**2 - 12*f - 3. Suppose -5*i - 11 = 2*u + 4, 0 = -5*u. Let j(d) = i*m(d) + 4*g(d). Determine w so that j(w) = 0.
0, 3
Let p = -4 - -1. Let a(g) = 5*g**3 + 3*g**2 + g - 3. Let c(q) = -14*q**3 - 8*q**2 - 2*q + 8. Let v(n) = p*c(n) - 8*a(n). Factor v(l).
2*l*(l - 1)*(l + 1)
Let i(p) be the first derivative of 2*p**3/33 + 2*p**2/11 + 2*p/11 - 35. Determine v so that i(v) = 0.
-1
Let -77*i**2 + 170*i**3 + i + 10 - 130*i**4 - 6*i + 35*i**5 - 3*i**2 = 0. What is i?
-2/7, 1
Let s be (-1)/((5 - 4)*-2). Let 3/2*i**4 + 0*i - 3/2*i**3 + s*i**2 + 0 - 1/2*i**5 = 0. Calculate i.
0, 1
Suppose 0*h + 3 = -3*h. Let k be h/(-1) + (3 - 2). Find g such that 4/5 + 6/5*g + 2/5*g**k = 0.
-2, -1
Let o(z) be the second derivative of 1/42*z**4 + 1/35*z**6 + 0 - 1/147*z**7 + 3*z - 3/70*z**5 + 0*z**3 + 0*z**2. Factor o(u).
-2*u**2*(u - 1)**3/7
Let f(w) be the first derivative of w**6/420 - w**5/105 - w**4/84 + 2*w**3/21 + w**2 + 1. Let u(t) be the second derivative of f(t). Factor u(i).
2*(i - 2)*(i - 1)*(i + 1)/7
Let p = 1/517 + 101814/18095. Let r = 45/7 - p. Factor 4/5*k + 2/5*k**2 - r*k**3 - 2/5.
-2*(k - 1)*(k + 1)*(2*k - 1)/5
Let h be 6*(-4)/(-12) + 3. Suppose 0 = 7*w - h*w. Let 0 + w*r - 1/3*r**2 = 0. Calculate r.
0
Let s(q) be the first derivative of q**6/24 + q**5/20 - q**4/16 - q**3/12 - 14. Factor s(n).
n**2*(n - 1)*(n + 1)**2/4
Let v(a) = -a**3 - 4*a**2 - 3. Let d be v(-3). Let s be 4/d - (-7)/3. What is r in 2*r**3 + 12*r**3 - 6*r**s - 16*r**4 + 4*r**2 - 32*r**5 = 0?
-1, 0, 1/4
Let p(n) be the first derivative of n**4/4 - n**3/3 - n**2/2 + n - 1. Factor p(t).
(t - 1)**2*(t + 1)
Let x = 135 - 135. Factor x*v**2 + 0 + 2/5*v**3 + 0*v.
2*v**3/5
Suppose 0 = -4*g + 57 - 57. Suppose 0*x + 1/5*x**2 - 3/5*x**3 + 3/5*x**4 - 1/5*x**5 + g = 0. What is x?
0, 1
Let z be (-2)/(-3) - 19/18. Let n = 143/90 + z. Solve 2/5*h**2 + 0 - 2/5*h**4 + n*h**3 - 6/5*h**5 + 0*h = 0 for h.
-1, -1/3, 0, 1
Let s be (70/50 - 11)*14/(-8). Suppose 64/5*r**2 - s*r - 16/5*r**3 + 36/5 = 0. Calculate r.
1, 3/2
Let r be -6*(2 - 16/6). Suppose -2*t + r*t = 6. Let -2*k + 2*k**4 + 8*k**t - 2*k**3 + 5*k**2 + 4*k + k**2 = 0. Calculate k.
-1, 0
Let u(r) be the third derivative of r**9/5040 + r**8/2240 - r**4/24 - 3*r**2. Let m(o) be the second derivative of u(o). Factor m(z).
3*z**3*(z + 1)
Let a = 340/3 + -112. Let l(u) be the first derivative of -3*u**2 + 1/3*u**6 + a*u**3 + 2*u + u**4 - 1 - 6/5*u**5. Factor l(g).
2*(g - 1)**4*(g + 1)
Let f(j) be the second derivative of 0 - 1/4*j**4 - 2*j + 0*j**2 + 0*j**3. Factor f(t).
-3*t**2
Determine i so that -27/5*i**2 + 0 - 72/5*i**3 - 3/5*i - 48/5*i**4 = 0.
-1, -1/4, 0
Let d(v) be the second derivative of 5*v**4/42 - v**3/3 + 2*v**2/7 - 2*v. Let d(b) = 0. What is b?
2/5, 1
Let z(n) be the third derivative of -n**6/240 - n**5/60 - 10*n**2. Factor z(q).
-q**2*(q + 2)/2
Let y(r) = 3*r**2 - 3*r - 9. Let z(u) = -1. Let k(v) = -y(v) + 9*z(v). Factor k(t).
-3*t*(t - 1)
Let l(a) be the second derivative of -a - 1/3*a**3 - 1/6*a**4 - 1/4*a**2 + 0. Let l(f) = 0. What is f?
-1/2
Let h(l) = -2*l - 19. Let y be h(-10). Let t(f) be the first derivative of -1/9*f**2 + y + 2/27*f**3 - 4/9*f. Factor t(b).
2*(b - 2)*(b + 1)/9
Suppose -5*g - 20 = -0*g. Let b be g*(-2 + (-20)/(-18)). Suppose 8/9 + b*f**4 + 16*f**3 + 194/9*f**2 + 8*f = 0. What is f?
-2, -1/4
Let v(j) be the third derivative of 7*j**8/480 - j**7/60 + j**6/180 - 4*j**3/3 + 2*j**2. Let h(l) be the first derivative of v(l). Factor h(b).
b**2*(7*b - 2)**2/2
Let p(j) = j**3 - 9*j**2 + j - 1. Let d be p(9). Let f(a) = a - 6. Let b be f(d). Factor 0 - 7/3*x**b - 2/3*x.
-x*(7*x + 2)/3
Let d(n) be the first derivative of 125*n**6/3 - 40*n**5 - 115*n**4/2 + 76*n**3/3 + 44*n**2 + 16*n + 2. Let d(u) = 0. Calculate u.
-2/5, 1
Factor -6*y**2 + 7*y**2 + 3*y**2 + 13 + 20*y + 3.
4*(y + 1)*(y + 4)
Suppose 4*b + 26 = -d, 2*b + 8 = -4*d + d. Let k = 7 + b. Determine t, given that 1/2*t**3 + k*t**2 + 0 + 1/2*t**4 + 0*t = 0.
-1, 0
Let v(r) be the second derivative of r**6/6 - r**5/2 + 5*r**4/12 - 15*r. Factor v(j).
5*j**2*(j - 1)**2
Let l(q) be the third derivative of -q**8/112 - 3*q**7/70 - 3*q**6/40 - q**5/20 - 4*q**2. Factor l(m).
-3*m**2*(m + 1)**3
Let o(k) be the third derivative of -1/105*k**5 + 0*k**3 - 1/420*k**6 + 0 + 0*k + 2*k**2 - 1/84*k**4. Let o(r) = 0. What is r?
-1, 0
Let z be (-2)/(-3) + 8 + 44/(-6). Solve -8/3*r - z*r**2 + 0 = 0.
-2, 0
Let w(d) be the second derivative of 2*d**4/3 + 7*d**3/3 - 2*d**2 + 7*d. Factor w(v).
2*(v + 2)*(4*v - 1)
Let w(v) be the first derivative of 4*v**5/45 - v**4/18 + 4. Factor w(h).
2*h**3*(2*h - 1)/9
Let u(i) be the first derivative of 3*i**4/4 - 3*i**3 - 4. Factor u(y).
3*y**2*(y - 3)
Let 10*x**3 + 16 + 17*x**2 + 16*x**2 + 41*x + x**4 - x = 0. What is x?
-4, -1
Let a(j) be the first derivative of 7*j**6/60 - j**5/8 - 3*j**4/8 + 5*j**3/12 + j**2/2 + 5*j - 5. Let t(g) be the first derivative of a(g). Factor t(x).
(x - 1)**2*(x + 1)*(7*x + 2)/2
Let n(j) be the third derivative of -4/45*j**5 + 4*j**2 - 8/315*j**7 + 0*j + 1/18*j**4 + 0 + 0*j**3 + 1/15*j**6 + 1/252*j**8. Determine u so that n(u) = 0.
0, 1
Let s = -902/3 + 301. Factor -1/3*u + 0 + 1/3*u**3 - s*u**4 + 1/3*u**2.
-u*(u - 1)**2*(u + 1)/3
Solve 1/3 - 1/3*d**3 + 1/6*d - 2/3*d**2 + 1/6*d**5 + 1/3*d**4 = 0 for d.
-2, -1, 1
Factor -o**2 + o**3 - 6*o**3 - 4*o**2.
-5*o**2*(o + 1)
Let r(m) = -3*m**3 - 2*m**2 - 3*m. Let q(d) be the first derivative of -d**4/4 - d**3/3 - d**2/2 + 1. Let b(y) = -4*q(y) + r(y). Let b(g) = 0. Calculate g.
-1, 0
Solve -t**4 - 3*t**2 - 2*t**4 + 0*t**4 - 6*t**3 = 0.
-1, 0
Solve -12/5*c**2 + 0 + 0*c - 3/5*c**3 = 0 for c.
-4, 0
Let f be 0 + -3 - (126/(-4))/7. Factor -f*x**2 + 0 + 3/2*x**3 + 1/2*x - 1/2*x**4.
-x*(x - 1)**3/2
Let w(k) be the second derivative of -k**7/56 + k**6/120 + k**5/16 - k**4/48 - k**3/12 - 8*k. Let w(d) = 0. Calculate d.
-1, -2/3, 0, 1
Let w(t) be the second derivative of -t**6/225 + t**5/50 - 40*t. Factor w(v).
-2*v**3*(v - 3)/15
Determine c, given that -193/2*c**2 - 120*c - 32 - 2*c**4 + 30*c**3 = 0.
-1/2, 8
Let c = -4 - -11. Let i = c - 3. Factor -2*r**2 - 8*r**2 + i - 5*r + 4*r**2 - 3.
-(r + 1)*(6*r - 1)
Let w(m) = 2*m**3 + 2*m**2 - 2. Let y(i) = 10*i**3 + 9*i**2 - i - 11. Suppose -3*o + 14 = 8. Let z(g) = o*y(g) - 11*w(g). Find v such that z(v) = 0.
-1, 0
Suppose -5*y = b - 2*b + 5, 5*y = 2*b - 10. Solve 1/4*n**3 + y*n**2 - 3/4*n + 1/2 = 0.
-2, 1
Let s(a) be th