k. Let m(y) be the first derivative of -1/2*y**4 + 0*y**3 + 1/2*y**g - 2 + 1/6*y**6 + 0*y + 0*y**5. Factor m(s).
s*(s - 1)**2*(s + 1)**2
Suppose o - 8 = -3, -3*x - 4*o = -20. Determine j so that 4*j**3 + x*j + 0 - 12*j**4 - 1/3*j**2 = 0.
0, 1/6
Let c(u) be the third derivative of -u**7/280 - u**6/120 + u**5/40 + u**4/8 - u**3/3 - 4*u**2. Let w(p) be the first derivative of c(p). Factor w(n).
-3*(n - 1)*(n + 1)**2
Let b(a) = -a**2 - a. Let w(p) be the first derivative of -p**2/2 - p + 7. Let v(d) = -4*b(d) + 4*w(d). Factor v(k).
4*(k - 1)*(k + 1)
Let n = 19 - 23. Let u = 14/3 + n. Find r such that 6*r - 32/3*r**2 + u*r**5 - 4/3 - 4*r**4 + 28/3*r**3 = 0.
1, 2
Let g(o) be the second derivative of o**9/37800 + o**8/5600 + o**7/2100 + o**6/1800 - o**4/4 + 5*o. Let u(a) be the third derivative of g(a). Factor u(b).
2*b*(b + 1)**3/5
Let o be 3*1 - (-124)/186. Determine k, given that -4*k - 7/3*k**4 + o*k**2 + 4*k**3 - 4/3 = 0.
-1, -2/7, 1, 2
Factor 3*y**2 + y - 5*y**2 - 4*y - 3*y.
-2*y*(y + 3)
Let x(d) be the first derivative of 25*d**3/12 - 5*d**2 - 5*d - 29. Find a such that x(a) = 0.
-2/5, 2
Let u(t) be the first derivative of 3*t**4/2 - 4*t**3 + 4*t**2 + 2*t - 1. Let m(p) be the first derivative of u(p). Factor m(b).
2*(3*b - 2)**2
Let g(x) be the first derivative of x**3/33 - x/11 - 2. Suppose g(r) = 0. What is r?
-1, 1
Let b(t) be the first derivative of -t**3 - 3*t**2 + 24. Suppose b(x) = 0. What is x?
-2, 0
Let m(g) = 2*g**4 - 4*g**3 + 10*g**2 + 4*g - 4. Let q(n) = -n**4 + 3*n**3 - 9*n**2 - 4*n + 3. Let b(x) = -3*m(x) - 4*q(x). Let b(h) = 0. What is h?
-1, 0, 2
Let j(a) = a**2. Let o(t) = 8*t + t - 12*t. Let s(r) = 3*j(r) - o(r). Determine c, given that s(c) = 0.
-1, 0
Let r(j) be the second derivative of j**6/225 + j**5/150 + 6*j. Factor r(w).
2*w**3*(w + 1)/15
Let q(n) be the first derivative of n**9/336 + n**8/80 + n**7/56 + n**6/120 - 3*n**3 - 2. Let t(d) be the third derivative of q(d). Let t(w) = 0. Calculate w.
-1, -1/3, 0
Factor -324*v**3 + 165*v**3 + 160*v**3 - 6*v**2.
v**2*(v - 6)
Suppose -a = -7*a. Let y(t) = t + 12. Let s be y(-10). Factor 0*v**3 - 2/3*v**4 - 4/3*v + s*v**2 + a.
-2*v*(v - 1)**2*(v + 2)/3
Factor 6*p + 144*p**2 - 142*p**2 + 4 + 3 - 3.
2*(p + 1)*(p + 2)
Let n be (-233)/(-21) + 9/(-21). Factor -14/3*a**3 - n*a**2 - 4/3 - 22/3*a.
-2*(a + 1)**2*(7*a + 2)/3
Let k(y) be the third derivative of -y**5/150 - y**4/60 - 11*y**2. Factor k(n).
-2*n*(n + 1)/5
Let x(y) be the third derivative of 0 - 9*y**2 + 0*y + 1/60*y**6 - 1/12*y**4 + y**3 - 1/10*y**5. Determine l, given that x(l) = 0.
-1, 1, 3
Let g = -5549/12 + 463. Let r = -1/12 + g. Factor r + 0*n**3 + 0*n + 1/2*n**4 - n**2.
(n - 1)**2*(n + 1)**2/2
Let d(s) be the second derivative of 0 + 1/10*s**5 + 4/75*s**6 + 0*s**2 - 2*s - 2/15*s**3 - 7/30*s**4. Determine b so that d(b) = 0.
-2, -1/4, 0, 1
Let j(m) = 10*m**2 - 6*m - 13. Let a(b) = 3*b**2 - 2*b - 4. Let t(d) = -7*a(d) + 2*j(d). Let y be t(2). Factor -1 + 3*i**2 + i**3 - 4*i - 2*i**2 + 0*i**y + 3*i.
(i - 1)*(i + 1)**2
Factor -67 - 52*i**2 + 20*i**3 - 24*i - 63 + 130.
4*i*(i - 3)*(5*i + 2)
Let w(z) be the third derivative of -z**7/140 - z**6/36 - z**5/60 + z**4/12 - z**3/2 - 2*z**2. Let s(f) be the first derivative of w(f). Factor s(l).
-2*(l + 1)**2*(3*l - 1)
Factor 8/3*z**3 + 0*z + 7/3*z**2 + 0 + 1/3*z**4.
z**2*(z + 1)*(z + 7)/3
Determine y, given that 148 - 1 + 45*y**2 + 15*y**3 - 18*y**3 - 189*y = 0.
1, 7
Let z(r) be the third derivative of r**6/120 - r**5/30 + r**4/24 + r**2. Factor z(s).
s*(s - 1)**2
Let a(o) be the third derivative of -o**6/540 + o**5/270 - o**2 - 23. Factor a(s).
-2*s**2*(s - 1)/9
Factor -2/11*k**5 - 2*k**3 - 14/11*k**4 + 0*k + 0 - 10/11*k**2.
-2*k**2*(k + 1)**2*(k + 5)/11
Suppose -2*s + 8 = -0*s. Determine b, given that -7 + 12*b + b**3 - 10*b**2 + s*b**2 - 1 = 0.
2
Factor 2*u**2 - u**2 - 2*u + u**3 + 3*u**2 - 3*u**3.
-2*u*(u - 1)**2
Let q be (2 + -3 - 0)*(1 + -3). Suppose -4/3 + 14/3*u + 4/3*u**3 - 14/3*u**q = 0. What is u?
1/2, 1, 2
Let t = 6 - 8. Let q = t + 4. Factor -2*j**3 - j**2 - j**2 + 0*j**q.
-2*j**2*(j + 1)
Let i be (8/78)/(4/(-6)). Let t = 23/65 + i. Factor -1/5 + 2/5*l - t*l**2.
-(l - 1)**2/5
Let -1/5*c**2 - 1/5 + 2/5*c = 0. Calculate c.
1
Suppose 5*w + 3*s = 35, -4*w + 4*s = -0*w + 4. Let a(g) be the first derivative of 0*g + w + 1/3*g**3 + 0*g**2 + 1/4*g**4. Factor a(h).
h**2*(h + 1)
Let g(b) be the third derivative of -b**6/720 - b**5/60 - b**4/16 + 8*b**2. Determine z so that g(z) = 0.
-3, 0
Factor p - 4/5 - 1/5*p**2.
-(p - 4)*(p - 1)/5
Let w(q) be the second derivative of -q**6/60 + q**4/2 - 4*q**3/3 + 21*q. Suppose w(o) = 0. Calculate o.
-4, 0, 2
Factor -2/7*r**2 + 0 - 2/7*r.
-2*r*(r + 1)/7
Let z(j) be the third derivative of j**8/80640 - j**7/20160 + j**5/30 + 2*j**2. Let q(a) be the third derivative of z(a). Factor q(r).
r*(r - 1)/4
Let t(n) = -n**2 + 1. Let i(l) = 2*l**2 - l - 3. Let z(f) = -i(f) - 3*t(f). Find v, given that z(v) = 0.
-1, 0
Let q be (-5)/(-2) + -2 + 1. Let 1/2 - 1/2*j**3 + q*j**2 - 3/2*j = 0. Calculate j.
1
Suppose -3*l = 5*p - 25, 6*l + 2*p = 2*l + 10. Let b be ((-1)/2)/((-2)/32). Factor -b*w**3 + 4*w**4 - 3*w + l*w + 5*w**2 + 2*w.
w*(w - 1)*(2*w - 1)**2
Let d be (-4 + 0 - -2) + (-20)/(-4). Let w(l) be the second derivative of d*l + 0 + 0*l**2 - 1/30*l**3 + 1/60*l**4. Factor w(r).
r*(r - 1)/5
Find a such that -2/9*a**5 + 2/3*a**4 - 4/9*a**3 + 0*a + 0*a**2 + 0 = 0.
0, 1, 2
Let t(w) be the first derivative of w**3/9 + 14. Factor t(z).
z**2/3
Let s be (6/2)/(-6)*-4. Solve -5*v**s + 0*v**3 + 4*v**3 - 10*v**4 - 4*v + 15*v**2 = 0 for v.
-1, 0, 2/5, 1
What is a in -4/5*a**2 + 0 + 4*a = 0?
0, 5
Factor 3*q**5 + 92 - 9*q**5 - 184*q**3 + 2*q**5 + 44*q**4 + 16 - 324*q + 360*q**2.
-4*(q - 3)**3*(q - 1)**2
Let m be 7 - -1*(3 + 0). Let u be 39/15 - 6/m. What is x in 0 + 0*x**u + 1/2*x - 1/2*x**3 = 0?
-1, 0, 1
Let o(g) be the third derivative of 0*g**4 + 0*g**3 + 0 + 0*g + 1/480*g**6 + 1/240*g**5 - 8*g**2. Factor o(s).
s**2*(s + 1)/4
Let t = -32 + 36. Suppose 0 = -t*w - 0*w. What is k in 0*k + 1/2*k**4 + 0 + w*k**3 - 1/2*k**2 = 0?
-1, 0, 1
Let t be ((-504)/(-5))/(-14) + 8. Determine h so that t + 2/5*h**2 - 6/5*h = 0.
1, 2
Factor 36/5*t - 6 - 6/5*t**2.
-6*(t - 5)*(t - 1)/5
Let l(z) = -z**3 + z - 1. Let x(b) = -3*b**4 - 13*b**3 - 6*b**2 + 4*b - 4. Let a(r) = -4*l(r) + x(r). Factor a(d).
-3*d**2*(d + 1)*(d + 2)
Let o = -15/2 + 31/4. Factor 0*q + 1/4*q**4 - 1/2*q**2 + o + 0*q**3.
(q - 1)**2*(q + 1)**2/4
Let r(u) be the first derivative of -2/9*u**3 + 2 + 2/9*u - 2/9*u**2. Factor r(w).
-2*(w + 1)*(3*w - 1)/9
Let j be -7 + 7 + 7*1. Factor 3*o**4 - 3*o**5 - 7*o**4 + 2*o + o**5 + j*o**2 - 3*o**2.
-2*o*(o - 1)*(o + 1)**3
Let x**4 - 9*x**2 - 6*x**4 - 10*x**3 + 10*x + 5*x**2 + 9*x**2 = 0. What is x?
-2, -1, 0, 1
Let m(x) be the first derivative of -1/10*x**2 + 0*x - 1 - 1/15*x**3. Find n such that m(n) = 0.
-1, 0
Let p = 33 + -97/3. Let t be (-9)/(-21) + 114/126. Find i such that -p*i**2 - 2/3*i + t = 0.
-2, 1
Let z(k) be the second derivative of k**4/3 - 4*k**3/3 - 3*k**2 - 2*k. Let j(s) = 9*s**2 - 17*s - 13. Let r(f) = 6*j(f) - 13*z(f). Determine n so that r(n) = 0.
-1, 0
Determine y so that 9/5*y**3 + 12/5*y**2 - 6/5*y**4 + 0 - 12/5*y - 3/5*y**5 = 0.
-2, 0, 1
Let w be (-4 + (-274)/(-80))*-4. Let j(p) be the second derivative of -7/15*p**6 + w*p**5 + 0 - 9/2*p**4 - 2*p**2 + 13/3*p**3 - 2*p. Factor j(h).
-2*(h - 1)**3*(7*h - 2)
Let q(t) be the third derivative of -t**7/315 - t**6/90 + t**5/30 + t**4/9 - 4*t**3/9 + 11*t**2. Let q(h) = 0. Calculate h.
-2, 1
Let z be (3/(-4))/((-4)/16). Factor -5*f**3 - 3*f - z*f**4 - 4*f**3 - f**2 - 8*f**2.
-3*f*(f + 1)**3
Let j(b) = b**4 - 10*b**2 + 4*b + 11. Let h(t) = t**2 + 1. Let i(w) = h(w) + j(w). Factor i(r).
(r - 2)**2*(r + 1)*(r + 3)
Let n(a) be the third derivative of a**6/660 - a**5/165 - a**4/44 + 6*a**2. Solve n(t) = 0 for t.
-1, 0, 3
Let p(w) = -8*w - w**2 + 2 - 4 + w - 1. Let b be p(-6). Determine h so that -6/5*h**2 + 2/5*h + 0 - 8/5*h**b = 0.
-1, 0, 1/4
Let r(z) be the second derivative of z**5/8 - 15*z**4/8 + 10*z**3/3 + 4*z + 2. Factor r(f).
5*f*(f - 8)*(f - 1)/2
Let h be (-10)/(1 + (-5)/1). Let b(v) be the first derivative of -2*v + 1 + h*v**2 + 7/3*v**3. Factor b(y).
(y + 1)*(7*y - 2)
Let r(i) be the second derivative of -i*