 that s(n) = 0.
-1, 1, 2
Suppose -20 - 14 = -2*m. Factor -m*a**2 + 2*a - 5*a + 16*a**2.
-a*(a + 3)
Solve 0 - 1/4*i**5 - i**4 - 1/4*i - i**2 - 3/2*i**3 = 0.
-1, 0
Let b(k) be the third derivative of -2*k**7/105 + k**6/9 - k**5/15 - 3*k**2. Factor b(j).
-4*j**2*(j - 3)*(3*j - 1)/3
Let f(k) = 6*k**3 + k**4 - 2*k**3 + 6*k**5 + 5*k**2 - 5*k + 5*k**3. Let w(r) = 5*r**5 + 8*r**3 + 4*r**2 - 4*r. Let c(j) = -4*f(j) + 5*w(j). Factor c(z).
z**3*(z - 2)**2
Let n(k) be the third derivative of -k**7/1155 + k**6/220 - k**5/330 - k**4/44 + 2*k**3/33 + 8*k**2. Suppose n(f) = 0. Calculate f.
-1, 1, 2
Let t be ((-6)/(-5))/(8/(-280)). Let f be (8/t)/((-4)/18). What is r in 0 + 0*r**3 + f*r**4 - 8/7*r**2 + 0*r - 2/7*r**5 = 0?
-1, 0, 2
Let w be (-60)/(-24)*2/10. Determine l, given that -1/2*l**3 + w*l + 0 + 0*l**2 = 0.
-1, 0, 1
Let l be 2/((1 - 2)/1). Let x be l/(-5) - 16/140. Factor x*d**3 - 2/7*d + 0 + 0*d**2.
2*d*(d - 1)*(d + 1)/7
What is p in 12*p**3 + 19*p**2 + 9*p**2 + 24*p**3 - 8*p = 0?
-1, 0, 2/9
Let r = -2 - -8/3. Let w(i) = i**2 + 14*i + 16. Let d be w(-13). Solve 0 + 4/3*h**2 - 2/3*h - r*h**d = 0 for h.
0, 1
Let x(a) = a**2 + 2*a + 3. Let f(t) = -t + 1. Let h(b) = -5*f(b) + 5*x(b). Factor h(i).
5*(i + 1)*(i + 2)
Let r(b) = b**4 + b**3 - b**2 - 8*b. Let y(i) = i**4 + i**3 - i**2 - 7*i. Let m(l) = -6*r(l) + 7*y(l). Factor m(g).
g*(g - 1)*(g + 1)**2
Let b(z) be the first derivative of z**6/1440 - z**5/480 + 2*z**3/3 - 1. Let s(w) be the third derivative of b(w). Factor s(q).
q*(q - 1)/4
Let w = -106 - -111. Let z(m) be the third derivative of 0*m - 3/10*m**3 + 0 - 2*m**2 + 1/20*m**4 - 1/300*m**w. Solve z(l) = 0.
3
Suppose k - 4*u + 5*u = 0, 2 = -4*k - 5*u. Determine w, given that -4/3*w - k + 2/3*w**2 = 0.
-1, 3
Let h be (3 + -2)/(8/32). Factor 3 - 28*z + 1 - 16 + h*z - 3*z**3 - 15*z**2.
-3*(z + 1)*(z + 2)**2
Let c = -1857/2 - -995. Let g = c - 65. Factor -g*n + 3/4*n**2 + 3/4.
3*(n - 1)**2/4
Let h(o) be the second derivative of o**5/4 - 25*o**4/12 - 5*o**3/6 + 25*o**2/2 + 20*o. Factor h(w).
5*(w - 5)*(w - 1)*(w + 1)
Factor 2/3*q**4 - 2*q + 2/3*q**2 - 4/3 + 2*q**3.
2*(q - 1)*(q + 1)**2*(q + 2)/3
Let x(n) = -4*n**4 - 12*n**3 - 16*n**2 - 6*n. Let g(q) = 9*q**4 + 25*q**3 + 32*q**2 + 11*q. Let l(d) = 4*g(d) + 10*x(d). Suppose l(v) = 0. What is v?
-2, -1, 0
Let s = -16 - -19. Let b(m) be the first derivative of 2/45*m**5 + 0*m**2 + 0*m**s + 0*m - 3 + 0*m**4. Solve b(n) = 0.
0
Suppose 1 - 2 = 2*o + 3*w, -w - 3 = 0. Factor 2*z - 9*z**3 + 11*z**3 - 2 + 2*z**2 - o*z**3.
-2*(z - 1)**2*(z + 1)
Let w = 48 - 142/3. Factor 4/3*v**3 - w*v**5 - 2/3*v + 2/3 - 4/3*v**2 + 2/3*v**4.
-2*(v - 1)**3*(v + 1)**2/3
Let -d**2 + 9*d + 5*d**2 - 2 - 15*d + 4*d**2 = 0. What is d?
-1/4, 1
Let q(r) be the second derivative of r**7/210 + r**6/60 - r**5/30 + 2*r**3/3 + 3*r. Let h(t) be the second derivative of q(t). Solve h(d) = 0 for d.
-2, 0, 1/2
Suppose 4*u = 15 - 7. Factor -9*q**3 - q**5 - 2*q**5 + 3*q**2 + 9*q**4 + 0*q**u.
-3*q**2*(q - 1)**3
Determine q, given that -2*q**2 + 4*q**3 - 266*q - 2*q**4 + 266*q = 0.
0, 1
Let r(q) be the first derivative of -q**4/20 - 22. Factor r(w).
-w**3/5
Let f(x) = -14*x**4 + 12*x**3 + 28*x**2 + 12*x - 32. Let n(c) = -c**4 + c**3 + c**2 + c. Let d(u) = -f(u) + 12*n(u). Factor d(o).
2*(o - 2)**2*(o + 2)**2
Let a(o) = o + 1. Let b(w) = 2*w**2 + 4*w + 2. Let m(k) = -6*a(k) + b(k). Factor m(c).
2*(c - 2)*(c + 1)
Let g(n) = n**4 - 8*n**3 - 20*n**2 - 24*n - 7. Let h(d) = 3*d**4 - 16*d**3 - 39*d**2 - 48*d - 13. Let t(j) = -5*g(j) + 2*h(j). Factor t(r).
(r + 1)**2*(r + 3)**2
Determine x so that 1/5*x**2 - 3/5*x**3 + 0*x + 0 - 4/5*x**4 = 0.
-1, 0, 1/4
Let d(b) = -b**2 + 10*b + 13. Let v be d(11). Factor 1/4*m**3 + 3*m - 3/2*m**2 - v.
(m - 2)**3/4
Suppose -75*w**2 - 99/2*w**3 - 34*w - 4 = 0. Calculate w.
-2/3, -2/11
Let o = 9 - 4. Suppose b = -0*b + o. Factor 2*f**5 + 15*f**3 + 2*f**b + 3*f + 13*f**4 + 7*f**2 - 2*f.
f*(f + 1)**3*(4*f + 1)
Let h(r) be the second derivative of r**5/20 - r**4/72 - r**3/6 + r**2/12 + 27*r. Let h(u) = 0. What is u?
-1, 1/6, 1
Let b(q) = q**4 - q**3 + 1. Let a(g) = 5*g**5 - 65*g**3 - 140*g**2 + 40*g + 155. Let y(h) = -a(h) - 5*b(h). Let y(o) = 0. Calculate o.
-2, 1, 4
Factor -3*m + 9 + 1/4*m**2.
(m - 6)**2/4
Let b(t) be the third derivative of -t**6/120 - 7*t**5/60 - t**4/3 - 4*t**3/3 - 4*t**2. Let a be b(-6). Find d, given that 3*d**2 - 5*d**2 + 6 - a = 0.
-1, 1
Suppose -3*z + 5*o = -39 + 13, -5*z + 6 = o. Find d such that z*d + 4*d + 2*d**2 - 4*d + 0*d**2 = 0.
-1, 0
Find b, given that -3/4*b**4 - 15/4*b**3 - 9/4*b**2 + 27/4*b + 0 = 0.
-3, 0, 1
Let j(c) be the first derivative of 7 + 0*c - 2/15*c**3 + 1/5*c**2. Find i, given that j(i) = 0.
0, 1
Let h(q) = -q**3 - q**2. Let r(m) = m**4 - 4*m**3 - 6*m**2 + 1. Let o(u) = -4*h(u) + r(u). Factor o(y).
(y - 1)**2*(y + 1)**2
Let l(r) be the second derivative of -1/15*r**6 - 1/18*r**4 + 0 + 0*r**3 - 1/10*r**5 + 2*r + 0*r**2 - 1/63*r**7. Solve l(d) = 0.
-1, 0
Factor -3*a**5 - 185 + 3*a**3 + 185.
-3*a**3*(a - 1)*(a + 1)
Factor -2*a**2 - 16*a**4 + 0*a**3 - 3*a**3 - 4*a**5 - 5*a**3 + 6*a**4.
-2*a**2*(a + 1)**2*(2*a + 1)
Let y = -779 + 2338/3. Factor 0 + y*g + 2/3*g**4 - 1/3*g**5 + 0*g**3 - 2/3*g**2.
-g*(g - 1)**3*(g + 1)/3
Let n be 2/(-7) - 24/14. Let s(a) = -a**2 + 12*a - 3*a**2 - 10*a + 2. Let g(y) = -8*y**2 + 4*y + 5. Let u(c) = n*g(c) + 5*s(c). Factor u(t).
-2*t*(2*t - 1)
Let d(n) be the third derivative of 0*n**4 + 0*n + 4*n**2 + 1/160*n**6 + 0*n**5 + 0 + 0*n**3. Factor d(g).
3*g**3/4
Factor 2/5*f**3 - 8/5 + 2/5*f**2 - 8/5*f.
2*(f - 2)*(f + 1)*(f + 2)/5
Let a = -1/12 + 3/4. Factor -a*y**3 - 2/9*y + 2/3*y**2 + 0 + 2/9*y**4.
2*y*(y - 1)**3/9
Let g(t) = 11*t - 14. Let z be g(7). Let f = z + -187/3. Factor 0 + 2/3*q**2 + f*q.
2*q*(q + 1)/3
Let g be -2*(-6)/(-18) - -1. Let u(h) be the first derivative of -4 - g*h**3 + 0*h**2 + 0*h. Factor u(o).
-o**2
Let x(c) be the third derivative of 0 - 1/6*c**4 + 0*c - 1/30*c**5 + 0*c**3 + 1/60*c**6 - 3*c**2. Let x(m) = 0. Calculate m.
-1, 0, 2
Factor -31*h**4 + 106*h**4 + 8*h**3 - 12 + 98*h - 38*h - 68*h**3 - 63*h**2.
3*(h - 1)*(h + 1)*(5*h - 2)**2
Let t = -11/14 + 27/14. Let o be (-8)/(-10)*10/7. Let -o - 2/7*p**2 - t*p = 0. Calculate p.
-2
Let z = -5 - 0. Let r(f) = 4*f**2 - f + 5. Let d = -2 + 4. Let g(v) = 2*v**2 + 2. Let a(c) = d*r(c) + z*g(c). Factor a(s).
-2*s*(s + 1)
Let t(n) be the first derivative of -n**9/1008 + n**7/140 - n**5/40 + 4*n**3/3 - 7. Let q(b) be the third derivative of t(b). Factor q(c).
-3*c*(c - 1)**2*(c + 1)**2
Let p be ((-50)/625)/(2/(-10)). Find a, given that -6/5*a**2 - p - 2/5*a**3 - 6/5*a = 0.
-1
Let z(p) be the second derivative of -50*p**7/21 - 2*p**6/3 + 66*p**5/5 - 44*p**4/3 + 16*p**3/3 - 3*p. Solve z(n) = 0 for n.
-2, 0, 2/5, 1
Factor -13*y**2 + 13*y**2 - 6*y + 6*y**3 - 15*y**2 + 15*y**4.
3*y*(y - 1)*(y + 1)*(5*y + 2)
Let a(p) = -5*p**2 - 15*p + 2*p**2 - 6*p**3 + p**3 - 11 + p**3. Let x(m) = 2*m**3 + 2*m**2 + 8*m + 6. Let c(b) = -6*a(b) - 11*x(b). Factor c(f).
2*f*(f - 1)**2
Let o(x) = 6*x**5 - 3*x**4 + 6*x**2 + 3. Let m(n) = 11*n**5 - 7*n**4 + 12*n**2 - n + 5. Let a(q) = 3*m(q) - 5*o(q). Factor a(v).
3*v*(v - 1)**3*(v + 1)
Factor -10*m**4 - 15*m**3 + 3*m + 17*m**4 + 24*m + 9*m**2 - 4*m**4.
3*m*(m - 3)**2*(m + 1)
Factor -2/7*j**5 - 4/7*j**2 + 0*j**3 + 2/7*j + 4/7*j**4 + 0.
-2*j*(j - 1)**3*(j + 1)/7
Suppose -2*s = 2*o - 8, 5*s + 2*o + 3 = 17. Factor 4*k**2 + k**s + 0*k - 4*k**2 + k.
k*(k + 1)
Let t(l) be the third derivative of 0 - 1/12*l**4 - 6*l**2 + 0*l**3 - 1/120*l**6 + 0*l + 1/20*l**5. Factor t(g).
-g*(g - 2)*(g - 1)
Let x = -1 + 3. Suppose -r = x*r. Solve -t**4 - 4/3*t + r + 7/3*t**3 + 0*t**2 = 0.
-2/3, 0, 1, 2
Let x = -7 + 11. Suppose 9*w = 4*w - 2*t + 13, -2*t - 2 = 0. Factor -h**w - 4*h**3 + x*h**3 - h**4 + h**2 + h**5.
h**2*(h - 1)**2*(h + 1)
Let t be (16/44)/((-50)/(-55)). Solve -2/5*u - t*u**2 + 0 + 2/5*u**3 + 2/5*u**4 = 0 for u.
-1, 0, 1
Let w(z) = -2*z - 8. Let a = -16 + 10. Let h be w(a). Factor -2*i**2 + 9*i**3 - 1 + i**2 + 3*i**4 - 9*i + h*i**2 - 5.
3*(i - 1)*(i + 1)**2*(i + 2)
Let 1/2*r - 5/4*r**4 + 1/4*r**5 + 0 - 7/4*r**2 + 9/4*r**3 = 0. Calculate r.
0, 1, 2
Let w be 4 - (2 + 2)/2. Factor 2 - 4 + 3 + w*t + 0*t**2 - 3*t**2.
-(t - 1)*(3*t + 1)
Let j be 2 + 1 + 0 + 1. Let o = j - 2. Factor 2*q**2 + q**o