*3 - k**3 + 4*k**4 = 0.
-1, 0
Let f(x) be the first derivative of 4*x - 3*x**2 + 1 + 2/3*x**3. Factor f(c).
2*(c - 2)*(c - 1)
Let y(i) be the first derivative of -1/2*i**4 - 3 + 1/6*i**6 + 0*i**5 + 0*i**3 + 0*i + 1/2*i**2. Factor y(p).
p*(p - 1)**2*(p + 1)**2
Let u = 22 - 18. Factor -20*b**u + 20*b**2 + 8*b + b**3 - 5*b**3 - 4*b**3.
-4*b*(b - 1)*(b + 1)*(5*b + 2)
Let x = 0 + 6. Suppose 0 = -4*j - x + 14. Solve -j*z**2 + 28*z**3 - 4 - 18*z + 13*z**5 + 15*z**5 + 34*z**3 + 78*z**4 = 0 for z.
-1, -2/7, 1/2
Factor 7*u**2 - 5*u**4 - 24*u**3 + 9*u**3 - 17*u**2.
-5*u**2*(u + 1)*(u + 2)
Factor 1/2*z + 0*z**2 + 0 - 3*z**3 - 3/2*z**5 + 4*z**4.
-z*(z - 1)**3*(3*z + 1)/2
Factor 1/2*x**2 + 3/4 + 7/4*x.
(x + 3)*(2*x + 1)/4
Let c be ((72/(-10))/6)/(6/(-15)). Let j(q) be the third derivative of 0*q**3 - c*q**2 + 0*q + 0*q**5 + 1/210*q**7 + 0*q**4 + 1/120*q**6 + 0. Factor j(p).
p**3*(p + 1)
Let y(o) be the second derivative of -o**6/225 + o**4/30 - 2*o**3/45 - o. Find q, given that y(q) = 0.
-2, 0, 1
Let n = 21 - 31. Let m(d) = -d**3 + d + 1. Let x(w) = 6*w**3 - 6*w - 5. Let b(a) = n*m(a) - 2*x(a). Factor b(u).
-2*u*(u - 1)*(u + 1)
Suppose q = -0*q. Let n(x) be the second derivative of -1/4*x**4 - 1/3*x**3 + 1/30*x**6 + 0*x**5 + 0*x**2 + q + 2*x. Factor n(d).
d*(d - 2)*(d + 1)**2
Let n = -1 - -3. Determine b so that 0*b**2 + b**3 + 6*b**2 - 2*b**n - 5*b**2 = 0.
0, 1
Let b(d) be the second derivative of -3*d**6/50 + 7*d**5/100 + d**4/30 - 34*d. Suppose b(i) = 0. Calculate i.
-2/9, 0, 1
Suppose 0 = 6*m - m - 10. Suppose -4*x = 2*r - m, -4 = -3*x + 3*r + 11. Let c**2 - 2 + 0*c**x - c**3 + c + 1 = 0. What is c?
-1, 1
Suppose -5*q - 27 = -o, -2*q + q = 2*o - 10. Let h(y) be the third derivative of 0*y + 0 + 0*y**3 + 0*y**5 - y**2 + 1/105*y**o + 0*y**4 + 0*y**6. Factor h(k).
2*k**4
Let t(o) be the third derivative of o**8/168 + 2*o**7/105 - o**6/60 - o**5/15 + 8*o**2. Find j, given that t(j) = 0.
-2, -1, 0, 1
Let o = 299/9 + -33. Let -o*n**2 + 0 + 2/9*n = 0. Calculate n.
0, 1
Let y = 384/7 - 761/14. Factor y*n**2 - 3*n + 9/2.
(n - 3)**2/2
Let r(g) = 17*g**4 - 12*g**3 + 4*g + 9. Let w(o) = -8*o**4 + 6*o**3 - 2*o - 4. Let z(l) = -4*r(l) - 9*w(l). Suppose z(v) = 0. Calculate v.
-1/2, 0, 1
Let g(z) = -2*z**2 - 4*z - 2. Let f(a) = -4*a**2 - 9*a - 5. Let i(w) = 2*f(w) - 5*g(w). Factor i(r).
2*r*(r + 1)
Let v(d) = 3*d**3 + 35*d**2 + 69*d + 32. Let z(j) = -j**3 - 17*j**2 - 35*j - 16. Let t(o) = 3*v(o) + 5*z(o). Factor t(w).
4*(w + 1)*(w + 2)**2
Let f(a) = a - 2. Let i be f(0). Let y = i - -4. Determine d so that 1/2*d**y + 0*d + 0 + 1/2*d**3 = 0.
-1, 0
Let u(f) = f**5 + f**4 - f**3 + f - 1. Let z(k) = 8*k**5 + 10*k**4 - 7*k**3 - 2*k**2 + 8*k - 8. Let y(m) = -18*u(m) + 2*z(m). Factor y(a).
-2*(a - 1)**3*(a + 1)**2
Let g be 2*2/(4 - 2). What is t in -1/3*t**g + 0 + 1/3*t**3 + 0*t = 0?
0, 1
Let n(g) = 6*g**2 - 22*g + 16. Let f(m) = m**2 - 1. Let c(t) = -4*f(t) + n(t). Factor c(i).
2*(i - 10)*(i - 1)
Let c(q) be the second derivative of -q**6/6 - q**5 - 25*q**4/12 - 5*q**3/3 + 12*q. Factor c(y).
-5*y*(y + 1)**2*(y + 2)
Let b be (-6)/(-1 + -1) - 1. Solve i**b + 0 + 1/3*i + 2/3*i**3 = 0.
-1, -1/2, 0
Let z(j) = -j**3 + 11*j**2 - 9*j - 2. Let s be z(10). Factor 2*x - x**2 + x**2 - s*x - 3*x**2.
-3*x*(x + 2)
Let c be -1 + -3 + 234/45. Solve 0 + 0*k + c*k**4 + 0*k**3 + 0*k**2 + 3/5*k**5 = 0 for k.
-2, 0
Let z = -5 + 7. Let c = 25 - 23. Factor 0*y**c - 2*y**z - y - y.
-2*y*(y + 1)
Suppose 7 = -5*z - 5*y - 3, -3*y - 12 = z. Let t = 5 - z. Factor -q**2 - 4*q**3 - 3*q**t + 2*q + 6*q**3.
2*q*(q - 1)**2
Let s be (0/(1 - -2))/(-3). Solve s*d - 2/5*d**2 + 2/5 = 0.
-1, 1
Let o(w) = 7*w**2 + 12*w + 10. Let g(t) = 15*t**2 + 25*t + 21. Let n(q) = 6*g(q) - 13*o(q). Let f be n(-4). What is l in -1 + f*l - l**2 - 1 - l**2 = 0?
1
Let -2 - 28*h + 3*h**2 + 10 + 6*h**2 + 3*h**2 = 0. What is h?
1/3, 2
Let s(j) = 9*j + 104. Let i be s(-11). Factor 1/5 + 9/5*x**4 - 2/5*x**i - 16/5*x**3 + 14/5*x**2 - 6/5*x.
-(x - 1)**4*(2*x - 1)/5
Factor 1/3*z**2 - 2/3*z**4 + 0 + 1/3*z**3 + 0*z.
-z**2*(z - 1)*(2*z + 1)/3
Suppose -4*z + 3*p + 6 = -5, -5*z - 2*p + 8 = 0. Suppose -3*b**z + 2*b**4 + 0*b**5 + b**4 + b**3 + 3*b**5 - 4*b**3 = 0. What is b?
-1, 0, 1
Let a = -8/87 + 301/435. Factor 3/5*y + 0 + a*y**2.
3*y*(y + 1)/5
Let y = -164 + 167. Factor 0*x + 4/5*x**y + 0 - 2/5*x**4 - 2/5*x**5 + 0*x**2.
-2*x**3*(x - 1)*(x + 2)/5
Let u(g) = -3*g**5 - 3*g**4 + 9*g**3 + 3*g**2 - 12*g + 6. Let s(f) = f**4 - f**2 + f - 1. Let a(m) = -6*s(m) - u(m). Find l, given that a(l) = 0.
-1, 0, 1, 2
Factor o + 2/5*o**2 + 3/5.
(o + 1)*(2*o + 3)/5
Let s be 10/(-25) + (-2)/(-5). Determine c so that 0 + 2/9*c**5 + 0*c + s*c**4 + 0*c**2 - 2/9*c**3 = 0.
-1, 0, 1
Let w(y) be the second derivative of y**7/42 + y**6/5 + 9*y**5/20 + y**4/3 + 26*y. Factor w(l).
l**2*(l + 1)**2*(l + 4)
Factor -5*s**2 + 7*s**2 - 4*s**2 - 2*s.
-2*s*(s + 1)
Let p(q) = 3*q**2 - 8*q + 8. Let s(y) = -3*y**2 + 7*y - 7. Let c(k) = 5*p(k) + 4*s(k). Let c(v) = 0. Calculate v.
2
Determine t, given that 3/5*t**4 + 21/5*t**3 + 36/5*t + 0 + 48/5*t**2 = 0.
-3, -2, 0
Let s(p) = -3*p**3 + 11*p**2 + 2*p + 5. Let v(d) = 10*d**3 + 5*d - 9*d - 2*d - 32*d**2 - 14. Let q(l) = 14*s(l) + 5*v(l). Determine y, given that q(y) = 0.
-1/4, 0, 1
Let y(c) = -c**3 + c**2 + c - 1. Let b(n) = 12*n**3 - 14*n**2 - 8*n + 10. Let z(f) = -2*b(f) - 20*y(f). Determine m so that z(m) = 0.
0, 1
Let c(q) be the first derivative of -q**6/100 + q**5/75 + q**4/20 - 2*q**3/15 + 5*q**2/2 + 4. Let z(g) be the second derivative of c(g). Factor z(p).
-2*(p - 1)*(p + 1)*(3*p - 2)/5
Let x(g) be the second derivative of -1/4*g**4 - 1/3*g**3 - g + 0 + 1/2*g**2. Factor x(v).
-(v + 1)*(3*v - 1)
Let t be (-15)/(-84) + 6/96*20. Suppose -l - 1 + 4 = 0. Factor 6/7*h**2 + 4/7*h + 0 - t*h**l.
-2*h*(h - 1)*(5*h + 2)/7
Let j = 16 - 7. Suppose j = 2*r - 9. Factor -2*v**2 + 2*v**2 - 5*v**2 + 2*v**2 - 9*v**3 - 3*v**5 - r*v**4.
-3*v**2*(v + 1)**3
Let b(d) be the second derivative of d**4/42 - 8*d**3/21 - 9*d**2/7 - 2*d - 13. Determine u, given that b(u) = 0.
-1, 9
Let t(f) be the second derivative of f**4/16 + f**3/2 + 3*f**2/2 + f. Solve t(q) = 0.
-2
Let q = -12 - -12. Let a be q/8 + (-2)/(-4). Factor a*x - 3/4*x**2 + 0.
-x*(3*x - 2)/4
Let i(u) be the third derivative of u**7/315 - u**6/180 - u**5/30 + u**4/36 + 2*u**3/9 + 24*u**2. Factor i(j).
2*(j - 2)*(j - 1)*(j + 1)**2/3
Let j(q) be the third derivative of 4*q**2 + 0*q - 1/84*q**4 - 1/210*q**5 + 0 + 0*q**3. Determine v so that j(v) = 0.
-1, 0
Let r(a) be the second derivative of a**5/5 - 2*a**3 - 4*a**2 - 12*a. Suppose r(c) = 0. Calculate c.
-1, 2
Let m(i) be the second derivative of -i**8/4320 + i**7/1260 - i**6/1620 + i**4/12 + 5*i. Let l(q) be the third derivative of m(q). Factor l(b).
-2*b*(b - 1)*(7*b - 2)/9
Let v be (1 - 2)/(-106 - -6). Let o(l) be the second derivative of 1/60*l**4 + 0 + 1/30*l**3 + 2*l - v*l**5 - 1/10*l**2. What is u in o(u) = 0?
-1, 1
Suppose 6 - 2*l - 4*l + 2*l - 2*l**2 = 0. What is l?
-3, 1
Suppose v - 2 - 23 = 0. Suppose -j - v = 5*l, -3*j + l + 3 + 2 = 0. Factor 0*w + 1/2*w**2 + j.
w**2/2
Let q be 4 + -2 + 126/(-90). Factor q*j + 2/5 + 1/5*j**2.
(j + 1)*(j + 2)/5
Let q(g) be the first derivative of 3*g**2 + 6 + 2*g + 1/2*g**4 + 2*g**3. Let q(t) = 0. Calculate t.
-1
Let w(m) be the first derivative of 2*m**3/3 + 4*m**2 + 6*m - 9. Let w(i) = 0. What is i?
-3, -1
Factor -2/7*b**2 - 8/7 - 17/7*b.
-(b + 8)*(2*b + 1)/7
Let a(j) be the third derivative of j**6/600 + j**5/100 + j**4/40 + j**3/30 - 6*j**2. Factor a(o).
(o + 1)**3/5
Suppose -c + 7 = 5. Suppose 4 - 7 = -v - 3*s, 0 = -4*v - c*s + 12. Factor 0*d**2 - 4/3*d**v + 0 + 2/3*d + 2/3*d**5 + 0*d**4.
2*d*(d - 1)**2*(d + 1)**2/3
Let i be (-6)/((294/(-4))/7). Factor 10/7*o**2 - 6/7*o**3 + i*o + 0.
-2*o*(o - 2)*(3*o + 1)/7
Let l(y) = y**2 + 5*y - 7. Let b be l(-3). Let a = 40/3 + b. Factor -a*z**3 + 0*z**2 + z + 2/3.
-(z - 2)*(z + 1)**2/3
Let -3*j**4 + 2*j**3 + j**3 + 0*j**4 + 2*j**4 = 0. Calculate j.
0, 3
Let z be 2*1*(-28)/(-168). Find x such that -1/3*x**4 + z*x**2 + 0 - 1/3*x**3 + 1/3*x = 0.
-1, 0, 1
Let t(q) be the first derivative of 12*q**5/5 - 9*q**4/4 - q**3 - 25. Let t(w) = 0. What is w?
-1/4, 0, 1
Let c = -2 - -5. Let t**3 - 6*t**c - 2*t**2 + t + 3*t + 3*t**3 = 0. Calculate t.
-2, 0, 1
Let n(y) = y*