 3*l**2 - 9*l + 9. Let h(m) = 9*a(m) - 4*j(m). Factor h(p).
-p**2*(p - 3)*(p - 1)**2
Let j(u) be the third derivative of -u**6/40 + u**4/8 + 17*u**2. Factor j(w).
-3*w*(w - 1)*(w + 1)
Let u(m) = 4*m**3 - 13*m**2 + 2*m + 17. Let b(g) = g**3 - g**2 - g - 1. Let x(h) = b(h) - u(h). Factor x(c).
-3*(c - 3)*(c - 2)*(c + 1)
Let -1 - 3*j - 1 + 6*j**5 - 4*j**5 + 5*j**2 + 19*j**4 - 10*j**4 + 13*j**3 = 0. What is j?
-2, -1, 1/2
Let d(f) be the second derivative of -f**7/15120 + f**6/2160 - f**5/720 + f**4/4 - 4*f. Let h(a) be the third derivative of d(a). Factor h(o).
-(o - 1)**2/6
Determine i so that 6/5*i**2 - 6/5 + 2/5*i - 2/5*i**3 = 0.
-1, 1, 3
Factor d**3 - 4*d - 7 + 0*d + 3 + d**3 + 3*d**2 - d**4.
-(d - 2)**2*(d + 1)**2
Let n(x) be the first derivative of 2 + 0*x + 0*x**2 + 1/9*x**3 + 1/15*x**5 - 1/6*x**4. Factor n(a).
a**2*(a - 1)**2/3
Let j(z) be the third derivative of z**6/60 - 18*z**2. Suppose j(y) = 0. What is y?
0
Let y = 13 + -10. Let r(u) be the first derivative of 1/3*u + 1/9*u**y + 1 - 1/3*u**2. Factor r(x).
(x - 1)**2/3
Let t be (-3 + 4)*10/2. Suppose -t*r + 35 + 5 = 0. Factor r*v - 3*v**2 - v**2 - 8 + 2*v**2.
-2*(v - 2)**2
Let r(z) be the second derivative of z**6/480 - z**5/240 - z**4/48 - 3*z**2/2 + 2*z. Let f(o) be the first derivative of r(o). Factor f(g).
g*(g - 2)*(g + 1)/4
Let i(x) = -45*x**5 - 65*x**4 - 20*x**3. Let u(w) = 22*w**5 + 32*w**4 + 10*w**3. Let c(l) = 3*i(l) + 5*u(l). Determine f so that c(f) = 0.
-1, -2/5, 0
Let u(b) = 3*b**3 - b**2 + 7*b + 2. Let a(n) = -n**3 + n**2 - 3*n - 1. Let j(x) = 9*a(x) + 4*u(x). Factor j(i).
(i + 1)**2*(3*i - 1)
Let z be ((-45)/20)/(3/(-8)). Factor 4*k**5 + 15*k**2 + 18*k**3 - 7*k**2 + z*k**3 + 18*k**4.
2*k**2*(k + 2)**2*(2*k + 1)
Factor 1/6*n**4 - 1/6*n + 1/2*n**2 - 1/2*n**3 + 0.
n*(n - 1)**3/6
Let k = -344 + 1034/3. Find c, given that -k*c**2 - 2/3*c**3 + 0*c + 0 = 0.
-1, 0
Let s(z) be the first derivative of z**4/16 - 5*z**3/12 + 3*z**2/4 - 33. Determine f so that s(f) = 0.
0, 2, 3
Let j(a) = -a**5 - 4*a**4 - a**3 - 2*a - 2. Let m(p) = p**5 + p**4 + p**3 - p - 1. Let g(n) = j(n) - 2*m(n). Let g(k) = 0. What is k?
-1, 0
Let z(q) be the first derivative of -q + 0*q**2 + 1 + 1/3*q**3. Factor z(o).
(o - 1)*(o + 1)
Let i(k) be the second derivative of -k**6/150 + k**4/60 - 3*k. Solve i(t) = 0 for t.
-1, 0, 1
Let p(k) = k**3 - k + 3. Let n be p(0). Factor -2 + 0 + 2 + 20*h**2 - 4*h - 25*h**n.
-h*(5*h - 2)**2
Let g(m) be the second derivative of 0*m**3 - 1/48*m**4 - 1/2*m**2 - 1/96*m**6 + 2*m - 7/240*m**5 + 0. Let k(x) be the first derivative of g(x). Factor k(c).
-c*(c + 1)*(5*c + 2)/4
Let h(f) be the second derivative of -f**8/1344 - f**7/280 - f**6/240 + f**5/120 - f**4/6 - 3*f. Let q(v) be the third derivative of h(v). Factor q(d).
-(d + 1)**2*(5*d - 1)
Suppose 3*c = m + 3*m + 3, 5*c - 19 = 2*m. Let s be ((-15)/(-4))/c + 0. Suppose -5/4*r**2 + s*r + 1/2 = 0. Calculate r.
-2/5, 1
Let g(q) be the second derivative of -q**4/16 + 3*q**2/2 + 18*q. Suppose g(h) = 0. Calculate h.
-2, 2
Let g(h) be the third derivative of -h**6/150 + h**5/300 + 11*h**4/120 + h**3/5 + 16*h**2. Factor g(c).
-(c - 2)*(c + 1)*(4*c + 3)/5
Let i(d) be the first derivative of d**6/6 - d**4 - 2*d**3/3 + 3*d**2/2 + 2*d + 6. Determine k, given that i(k) = 0.
-1, 1, 2
Let q(m) = m**3 + 4*m**2 + m - 1. Let f = 3 + -6. Let b be q(f). Suppose -2/3*u**4 + 4/3*u**2 + 2/3*u**b - 4/3*u**3 + 2/3*u - 2/3 = 0. What is u?
-1, 1
Let o be (-24)/(-40)*(88/4 + -4). Let -2/5*m**3 - o*m - 54/5 - 18/5*m**2 = 0. Calculate m.
-3
Let c be -1 + (-2)/2 - -2. Let v be (c/3 - -3) + 2. Solve 4*l**2 + 2 - 6*l**4 - 4*l**5 + 5*l**v + 6*l - 4*l**3 + 0*l - 3*l**5 = 0.
-1, 1
Let l(n) = -13*n**3 + 21*n**2 - 16*n + 8. Let w(r) = 25*r**3 - 42*r**2 + 32*r - 15. Let o(t) = -7*l(t) - 4*w(t). Factor o(a).
-(a - 1)*(3*a - 2)**2
Let y(n) be the second derivative of 7*n**4/72 + n**3/18 - 2*n. Factor y(f).
f*(7*f + 2)/6
Let m(j) be the first derivative of 2/5*j - 1/15*j**3 + 1/10*j**2 - 2. Factor m(o).
-(o - 2)*(o + 1)/5
Let k(h) be the second derivative of -h**6/10 + 3*h**5/4 - 9*h**4/4 + 7*h**3/2 - 3*h**2 - 2*h. Factor k(o).
-3*(o - 2)*(o - 1)**3
Let o(c) be the second derivative of c**5/40 - c**3/12 - 5*c. Determine r, given that o(r) = 0.
-1, 0, 1
Let s(b) be the third derivative of -b**5/140 - b**4/24 + b**3/7 - 5*b**2. Suppose s(a) = 0. What is a?
-3, 2/3
Suppose 2/3*u**4 + 2/3*u**3 + 0*u + 0 - 4/3*u**2 = 0. What is u?
-2, 0, 1
Suppose -3*h + 11 + 1 = 0. Solve -2*y**5 + 5*y**h - 2*y**4 - 5*y**4 + 0*y**4 = 0 for y.
-1, 0
Let o(w) = w - 8. Let t be o(6). Let v = 2 + t. Determine x so that -2*x**4 + 0 + v - 2*x**3 = 0.
-1, 0
Let k(h) be the first derivative of 3*h**5/5 + 15*h**4/4 + 9*h**3 + 21*h**2/2 + 6*h + 4. Factor k(q).
3*(q + 1)**3*(q + 2)
Factor 0*z**3 - 20*z + 4*z**3 + 0*z**2 + 4*z**4 - 12*z**2 - 8.
4*(z - 2)*(z + 1)**3
Let j = -3 + 5. Suppose g + 5*q + 10 = -5, 2*q - j = -2*g. Factor 2 + m**3 - g*m**3 - 2*m**5 + 6*m**4 - 2.
-2*m**3*(m - 2)*(m - 1)
Determine a, given that 4/5*a**2 + 14/5*a**4 + 18/5*a**3 + 0 + 0*a = 0.
-1, -2/7, 0
Factor -11*d - 7*d + 4*d**3 + 25*d - 11*d.
4*d*(d - 1)*(d + 1)
Let d(q) = 5*q + 99. Let a be d(-19). Solve -2/9*b**2 + 2/3*b**a + 0 - 4/9*b + 8/9*b**3 = 0 for b.
-1, 0, 2/3
Let k(n) be the second derivative of -n**4/3 - 20*n**3/3 + 22*n**2 - 2*n. Factor k(f).
-4*(f - 1)*(f + 11)
Let s(d) be the third derivative of d**6/80 - d**5/120 - 11*d**4/48 - 7*d**3/12 + 30*d**2. Find n such that s(n) = 0.
-1, 7/3
Let p = -1 + 1. Suppose 5*j = -p*j. Factor 3*m**4 - 7*m**5 - 4*m**2 + j*m**5 + 8*m**5.
m**2*(m - 1)*(m + 2)**2
Let -4*c**4 - 14*c**3 + 20*c**2 + 7*c - 6*c**3 + 9*c - 2*c**5 - 16 + 6*c**5 = 0. Calculate c.
-2, -1, 1, 2
Let l(o) be the second derivative of -o**8/420 + o**7/840 + o**6/90 - o**5/120 - 7*o**3/6 - 8*o. Let s(p) be the second derivative of l(p). Factor s(z).
-z*(z - 1)*(z + 1)*(4*z - 1)
Determine y, given that 2/9*y**2 + 0*y - 2/9 = 0.
-1, 1
Suppose 0 = -8*b + 3*b + 15. Find w, given that 1/2*w**b - 1/2*w**2 - 1/2*w + 1/2*w**4 + 0 = 0.
-1, 0, 1
Suppose -4/7*k**2 + 0 + 24/7*k = 0. What is k?
0, 6
Let z(n) be the second derivative of -n**6/120 + n**5/60 + 3*n**2/2 + 4*n. Let a(r) be the first derivative of z(r). Let a(t) = 0. What is t?
0, 1
Let y(u) be the first derivative of 2*u**5/45 + u**4/18 - 2*u**3/27 - u**2/9 + 1. Factor y(w).
2*w*(w - 1)*(w + 1)**2/9
Let n = -37 + 37. Let i(y) be the second derivative of -1/75*y**6 - 1/105*y**7 - 2*y + 0*y**2 + 1/30*y**4 + 0 + 1/50*y**5 + n*y**3. Factor i(b).
-2*b**2*(b - 1)*(b + 1)**2/5
Let z(f) = -f**5 - 5*f**4 - 4*f**3 + 2*f**2 + 2*f + 2. Suppose 0*u + u - 1 = 0. Let o(l) = -l**4 - l**3 + l**2 + l + 1. Let s(j) = u*z(j) - 2*o(j). Factor s(h).
-h**3*(h + 1)*(h + 2)
Suppose 5*j - 6 = -11. Let u be -1 + (j - (1 - 3)). Let w**3 + 1/2*w**2 + 0*w - 3/2*w**4 + u = 0. What is w?
-1/3, 0, 1
Let x(h) = -h**2 + 1. Let q = -17 + 12. Let f(l) = -5*l**3 - 2*l**2 + 2*l + 5. Let m(g) = q*x(g) + f(g). Factor m(z).
-z*(z - 1)*(5*z + 2)
Let y(f) be the first derivative of 4/3*f**3 + 3 + f - 2*f**2. Find q, given that y(q) = 0.
1/2
Let y(z) = -3*z**4 - 20*z**3 - 9*z**2 + 15*z + 12. Let s(o) = -3*o**4 - 21*o**3 - 9*o**2 + 15*o + 12. Let x(p) = -5*s(p) + 6*y(p). Solve x(k) = 0 for k.
-4, -1, 1
Let y(q) be the second derivative of -q**5/10 - q**4/2 + 4*q**2 - 7*q. Let y(u) = 0. What is u?
-2, 1
Let x = 2 - 0. Suppose -j + 4*a = -3, -j - x*a = -0*j - 3. Solve -s**3 - s**3 + 2*s + 0*s**j = 0.
-1, 0, 1
Let i(f) be the second derivative of -3*f**5/20 - f**4/4 + f**3 - 16*f. Solve i(h) = 0 for h.
-2, 0, 1
Let j(m) = m**5 + m**3 - m**2. Let k(z) = -8*z**5 - 28*z**4 - 64*z**3 - 16*z**2 + 64*z + 48. Let b(i) = 4*j(i) + k(i). Suppose b(p) = 0. Calculate p.
-3, -2, -1, 1
Let c(s) = s**2 + 5*s + 1. Let i(u) = u. Suppose -4 = 2*f + 8. Let r(n) = f*i(n) + 2*c(n). Let r(a) = 0. What is a?
-1
Suppose 0 = -4*o + 5*o - 2. Let y be 6/12*1/o. Factor 0*a - y*a**4 + 0 + 0*a**3 + 1/4*a**2.
-a**2*(a - 1)*(a + 1)/4
Suppose -2*q - 6 = -4*q. Factor 1/2*g**4 + 0*g + 0 - 1/2*g**2 + 0*g**q.
g**2*(g - 1)*(g + 1)/2
Let c(a) = -8*a**3 - 4*a**2 + 2*a - 2. Let d be (-1*(3 - 12))/1. Let o(z) = 33*z**3 + 16*z**2 - 8*z + 9. Let m(l) = d*c(l) + 2*o(l). What is j in m(j) = 0?
-1, 0, 1/3
Let r(q) be the third derivative of -q**6/360 +