tive of d**6/6 - d**5 + 25*d**4/12 - 5*d**3/3 - 13*d. Factor s(k).
5*k*(k - 2)*(k - 1)**2
Let w(l) = l**3 - l**2 + 3*l + 3. Let y(u) = 2*u**3 - 2*u**2 + 2*u + 2. Let m(p) = -2*w(p) + 3*y(p). Factor m(k).
4*k**2*(k - 1)
Let n(s) = s**2 + 12*s - 10. Let q be n(-13). Suppose 6 = c + q. Factor 0*w**2 - 2 - c*w**2 + 8*w + w**2 - 4*w.
-2*(w - 1)**2
Factor -4/5 + 2/5*v**2 + 6/5*v + 2/5*v**4 - 6/5*v**3.
2*(v - 2)*(v - 1)**2*(v + 1)/5
Let 0*n**2 + 2/13*n - 2/13*n**3 + 0 = 0. What is n?
-1, 0, 1
Let j(u) = u - 12. Let x be j(15). Let -h**2 - x*h**2 + 8*h**2 = 0. What is h?
0
Let r(c) be the first derivative of 3/11*c**2 - 1/11*c**4 - 6/55*c**5 + 4/33*c**3 - 1/33*c**6 + 2 + 2/11*c. Factor r(l).
-2*(l - 1)*(l + 1)**4/11
Suppose 1 = 2*l - 3. Let z be l/(2*1/5). What is b in 2*b**4 + 6*b**2 - 6*b**3 - 2*b + z - 5 = 0?
0, 1
Suppose -2*u = -3*u + 2. Suppose 0 = -u*y + 5*p - 21, -y - y + 4*p = 16. Suppose 2/7*a**y + 0 + 0*a = 0. What is a?
0
Let c(j) = -j**3 + 7*j**2 - 4*j - 8. Let q be c(6). Suppose -13 = -5*o - 3. Factor 2*t**2 - o*t - q - 3*t + 3*t.
2*(t - 2)*(t + 1)
Solve 8/5*i + 12/5*i**3 - 4*i**5 + 0 - 28/5*i**2 + 28/5*i**4 = 0.
-1, 0, 2/5, 1
Let d(x) = 3*x. Let j be d(1). Suppose -1 = -2*w + j. Solve -1/2*g**3 + 1/2*g + 0 - 1/2*g**4 + 1/2*g**w = 0.
-1, 0, 1
Let f(m) be the first derivative of -3*m**4/2 + 14*m**3/3 - 8*m + 10. Factor f(c).
-2*(c - 2)*(c - 1)*(3*c + 2)
Let h(b) be the first derivative of -b**4/20 + 4*b**3/15 - 2*b**2/5 + 10. Factor h(q).
-q*(q - 2)**2/5
Let h(c) be the second derivative of c + 1/24*c**3 + 0*c**2 + 0 + 1/48*c**4. Suppose h(r) = 0. What is r?
-1, 0
Let i(c) be the third derivative of c**5/6 - 25*c**4/24 + 5*c**3/3 - 25*c**2. Factor i(f).
5*(f - 2)*(2*f - 1)
Let l(n) be the second derivative of -n**6/270 + n**4/36 - n**3/27 + 12*n. Factor l(x).
-x*(x - 1)**2*(x + 2)/9
Let v(g) be the third derivative of g**6/240 + g**5/24 - 17*g**2. Factor v(r).
r**2*(r + 5)/2
Let a(z) be the first derivative of z**5/60 + z**4/36 - 2*z - 5. Let d(x) be the first derivative of a(x). Factor d(b).
b**2*(b + 1)/3
Factor 0*x**3 - 2*x**2 - 264*x + 264*x + 5*x**3.
x**2*(5*x - 2)
Let j(i) be the second derivative of i**6/15 + i**5/5 + 5*i**4/24 + i**3/12 - 2*i. Factor j(x).
x*(x + 1)*(2*x + 1)**2/2
What is t in 5*t**5 + 10*t**2 - 4*t - 6*t**3 - 10*t**5 - 2*t**4 + 7*t**5 + 0*t**2 = 0?
-2, 0, 1
Let g(u) be the second derivative of -3/20*u**5 - 1/2*u**3 + 0 + 1/2*u**4 + 0*u**2 + 6*u. Factor g(c).
-3*c*(c - 1)**2
Let r(d) be the first derivative of d**5/70 - d**4/21 - d**3/21 + 2*d**2/7 + 5*d - 6. Let c(q) be the first derivative of r(q). Factor c(p).
2*(p - 2)*(p - 1)*(p + 1)/7
Let c(b) be the first derivative of -3*b**5/2 + 9*b**4/2 + b**3/2 - 9*b**2 + 6*b - 22. Suppose c(m) = 0. Calculate m.
-1, 2/5, 1, 2
Let h(d) = -d**3 + 5*d + 2*d**2 + 0 + 2*d**2 + 1. Let o be h(5). Factor n**3 + 5*n + 9*n**2 - 5*n**2 + 1 + o.
(n + 1)**2*(n + 2)
Factor -4/3*q + 4/3*q**2 + 0 + q**3 - 4/3*q**4 + 1/3*q**5.
q*(q - 2)**2*(q - 1)*(q + 1)/3
Suppose 4*u - 8*s + 4*s = 4, -s - 1 = 5*u. Suppose -w - 5*z = -7, 5*z - 6 = -1. Suppose u + 5/2*x**w + x = 0. What is x?
-2/5, 0
Let n(u) = -u**2 - 4*u + 1. Let s be n(-3). Suppose -4*r = -s - 4. Suppose 0*k**r + 2*k + 0 + k**2 + 0 = 0. What is k?
-2, 0
Let b(s) = -s**2 + 3*s - 2. Let i(k) = 2 - k**2 + 2*k - 3 - 1 + k. Let w(f) = -3*b(f) + 2*i(f). Factor w(t).
(t - 2)*(t - 1)
Find d such that 120/7*d**2 + 153/7*d + 3*d**3 - 54/7 = 0.
-3, 2/7
Let w(z) be the first derivative of -1/6*z**2 + 3 + 0*z + 1/9*z**3. Factor w(b).
b*(b - 1)/3
Let d(h) be the second derivative of 4*h + 2/15*h**5 + 0*h**2 + 1/9*h**3 - 1/30*h**6 - 7/36*h**4 + 0. Suppose d(j) = 0. What is j?
0, 2/3, 1
Let f(i) = -4*i**3 + 7*i**2 - 5*i + 2. Let k(g) = -g**3 + g**2 + g - 1. Let x(v) = f(v) + 2*k(v). Factor x(c).
-3*c*(c - 1)*(2*c - 1)
Let k(m) be the third derivative of -m**9/3024 + m**7/840 - m**3/6 - m**2. Let r(b) be the first derivative of k(b). Solve r(s) = 0.
-1, 0, 1
Suppose 68 - 86 = -9*b. Factor 1/4*j**b + 0*j - 1/4.
(j - 1)*(j + 1)/4
Let -1/2 + 2/3*l - 1/6*l**2 = 0. What is l?
1, 3
Let x = -17/3 - -6. Let -x*o - 1/3*o**3 + 0 + 2/3*o**2 = 0. What is o?
0, 1
Suppose -3*b + 110 = 104. Suppose -3/2 - 3/2*n**3 + 3/2*n**b + 3/2*n = 0. What is n?
-1, 1
Let x(z) be the first derivative of 0*z**2 + 1/16*z**4 + 0*z + 1 - 1/12*z**3. Let x(q) = 0. What is q?
0, 1
Solve 4/3 - 16/3*a - 16/3*a**3 + 8*a**2 + 4/3*a**4 = 0 for a.
1
Let k(g) be the second derivative of -g**4/48 - g**3/24 + 6*g. Solve k(y) = 0 for y.
-1, 0
Let f(w) = 48*w**2 - 1. Let d be f(-1). Let l = -187/4 + d. Factor -1/4 - l*m**2 + 1/2*m.
-(m - 1)**2/4
Let x = 51 - 457/9. Factor x*u**4 + 2/9*u**5 - 4/9*u**2 + 2/9 - 4/9*u**3 + 2/9*u.
2*(u - 1)**2*(u + 1)**3/9
Let q(d) = 8*d**4 - 12*d**3 + 8*d**2 + 2*d. Let g(h) = -h**5 - 15*h**4 + 23*h**3 - 17*h**2 - 5*h. Let l(y) = -2*g(y) - 5*q(y). Factor l(r).
2*r**2*(r - 3)*(r - 1)**2
Factor 0 + 4/5*h - 6/5*h**2 + 2/5*h**3.
2*h*(h - 2)*(h - 1)/5
Let u(x) be the second derivative of -x**7/105 - x**6/25 - 3*x**5/50 - x**4/30 + 2*x - 22. Factor u(l).
-2*l**2*(l + 1)**3/5
Suppose 5*z + 4*w + 3 - 5 = 0, 2*w = -4. Let c(y) = 7*y**2 - 4*y. Let a(b) = 0*b**2 + b**2 - 3*b**2 + b**2 + b. Let f(d) = z*c(d) + 6*a(d). Factor f(l).
2*l*(4*l - 1)
Let g(d) = -6*d**4 + 5*d**3 + 16*d**2 - 18*d + 8. Let n(k) = -k**4 + k**3 + k**2. Let h(w) = -g(w) + 5*n(w). Let h(m) = 0. What is m?
-4, 1, 2
Suppose 0*h + 0*h**2 + 4/15*h**3 - 2/15*h**4 + 0 = 0. Calculate h.
0, 2
Factor 152/5*c + 252/5*c**2 + 162/5*c**3 + 27/5*c**4 + 32/5.
(c + 4)*(3*c + 2)**3/5
Let o = 5/18 - 1/36. Factor 1/2 + o*s**2 - 3/4*s.
(s - 2)*(s - 1)/4
Suppose 0 = -4*z + 1 + 23. Factor 2*j**2 + 2*j**4 + 4*j**2 - 2*j + 0*j**4 - z*j**3 + 0*j.
2*j*(j - 1)**3
Solve 1/3*f**2 - 1/6*f - 1/3 + 1/6*f**3 = 0.
-2, -1, 1
Let c(u) be the third derivative of 0 + 0*u + 1/9*u**3 + 0*u**4 - 4*u**2 - 1/90*u**5. Solve c(k) = 0.
-1, 1
Let m(p) be the second derivative of -p**6/75 + p**5/50 + p**4/30 - p**3/15 + 3*p. Solve m(c) = 0 for c.
-1, 0, 1
Let k = 52 + -155/3. Let d(l) be the first derivative of 1/3*l + 1/15*l**5 - 2/3*l**2 - k*l**4 + 2/3*l**3 + 3. Suppose d(n) = 0. What is n?
1
Suppose 4*m = 2*m + 10. Solve -m*d**2 + 6*d**2 - 9 - 12*d - 4*d**2 = 0 for d.
-3, -1
Let s(z) be the second derivative of 1/3*z**2 + 1/3*z**5 + 5/9*z**4 + 3*z + 0 + 1/9*z**6 + 1/63*z**7 + 5/9*z**3. Determine b, given that s(b) = 0.
-1
Let w(o) be the first derivative of o**6/40 + o**5/20 - o**4/4 - 2*o**2 - 2. Let k(q) be the second derivative of w(q). Let k(a) = 0. Calculate a.
-2, 0, 1
Let d(w) be the first derivative of -w**4/4 - w**3/2 + 5*w - 3. Let o(h) be the first derivative of d(h). Factor o(p).
-3*p*(p + 1)
Let q(d) = 13*d**2 - 8*d - 10. Let t(m) = -7*m**2 + m - 5. Let u(l) = l**2 + 1. Let o(v) = -t(v) - 6*u(v). Let a(p) = -22*o(p) + 2*q(p). Factor a(c).
2*(c + 1)*(2*c + 1)
Let k(f) = -6*f**2 + 78*f - 504. Let q(p) = 11*p**2 - 156*p + 1009. Let y(m) = 5*k(m) + 3*q(m). Determine z, given that y(z) = 0.
13
Determine g, given that -145*g - 193 - 71*g - 2*g**3 - 445 - 36*g**2 + 206 = 0.
-6
Let f = -17 - -17. Let y(q) be the second derivative of f*q**2 + 1/3*q**3 - 1/10*q**5 + 0 + 1/6*q**4 - 1/15*q**6 + 2*q. Factor y(p).
-2*p*(p - 1)*(p + 1)**2
Let s = 273 - 273. Factor 7/3*y**4 + 11/3*y**2 - 2/3*y + s - 16/3*y**3.
y*(y - 1)**2*(7*y - 2)/3
Let d be (8*(-3 + 2))/(-2). Let 1/3*i**d + 0 - 5/3*i**2 - 2/3*i - i**3 + 1/3*i**5 = 0. What is i?
-1, 0, 2
Let v(f) = f**5 - f**4 - f**3 - f**2 - f - 1. Let w(j) = 30*j**5 - 65*j**4 + 15*j**3 - 5*j**2 - 5*j - 5. Let y(p) = -5*v(p) + w(p). Let y(u) = 0. Calculate u.
0, 2/5, 2
Suppose 6*q - 26 = 4. Let v(a) be the first derivative of 0*a + 8/15*a**3 - 4/15*a**6 + 1/5*a**2 + 3/10*a**4 - 1 - 8/25*a**q. Let v(n) = 0. What is n?
-1, -1/2, 0, 1
Let v(z) be the first derivative of -z**5/20 + z**4/2 - 3*z**3/2 - z**2 + 4. Let i(j) be the second derivative of v(j). Solve i(u) = 0 for u.
1, 3
Let n(h) be the second derivative of 9/4*h**2 + h + 5/8*h**4 + 3/40*h**5 + 0 + 7/4*h**3. Solve n(z) = 0 for z.
-3, -1
Let z(j) = -j**2 + 5*j - 1. Let u be z(4). Suppose 3*r - 5*p = 14, -r + 4 = -2*p - 1. Factor 3*s**3 - u*s**r + s**4 + s**2 + 2*s**3.
s**2*(s + 1)**2
What is g in -1/2*g + 0 - 1/2*g**3 - g**2 = 0?
-1, 0
Find l, given that -2/3*l*