**2 - 4*o**r + 3*o**3 + 6 + 15*o + o**2.
3*(o + 1)**2*(o + 2)
Let p(u) = -2*u - 9. Let v be p(-6). Suppose -v*a + 4 = -2*a. Factor 0 + 0*z**2 - 1/4*z**a + 0*z + 1/4*z**3.
-z**3*(z - 1)/4
Let x(j) = -j**3 - 4*j**2 - j - 2. Let w(k) = 2*k**3 + 11*k**2 + 2*k + 7. Let v(y) = -2*w(y) - 7*x(y). Factor v(i).
3*i*(i + 1)**2
Let v(q) = -q**3 + 4*q**2 + 2*q + 5. Let p be v(5). Let b be (8/12)/(p/(-6)). Factor -4/5 - b*u**3 - 2*u - 8/5*u**2.
-2*(u + 1)**2*(u + 2)/5
Suppose -6*p = -p + m + 112, 2*m + 4 = 0. Let w = 22 + p. Factor 0*u**2 - 2/3*u**3 + 0 + w*u + 1/3*u**4.
u**3*(u - 2)/3
Suppose -5*o + 40 = -4*a, 6*o - 28 = 4*o + 4*a. Factor -3/5*n**o + 0*n + 0 - 6/5*n**3 - 3/5*n**2.
-3*n**2*(n + 1)**2/5
Let z(s) be the first derivative of -s**6/1800 + s**5/300 - s**4/120 - s**3/3 + 4. Let c(p) be the third derivative of z(p). Factor c(m).
-(m - 1)**2/5
Let k(x) be the third derivative of 0*x + 8*x**2 + 0*x**3 - 11/270*x**5 - 1/54*x**4 - 4/135*x**6 + 0 - 1/135*x**7. Factor k(o).
-2*o*(o + 1)**2*(7*o + 2)/9
Let h = -6 + 9. Let a be -3*(-2 - (2 - -2)). Determine t so that -36*t**4 - t - 4 + a*t**5 - t - 4*t + 4*t**h + 24*t**2 = 0.
-2/3, -1/3, 1
Suppose 0 = -5*p + j - 0*j + 17, j = -4*p + 19. Suppose -2*f + m + 9 = 0, -m - p = -f + 3. Factor -2/7*z + 2/7*z**4 + 0 + 2/7*z**3 - 2/7*z**f.
2*z*(z - 1)*(z + 1)**2/7
Let a(j) = -j**2 + j + 1. Let f(o) = 4*o**2 - 3*o - 3. Let v(q) = -35*a(q) - 5*f(q). Factor v(m).
5*(m - 2)*(3*m + 2)
Find y, given that 2*y - 2*y**3 + 1/3*y**2 + 0 - 1/3*y**4 = 0.
-6, -1, 0, 1
Suppose 2*t + 1 = 7. Suppose -7 - 3*n**t - 10 + 17 = 0. What is n?
0
Let d(o) = -17*o**2 - o + 9. Let k(n) = -4*n**2 + 2. Suppose -5*w = 2*t + 43, 3*w = -3 - 12. Let r(x) = t*k(x) + 2*d(x). Let r(z) = 0. What is z?
0, 1
Let b(x) be the third derivative of 0*x**4 - 1/25*x**5 + 0 - 1/350*x**7 - 1/50*x**6 + 0*x**3 + 0*x - x**2. Suppose b(r) = 0. What is r?
-2, 0
Suppose 0 = s + 1 - 3. Let p(a) = -2*a. Let r = -11 - -5. Let i(x) = -x**4 + 2*x**3 - 8*x + 1. Let z(g) = r*p(g) + s*i(g). Factor z(k).
-2*(k - 1)**3*(k + 1)
Let q(a) be the first derivative of -1/2*a + 3 - 1/6*a**3 + 1/2*a**2. What is h in q(h) = 0?
1
Let a(c) be the first derivative of -2/5*c + 0*c**4 + 4/15*c**3 + 0*c**2 - 3 - 2/25*c**5. Factor a(p).
-2*(p - 1)**2*(p + 1)**2/5
Factor -18 + 0*i**3 - 5*i**3 + 14*i + 2*i**3 - 53*i - 24*i**2.
-3*(i + 1)**2*(i + 6)
Let m(q) = 27*q + 108. Let y be m(-4). Solve 2/9*w**5 - 4/9*w**4 + 0 + y*w + 2/9*w**3 + 0*w**2 = 0.
0, 1
Let h(x) be the third derivative of -2*x**2 + 0 - 1/30*x**6 + 0*x - 1/3*x**3 + 1/105*x**7 + 0*x**5 + 1/6*x**4. Solve h(w) = 0 for w.
-1, 1
Let g be 71/(-36) - 3/(-12). Let m = -2/9 - g. Factor m*p**2 + 1/2*p**3 - 2 + 0*p.
(p - 1)*(p + 2)**2/2
What is n in 428*n**2 - 3*n - 424*n**2 + 27*n + 36 = 0?
-3
Let r be -10*(5 + 66/(-12)). Let x(s) be the third derivative of -4*s**2 + 0 + 1/3*s**3 - 1/30*s**r + 0*s + 0*s**4. Factor x(g).
-2*(g - 1)*(g + 1)
Suppose 0 = -x - x + 10. Let j(u) be the first derivative of 0*u**3 - 1/21*u**6 + 0*u**4 + 2/35*u**x + 0*u**2 + 0*u + 1. Factor j(i).
-2*i**4*(i - 1)/7
Let l(u) = u**2 - 1. Let d(y) = -y**3 - 6*y**2 - 8*y - 3. Let i(o) = d(o) + l(o). Factor i(v).
-(v + 1)*(v + 2)**2
Suppose 3*q + 6 = 6*q. Factor 24*u - 2*u**3 + u**q - 24*u + u**2.
-2*u**2*(u - 1)
Let w(s) = 48*s**3 - 15*s**2 - 57*s + 168. Let x(y) = -7*y**3 + 2*y**2 + 8*y - 24. Let l be 2/(-8) + 170/40. Let z(i) = l*w(i) + 27*x(i). Factor z(t).
3*(t - 2)**2*(t + 2)
Let v(s) = -s**2 - 4*s. Let n be v(-3). Let g be (-1 - (3 - 1)) + n. Factor 2/5*r**3 + g*r - 2/5*r**4 - 2/5*r**5 + 0 + 2/5*r**2.
-2*r**2*(r - 1)*(r + 1)**2/5
Let h = 21 + -18. Suppose 0 = -2*q + 5*u + 11, h*u = 5*q - u - 19. Find t such that 4/11*t**q + 2/11*t**5 + 4/11*t**2 - 6/11*t**4 + 2/11 - 6/11*t = 0.
-1, 1
Let j(z) be the second derivative of -2*z + 1/48*z**4 + 1/120*z**6 + 0*z**3 - 1/40*z**5 + 0*z**2 + 0. Factor j(a).
a**2*(a - 1)**2/4
Let n be 16 - (1 - -2) - 3. Suppose 2*g = -0*g + n. Factor 3/4*l**4 + 1/4*l**g - 3/4*l + 1/2*l**3 - 1/4 - 1/2*l**2.
(l - 1)*(l + 1)**4/4
Determine s so that -18/7 - 9/7*s**2 + 3/7*s**4 - 33/7*s + 9/7*s**3 = 0.
-3, -1, 2
Let q(x) be the first derivative of -x**5/15 + x**3/9 - 3. Factor q(m).
-m**2*(m - 1)*(m + 1)/3
Let m be (-50)/(-12) - (-12)/(-72). Let a(s) be the first derivative of 2/45*s**5 + 4/9*s**3 - 4/9*s**2 - 2/9*s**m - 2 + 2/9*s. Factor a(p).
2*(p - 1)**4/9
Factor 63/4*v - 6*v**2 + 3/4*v**3 - 27/2.
3*(v - 3)**2*(v - 2)/4
Let v(c) be the first derivative of -1/24*c**4 + 0*c**2 + 0*c - c**3 - 2 - 1/60*c**5 - 1/360*c**6. Let f(d) be the third derivative of v(d). Factor f(h).
-(h + 1)**2
Suppose -z = 2*d + 4*z + 2, -4*d - 4*z = 16. Let v be ((-15)/(-10))/(d/(-8)). Factor 1/3*j**v + 0 + 1/3*j.
j*(j + 1)/3
Let l(a) be the third derivative of a**5/270 + 5*a**4/54 + 25*a**3/27 + 4*a**2. Factor l(u).
2*(u + 5)**2/9
Suppose 5*b = 5*b + 2*b. Find u, given that u - 1/2*u**2 + b - 1/2*u**3 = 0.
-2, 0, 1
Let t(b) = 11*b**3 - 10*b**3 + 3*b**2 - 7*b**2 - 5*b. Let z be t(5). Determine m, given that 0*m + 0*m**4 + 2/3*m**5 - 2/3*m**3 + z + 0*m**2 = 0.
-1, 0, 1
Let u(n) be the third derivative of -3*n**2 + 0*n**3 + 0 + 0*n + 1/18*n**4 + 1/90*n**5. Factor u(h).
2*h*(h + 2)/3
Let r(z) be the third derivative of -z**7/840 + z**5/40 - z**4/8 + 3*z**2. Let f(y) be the second derivative of r(y). Factor f(n).
-3*(n - 1)*(n + 1)
Suppose 57*b**2 - 14*b**3 + 7 - 40*b - 21*b**2 - 8 + 17 + 2*b**4 = 0. What is b?
1, 2
Let n(g) = 2*g**5 + 7*g**4 - 2*g**3 + 2*g**2 - 3*g - 3. Let y(v) = -v**5 - v**4 - v**3 + v + 1. Let q(u) = -2*n(u) - 6*y(u). Factor q(k).
2*k**2*(k - 2)*(k - 1)**2
Let n(z) = 5*z**4 + 29*z**3 + 24*z**2 - 19*z - 32. Let g(h) = h**4 + 7*h**3 + 6*h**2 - 5*h - 8. Let i(k) = -26*g(k) + 6*n(k). What is r in i(r) = 0?
-1, 2
Let h(m) = -5*m**2 - 6*m - 9. Let d(k) = 2*k - 4*k + 2 + 1. Let z be d(4). Let c(j) = -6*j**2 - 6*j - 9. Let p(v) = z*h(v) + 4*c(v). Factor p(u).
(u + 3)**2
Let l(v) be the first derivative of v**6/15 - v**5/20 - v**4/12 - 2*v - 2. Let r(n) be the first derivative of l(n). Solve r(h) = 0 for h.
-1/2, 0, 1
Let a(t) be the second derivative of t**4/3 - 4*t**3/3 + 2*t**2 - 3*t. Factor a(m).
4*(m - 1)**2
Let m(q) be the third derivative of q**8/20160 - q**7/5040 - q**6/360 + q**5/60 + q**2. Let i(u) be the third derivative of m(u). Factor i(j).
(j - 2)*(j + 1)
Suppose 13*l + 20 = 18*l. Find p such that -p**l - p**4 + 2*p**4 - 2*p**2 - 4*p**3 - 2*p**4 = 0.
-1, 0
Find k, given that -2*k**3 - 25*k**2 + 19*k**2 + 0*k**3 = 0.
-3, 0
Let m(k) = 2*k**2 + k. Let c be m(-2). Let j be 6/16*4/c. Suppose -1/4*q**2 - j*q + 0 = 0. Calculate q.
-1, 0
Let k = 30 - 30. Factor k*c + 0 + 1/2*c**2.
c**2/2
Factor 16*m + 3 + 3 - 3 + 1 - 20*m**2.
-4*(m - 1)*(5*m + 1)
Solve -8*r**3 - 3*r**5 - 12*r**4 + 2*r**3 + 3*r**4 = 0 for r.
-2, -1, 0
Let l(x) be the third derivative of 0*x + 0 - 1/180*x**6 + 0*x**4 + 4*x**2 + 0*x**5 + 0*x**3 - 2/315*x**7 - 1/504*x**8. Find y such that l(y) = 0.
-1, 0
Let h be 12/6*11/88. Factor -5/4*z**2 - h*z**3 - 2*z - 1.
-(z + 1)*(z + 2)**2/4
Suppose 2*d = -3*i + 6*d - 10, 3*i + 3*d = 18. Let l(o) be the first derivative of 2*o + 1/3*o**3 - 1 + 3/2*o**i. Suppose l(p) = 0. Calculate p.
-2, -1
Let k = -65 - -196/3. Factor -k*u**3 + 2/3*u**4 + 0*u + 0*u**2 + 0.
u**3*(2*u - 1)/3
Let f be (3 - 0)/((-3)/(-7)). Let r(p) be the second derivative of 0*p**6 + 0*p**2 + 0 + 0*p**3 + 0*p**5 + p + 1/105*p**f + 0*p**4. Factor r(g).
2*g**5/5
Factor -3*o**4 + 2*o + 2 - 4*o**2 - 4*o**3 + 5*o**4 + 9*o**5 - 7*o**5.
2*(o - 1)**2*(o + 1)**3
Let k(i) = -i - 17. Let c be k(-17). Let 4/7*s - 10/7*s**5 + 2/7*s**2 - 26/7*s**4 - 18/7*s**3 + c = 0. Calculate s.
-1, 0, 2/5
Let u(z) = 7*z**3 + 2*z**2 - z + 4. Let c(o) = -o**3 - 1. Let w(j) = 6*c(j) + u(j). Determine y, given that w(y) = 0.
-2, -1, 1
Let v be 7 - ((-102)/(-30) + (-4)/10). Solve -v*r - 4/3 - 2*r**3 - 1/3*r**4 - 13/3*r**2 = 0 for r.
-2, -1
Factor 48/5*j**2 - 24/5*j**3 - 32/5*j + 4/5*j**4 + 0.
4*j*(j - 2)**3/5
Let x = 167 - 167. Factor 0 - 2/3*d**2 - 8/3*d**3 - 2*d**4 + x*d.
-2*d**2*(d + 1)*(3*d + 1)/3
Suppose -318 = -4*w - 1350. Let p = w - -529/2. Suppose -7/2*o**4 + p*o - 27/2*o**2 + 23/2*o**3 - 1 = 0. Calculate o.
2/7, 1
What is l in 8/5*l**2 + 12/5*l**3 + 0*l + 0 + 4/5*l**4 = 0?
-2, -1, 0
Let x(q) be the first deri