- d**5/40 + d**3/3 - 3*d**2 + 8*d. Let i(s) be the first derivative of k(s). Factor i(n).
-(n - 1)*(n + 2)**2/2
Let s(i) = i**2 - 4*i**2 - 5*i + 2*i**2 + 1 + 7. Let g be s(-6). Let -6/7*l**3 + 6/7*l - 4/7 + 4/7*l**g = 0. Calculate l.
-1, 2/3, 1
Determine m so that 0*m**3 + 1/4*m**2 - 1/4*m**4 + 0*m + 0 = 0.
-1, 0, 1
Suppose 0 = 23*l - 26*l. Let b(t) be the second derivative of 1/3*t**3 + 0 + l*t**2 - 1/12*t**4 + 2*t. Factor b(m).
-m*(m - 2)
Let f(y) = y - 5. Let k be f(5). Let o = -95 + 95. Factor k + 1/4*s**3 + o*s**2 + s**5 + 0*s + 5/4*s**4.
s**3*(s + 1)*(4*s + 1)/4
Let 5 + 7*t - 8 - 10*t + 1 - t**2 = 0. What is t?
-2, -1
Let r(s) = s**4 + s - 1. Let f be (-2)/5 + (-210)/(-25). Let n(k) = 5*k + 2*k**3 + 8*k**4 - 6*k**2 + 6*k**2 - f. Let i(l) = 2*n(l) - 14*r(l). Factor i(z).
2*(z - 1)*(z + 1)**3
Let f be 24 - (0 - (-36)/6). Factor 2/9*t**4 + 12*t**2 + f + 24*t + 8/3*t**3.
2*(t + 3)**4/9
Solve 6*s**4 + 0 + 0*s - 4*s**3 - 8/3*s**2 + 9*s**5 = 0 for s.
-2/3, 0, 2/3
Let b(f) be the first derivative of 2*f**3/45 + 2*f**2/5 + 2*f/3 + 12. Solve b(k) = 0.
-5, -1
Let u be (2/(-2))/(1/(-3)). Factor -3 + u*z**2 - 4*z**2 - 1 + 5.
-(z - 1)*(z + 1)
Let p(o) be the first derivative of -o**6/9 + 2*o**5/5 - o**4/3 - 4*o**3/9 + o**2 - 2*o/3 - 6. Factor p(n).
-2*(n - 1)**4*(n + 1)/3
Factor -6*t**2 + 14 + 4*t**3 - 2*t**3 - 14.
2*t**2*(t - 3)
Let r(u) be the second derivative of -u**6/20 - 19*u**5/120 - u**4/6 - u**3/12 - u**2/2 + 2*u. Let a(z) be the first derivative of r(z). Factor a(i).
-(i + 1)*(3*i + 1)*(4*i + 1)/2
Let c(r) = 8*r**3 - r**4 + 6*r**2 + 1 + 6*r**4 - r + 5*r. Let l(j) = 9*j**4 + 15*j**3 + 12*j**2 + 8*j + 2. Let s(m) = 7*c(m) - 4*l(m). Factor s(v).
-(v + 1)**4
Let c(v) be the first derivative of -v**5/40 - v**4/32 + v**3/24 + v**2/16 - 14. Factor c(f).
-f*(f - 1)*(f + 1)**2/8
Factor 0*s**3 - s**2 - 4*s**3 + 5*s**2.
-4*s**2*(s - 1)
Let t(k) be the second derivative of k**8/6720 - k**6/480 + k**5/240 - k**3/2 - 2*k. Let x(p) be the second derivative of t(p). Factor x(c).
c*(c - 1)**2*(c + 2)/4
Suppose 2*d = -5*g + 11, 4*d - 4 = -2*g + 3*d. Factor 28/5*z**4 + 22/5*z + 52/5*z**g + 4/5 + 48/5*z**2 + 6/5*z**5.
2*(z + 1)**4*(3*z + 2)/5
Let j be 12/15*180/(-8). Let q be 15/(-75) - j/40. Factor 0*h - q*h**2 + 1/4.
-(h - 1)*(h + 1)/4
Let h = 3 - 1. Factor 4 + 2*z**h - 44*z - 3*z**2 + 41*z.
-(z - 1)*(z + 4)
Let i(a) be the third derivative of -a**5/12 - 5*a**4/12 - 44*a**2. Determine k so that i(k) = 0.
-2, 0
Let p(v) be the third derivative of v**7/420 - v**6/240 - v**5/120 + v**4/48 + 8*v**2. Solve p(j) = 0 for j.
-1, 0, 1
Suppose 21 = 5*a + 6. What is m in 0*m**a + 4*m**2 + 2*m**2 + 3*m**3 + 0*m**2 = 0?
-2, 0
Let p(s) be the first derivative of -4*s**6/3 - 5*s**4/2 + s**3/3 + 17*s + 6. Let j(r) = -3*r**5 - 3*r**3 + 6. Let g(y) = 17*j(y) - 6*p(y). Factor g(c).
-3*c**2*(c - 1)**2*(c + 2)
Let c be 2/(-8) - 81/(-36). Solve -5*b**4 - 3*b**4 + 6*b**4 + 4*b**c - 2*b**4 = 0 for b.
-1, 0, 1
Suppose -4*q = -14 - 2. Factor -3*r**2 - q*r - r**2 - 4*r**2 - 4*r**3.
-4*r*(r + 1)**2
Suppose 3*m - 10 = 14. Find k, given that 15*k**4 - 38*k**3 + 13*k**4 - 6*k**5 + 0*k**5 + m*k**2 + 8*k = 0.
-1/3, 0, 1, 2
Let 0 - 1/5*q - 1/5*q**2 = 0. What is q?
-1, 0
Solve 0 + 4/7*f - 6/7*f**2 - 4/7*f**3 = 0.
-2, 0, 1/2
Suppose -4*y = -28 + 16. Let k be (-21)/(-5) + 1*-3. Factor 0 + k*f**4 + 0*f**2 - 2/5*f**5 - 4/5*f**y + 0*f.
-2*f**3*(f - 2)*(f - 1)/5
Let t(y) be the first derivative of y**6/60 - y**5/30 - 4*y**3/3 + 3. Let p(f) be the third derivative of t(f). Factor p(q).
2*q*(3*q - 2)
Let y be (-4)/22 - (-58)/198. Let u(b) be the second derivative of y*b**3 + 1/90*b**5 + 0 + 1/9*b**2 + 1/18*b**4 + 2*b. Suppose u(t) = 0. Calculate t.
-1
Let m(h) = 4*h - 10. Let r be m(3). Let d(s) be the third derivative of 0*s + 0 + r*s**2 + 1/60*s**4 - 1/50*s**5 + 0*s**3. Factor d(c).
-2*c*(3*c - 1)/5
Let d = 28 - 32. Let f be 18/d*3/(-18). Determine j, given that -1/4 + f*j - 3/4*j**2 + 1/4*j**3 = 0.
1
Let y(s) = -6*s**4 + 3*s**3 - 7*s**2 - 5*s. Let n(j) = 0*j**2 - 4*j - j**4 + j - j**2 + 2*j. Let u(m) = -5*n(m) + y(m). Factor u(t).
-t**2*(t - 2)*(t - 1)
Let b(t) be the second derivative of -t**4/4 + 3*t**2/2 - 6*t. Suppose b(m) = 0. What is m?
-1, 1
Let g be (-1)/(-5) - ((-78)/(-90) - 1). Determine u, given that 0*u - 1/3*u**4 + 0 + g*u**2 + 0*u**3 = 0.
-1, 0, 1
Let q(m) = m. Let l(j) = -j**3 + 3*j**2 - j + 3. Let o be l(3). Let g be q(o). Factor -1/2*x**3 + 0 - 1/2*x**2 + g*x.
-x**2*(x + 1)/2
Let q(p) be the second derivative of -p**7/1260 - p**6/180 - p**5/60 + p**4/6 + 2*p. Let w(c) be the third derivative of q(c). Factor w(i).
-2*(i + 1)**2
Suppose -o - 32 = 3*o. Let w = o + 8. Find g such that -6*g**3 + 2 + 3*g**3 - 3*g**3 + w*g**2 - 2*g**2 + 6*g = 0.
-1, -1/3, 1
Let o = -73 + 147/2. Factor 0*z**3 - z**4 + z**2 + 0 - 1/2*z**5 + o*z.
-z*(z - 1)*(z + 1)**3/2
Let r(j) be the first derivative of -j**4/4 - 5*j**3/3 - j**2 - 6*j + 2. Let x be r(-5). Factor -w + 2*w**2 - 2 - 3*w + x.
2*(w - 1)**2
Solve -2/3*j**2 - 2/3 + 4/3*j = 0.
1
Factor -1/4*v**2 + 1/4*v**4 + 0 + 3/4*v - 3/4*v**3.
v*(v - 3)*(v - 1)*(v + 1)/4
Suppose 0 - 243/2*v - 3/2*v**3 - 27*v**2 = 0. What is v?
-9, 0
Let w(v) be the first derivative of v**6/9 + 8*v**5/15 + v**4 + 8*v**3/9 + v**2/3 + 1. Determine u so that w(u) = 0.
-1, 0
Let a(m) = -60*m**2 - 8*m + 4. Let b(d) = -60*d**2 - 8*d + 3. Let y(s) = -3*a(s) + 4*b(s). Factor y(n).
-4*n*(15*n + 2)
Factor 1/4*w**4 - 3/4*w**3 + 0*w**2 + w + 0.
w*(w - 2)**2*(w + 1)/4
Factor 2*w - 202*w**2 + 162*w**2 - 80 - 88*w - 14*w - 5*w**3.
-5*(w + 2)**2*(w + 4)
Let o = 577/155 - 10/31. Suppose o*y - 1/5*y**2 - 17/5*y**3 + 6/5 - y**4 = 0. What is y?
-3, -1, -2/5, 1
Let f(h) be the first derivative of -h**2 + 2 + h + 1/3*h**3. Factor f(m).
(m - 1)**2
Let s(p) be the third derivative of p**2 + 0 - 1/96*p**4 + 0*p**6 + 0*p**3 + 1/1344*p**8 - 1/420*p**7 + 0*p + 1/120*p**5. Factor s(h).
h*(h - 1)**3*(h + 1)/4
Let m(c) be the third derivative of -c**7/35 - 9*c**6/140 + 6*c**5/35 + c**4/7 - 12*c**2. Let m(d) = 0. What is d?
-2, -2/7, 0, 1
Let g(w) = -w**2 - 2*w + 3. Let x be g(-3). Suppose -3*l + x = -6. Suppose 0 - 1/4*i - 1/4*i**l = 0. What is i?
-1, 0
Let l(h) = -50*h**3 + 375*h**2 - 390*h + 135. Let i(p) = -3*p**3 + 22*p**2 - 23*p + 8. Let a(t) = 35*i(t) - 2*l(t). Factor a(o).
-5*(o - 2)*(o - 1)**2
Let d(b) be the first derivative of 1/4*b - 3/8*b**2 + 1 - 1/16*b**4 + 1/4*b**3. Find u, given that d(u) = 0.
1
Let q = 1 + 1. Factor -3*d**q + d**3 + 2 + 2 + 0*d**2.
(d - 2)**2*(d + 1)
Let 0 + 0*v - 3/7*v**2 = 0. Calculate v.
0
Suppose 3*j - 23 = 3*s - 80, 0 = 4*j + 5*s + 31. Let n = j + 14. Let -2/9 + n*p + 2/9*p**2 = 0. Calculate p.
-1, 1
What is c in 23 - 32*c**2 + 157 + 19*c**2 + 60*c + 18*c**2 = 0?
-6
Find q, given that -2/7*q**2 + 2/7*q**4 - 2/7*q**3 + 2/7*q + 0 = 0.
-1, 0, 1
Find n, given that -16/5*n**3 + 0*n + 0 - 4/5*n**4 - 12/5*n**2 = 0.
-3, -1, 0
Let p(n) be the first derivative of -n**5/15 - n**4/4 + 2*n**2/3 + 1. Find w, given that p(w) = 0.
-2, 0, 1
Let m**2 - 5*m + 3 - m**3 + 0*m**3 + 2*m**3 = 0. What is m?
-3, 1
Let b(c) = -2*c**4 - 12*c**3 + 8*c**2 - 8*c + 2. Let h(s) = -s**4 - 11*s**3 + 9*s**2 - 8*s + 2. Let j(n) = -3*b(n) + 4*h(n). Solve j(i) = 0.
1
Let l = -5 - -10. Let y = 8 - l. Let 0*d**5 - 2*d**2 + 6*d**3 + y*d**4 - 4*d**4 + 2*d**5 - 5*d**4 = 0. What is d?
0, 1
Let k = -9 - -15. Let r be 4/8*8/k. Solve r*m**2 + 0*m + 0 + 1/3*m**3 = 0 for m.
-2, 0
Let d = 28/45 - 1/45. Factor -9/5*m - 9/5*m**2 - d*m**3 - 3/5.
-3*(m + 1)**3/5
Let w be 48/108*(-3)/12*-3. Factor 1/6*s**3 - 2/3*s**2 + 5/6*s - w.
(s - 2)*(s - 1)**2/6
Let d(w) be the first derivative of w**5/100 + w**4/60 + 2*w + 2. Let z(t) be the first derivative of d(t). Factor z(x).
x**2*(x + 1)/5
Let t(a) = a**3 + a - 1. Let j(g) = g**5 + 3*g**4 - 7*g**3 - 12*g**2 - 13*g + 5. Let d(m) = -j(m) - 5*t(m). What is z in d(z) = 0?
-2, -1, 0, 2
Let r(a) = a**2 + a + 3. Let s be r(0). Suppose -4*f = -5*d - 15, -s*f = 2*f + 2*d + 6. Factor 2/5*l**2 + f + 2/5*l.
2*l*(l + 1)/5
Let o be (-50)/4*((-576)/140 + 4). Let l be (-27)/(-7) - (0 - -1). Factor -l*n**2 - 10/7*n - 2/7*n**5 - o*n**4 - 20/7*n**3 - 2/7.
-2*(n + 1)**5/7
Solve 2/7*n**4 + 0*n**2 + 4/7*n**3 + 0*n + 0 = 0 for n.
-2, 0
Let t(b) be the second derivative of 0*b**2 + 9*b + 0 + 1/42*b**