d derivative of -u**8/560 + u**6/40 + u**5/20 + 5*u**3/6 + 8*u. Let y(k) be the second derivative of r(k). Factor y(p).
-3*p*(p - 2)*(p + 1)**2
Suppose -4*x = -5*o - 12, 0*x + 3*x - 5*o - 4 = 0. Let t**2 - t**3 + 2*t**2 - x*t**3 - 12*t**4 = 0. Calculate t.
-1, 0, 1/4
Let m be (-2 + 2)*1/((-4)/(-4)). Let k(i) be the second derivative of 0*i**2 + 0*i**3 - 2*i - 1/50*i**5 + m + 1/15*i**4. What is d in k(d) = 0?
0, 2
Let v = 18 + -10. Let u be ((-5)/35)/((-4)/v). Factor -u*p**2 + 0 - 2/7*p + 2/7*p**4 + 2/7*p**3.
2*p*(p - 1)*(p + 1)**2/7
Let g(r) be the third derivative of r**6/1800 - r**5/300 + r**4/120 - r**3/2 + r**2. Let b(x) be the first derivative of g(x). Factor b(s).
(s - 1)**2/5
Factor 1/3*c**3 + 0*c - c**2 + 0.
c**2*(c - 3)/3
Let j be (-4)/10 + (-152)/36. Let n = -38/9 - j. Determine t so that 2/5*t**4 + 0*t - n*t**2 + 0 - 2/5*t**5 + 2/5*t**3 = 0.
-1, 0, 1
Determine u, given that 0 + u - 3/2*u**3 + 1/2*u**2 = 0.
-2/3, 0, 1
Let m(o) be the first derivative of o**3/30 - o**2/10 - 13. Factor m(l).
l*(l - 2)/10
Factor 4*z**4 + 8*z**3 - 9 + 4*z**2 - 22 + 31.
4*z**2*(z + 1)**2
Let o(v) be the third derivative of 2*v**7/35 - v**6/30 - 7*v**5/5 - 11*v**4/6 + 4*v**3 - 31*v**2. Let o(s) = 0. What is s?
-2, -1, 1/3, 3
Factor -4/3*z**2 - 2/3 - 1/3*z**3 - 5/3*z.
-(z + 1)**2*(z + 2)/3
Let p = 129/140 - 6/35. Let r be ((-3)/(-2))/(1 + 2). Factor -p*v - 5/4*v**2 + r.
-(v + 1)*(5*v - 2)/4
Let v(a) = 2*a + 4. Let h be v(-4). Let b(d) = -d**2 - 6*d - 6. Let w be b(h). Determine s so that 1/4*s**3 + 0*s**w + 0*s + 0 = 0.
0
Let r be 2*1 - (7 - 24). Factor -r*a**3 - 9*a**3 + 2 + 18*a**4 - 4*a**3 + 28*a**2 - 4*a**5 - 12*a.
-2*(a - 1)**4*(2*a - 1)
Suppose 4*n = 12, -s + n = 2*n + 2. Let l = 1 + 0. Let x(a) = a**3 - a**2. Let r(k) = 4*k**3 - 5*k**2 + 3*k + 2. Let t(y) = l*r(y) + s*x(y). Factor t(m).
-(m - 2)*(m + 1)**2
Let c be ((-4)/22 - (-224)/990)*5. Factor -4/9*b**2 + c + 2/9*b.
-2*(b - 1)*(2*b + 1)/9
Let u(r) be the second derivative of -r - r**2 - 3/4*r**4 + 1/20*r**5 + 9/2*r**3 + 0. Let k(w) be the first derivative of u(w). Solve k(i) = 0 for i.
3
Suppose -67 = 6*t - 79. Let c be (-6)/(1 + (-5)/2). Factor -2/3*h**3 + 0 + 2/3*h**c - 4/3*h**t + 0*h.
2*h**2*(h - 2)*(h + 1)/3
Let m be (2 - (-12)/(-8))/4. Let w(g) be the first derivative of 0*g + 1 - 1/16*g**4 - m*g**2 + 1/6*g**3. Let w(f) = 0. Calculate f.
0, 1
Let q(o) be the second derivative of -o**6/50 + 3*o**5/50 + 11*o. Suppose q(s) = 0. Calculate s.
0, 2
Let o(t) be the second derivative of -t**6/105 + t**5/140 + 3*t**4/14 - 3*t**3/14 + 27*t. Factor o(q).
-q*(q - 3)*(q + 3)*(2*q - 1)/7
Determine t, given that 4*t**5 + 32*t**3 + 16*t**4 + 4*t**4 + 0*t**3 + 9*t**2 + 7*t**2 = 0.
-2, -1, 0
Let u(x) be the first derivative of 2*x**5/5 - x**4/2 - 2*x**3/3 + x**2 + 4. Factor u(s).
2*s*(s - 1)**2*(s + 1)
Let l = 78 - 623/8. Let d(z) be the third derivative of -1/20*z**5 - 1/120*z**6 - 1/6*z**3 + 0*z + 0 - z**2 - l*z**4. Factor d(u).
-(u + 1)**3
Let q(k) = -2*k**5 + 8*k**4 + 2*k**3 - 4*k**2 + 4*k + 4. Let s(n) = -n**5 + n**4 - n**2 + n + 1. Let y(d) = q(d) - 4*s(d). Factor y(i).
2*i**3*(i + 1)**2
Let o(d) be the third derivative of 1/60*d**4 + 0 + 2*d**2 - 1/300*d**6 - 1/75*d**5 + 0*d + 2/15*d**3. Determine y so that o(y) = 0.
-2, -1, 1
Let i(a) = -a**2 - a + 1. Let l(y) = 15*y**2 + 36*y - 12. Let f(u) = u**3 - u**2 + u - 1. Let x be f(0). Let q(o) = x*l(o) - 3*i(o). Factor q(n).
-3*(n + 3)*(4*n - 1)
Let b = 80 + -74. Let v(s) be the second derivative of -2*s + 0*s**2 + 1/9*s**3 + 1/45*s**b - 1/18*s**4 + 0 - 1/30*s**5. Suppose v(f) = 0. Calculate f.
-1, 0, 1
Suppose 5*y + 15 = c, 2*y + 8 = -3*c + 2. Let u be (0 - 2)/(2/y). Factor -o**u + 0*o**3 + 1 + o - 4*o + o**2 + 2*o**2.
-(o - 1)**3
Let w(r) be the first derivative of 49*r**5/10 + 77*r**4/8 - 11*r**3 - 13*r**2 - 4*r + 4. Suppose w(v) = 0. Calculate v.
-2, -2/7, 1
Suppose -2*r = -6*r + 36. Factor r*d**3 + 0*d**4 - d**3 + 8*d**2 + 2*d**4.
2*d**2*(d + 2)**2
Let x(g) be the first derivative of -2*g**4/5 - 14*g**3/15 + 2*g**2/5 + 4. Factor x(k).
-2*k*(k + 2)*(4*k - 1)/5
Suppose 16 = 3*y - y. Find a, given that 5*a**3 - a**4 - y*a + a**3 - a**4 = 0.
-1, 0, 2
Let k be ((-32)/5)/(-8)*20/8. Factor 8/7*n**k - 2/7*n + 0 - 6/7*n**3.
-2*n*(n - 1)*(3*n - 1)/7
Let b(v) = v**2 + 15*v - 16. Let k(l) = l**2 + 7*l - 8. Let a(h) = -6*b(h) + 10*k(h). Let a(i) = 0. What is i?
1, 4
Let z(k) be the third derivative of -k**5/180 - k**4/36 - 12*k**2. Factor z(y).
-y*(y + 2)/3
Suppose 2*v + 12 = 6*v. Let t be 6/(-10)*v/(-9). Determine p so that 2/5*p - 1/5 - t*p**2 = 0.
1
Let m(b) = -2*b**4 - 16*b**3 - 14*b**2 - 4*b - 4. Let q(h) = 2*h**4 + 17*h**3 + 15*h**2 + 5*h + 5. Let n(y) = -5*m(y) - 4*q(y). Factor n(c).
2*c**2*(c + 1)*(c + 5)
Let y(m) be the first derivative of -1/3*m**3 + 0*m**2 + 1/4*m**4 - 2 + 0*m. Factor y(l).
l**2*(l - 1)
Let f be 2/3*(-6)/(-16). Let y(a) = -a - 4. Let b be y(-6). Let f*q**b + 0 + 1/2*q = 0. What is q?
-2, 0
Suppose 122*a = 120*a + 4. Factor 0 + 1/4*z**a + 1/4*z.
z*(z + 1)/4
Let s(p) be the first derivative of -p**6/18 - p**5/15 + p**4/12 + p**3/9 + 5. Factor s(g).
-g**2*(g - 1)*(g + 1)**2/3
Let y(v) be the first derivative of 1 + 1/4*v**4 - 2/3*v**3 + 0*v**2 + 0*v. Factor y(h).
h**2*(h - 2)
Let m(b) be the second derivative of -b**6/90 - b**5/30 + b**3/9 + b**2/6 + 4*b. Solve m(q) = 0.
-1, 1
Let f(k) be the second derivative of -1/5*k**2 - 1/15*k**3 + 1/50*k**5 + 0 + 3*k + 1/30*k**4. Factor f(y).
2*(y - 1)*(y + 1)**2/5
Suppose 0 = 4*n - 6*n + 8. Let f be (30/100)/(3/n). Let f*a**3 + 0 + 2/5*a**5 - 6/5*a**4 - 4/5*a + 6/5*a**2 = 0. Calculate a.
-1, 0, 1, 2
Let i be ((-68)/(-28) + -2)*7. Suppose 1/5*q - 1/5*q**5 + 0*q**i - 2/5*q**4 + 0 + 2/5*q**2 = 0. Calculate q.
-1, 0, 1
Suppose n - a + 4 = 4*n, 4 = 2*n + a. Suppose 4*o + 5*s + 8 = -0*s, n = 4*o - s - 16. Find j, given that -2/7*j + 0 - 4/7*j**2 - 2/7*j**o = 0.
-1, 0
Let d be 2/(8/((-40)/15) - -11). Determine u so that -1/4*u**4 + 0*u + 0*u**2 + 0 - d*u**3 = 0.
-1, 0
Suppose 0 = -0*l + l - 2. Factor -m**l + 0*m - 1/2*m**3 + 0.
-m**2*(m + 2)/2
Let s(m) be the second derivative of 0*m**3 + 0 + 3/10*m**5 - 3*m - 7/12*m**4 + 1/2*m**2. Determine k so that s(k) = 0.
-1/3, 1/2, 1
Let l be 6/9*(-69)/(-2). Suppose 21 = n + h + 4, l = 4*n - 5*h. Solve 0*x + 2*x**2 + 0*x + n*x**2 + 4*x = 0.
-2/7, 0
Let v = 22 - 29. Let p be 16/70 - 4/v. Factor -p*d**3 + 4/5*d**2 + 2/5*d**5 - 2/5*d**4 + 2/5*d - 2/5.
2*(d - 1)**3*(d + 1)**2/5
Let s(v) be the third derivative of -v**5/240 + v**4/96 + v**3/12 - 11*v**2. Solve s(l) = 0 for l.
-1, 2
Let v(c) be the third derivative of 1/24*c**4 - 1/120*c**6 + 4*c**2 + 0 + 0*c**5 + 0*c**3 + 0*c. Let v(q) = 0. What is q?
-1, 0, 1
What is o in 0 + 1/4*o - 1/4*o**2 = 0?
0, 1
Let w(z) be the second derivative of -z**5/40 + z**4/12 + z**3/12 - z**2/2 - 5*z. Suppose w(s) = 0. What is s?
-1, 1, 2
Suppose 4*d**2 + 6*d - 4*d**3 - 2*d + 5*d**3 = 0. What is d?
-2, 0
Let f = -3 - 0. Let y be 1*(-2 + 1)*f. Factor 3*r**4 + 3 + 1 + 6*r**2 - 2*r**y - 5*r**4 + 10*r.
-2*(r - 2)*(r + 1)**3
Let j(d) = d**3 + d**2 - d + 1. Let w(p) = 5*p**3 - 3*p**2 - 3*p + 11. Let g(i) = 3*j(i) - w(i). Factor g(s).
-2*(s - 2)**2*(s + 1)
Let z(y) be the third derivative of -3*y**8/728 + 11*y**7/455 + 31*y**6/390 - y**5/65 - 7*y**4/52 + 5*y**3/39 - 20*y**2. Solve z(n) = 0.
-1, 1/3, 5
Let j be 10/(-35) - 268/(-840). Let c(k) be the third derivative of j*k**5 + 0*k + 0 + 1/12*k**4 + 0*k**3 + 2*k**2. Let c(s) = 0. Calculate s.
-1, 0
Let y be -1 + -1 - 6/(-3 - 0). Let -2/7*w**5 + y + 0*w**3 - 2/7*w**4 + 0*w + 0*w**2 = 0. What is w?
-1, 0
Let c = 263 + -523/2. Let u(o) = o + 8. Let g be u(-6). Let 3*j + 0 - c*j**g = 0. Calculate j.
0, 2
Let w(a) = -3*a. Let x be w(-6). Factor -4*b - 5*b - x*b**2 + 5*b.
-2*b*(9*b + 2)
Let i(w) be the first derivative of -6*w**3/11 - 12*w**2/11 - 6*w/11 + 21. Find j, given that i(j) = 0.
-1, -1/3
Let w(i) be the first derivative of 4/3*i**3 + 3 - 7/2*i**4 + 0*i**2 + 0*i. Factor w(h).
-2*h**2*(7*h - 2)
Let g(l) be the third derivative of l**7/735 - l**6/84 + l**5/30 - l**4/28 - 5*l**2. Let g(b) = 0. Calculate b.
0, 1, 3
Let r(a) be the first derivative of -a**5/5 + a**4/2 - a**3/3 + 35. Factor r(p).
-p**2*(p - 1)**2
Determine g, given that 3/5 - 1/5*g**2 + 2/5*g = 0.
-1, 3
Let j be 1 + -1 - 4*-1. S