ivative of c**4/4 - c**3/3 - c**2/2 - 8. Let k(j) = 22*g(j) + 2*y(j). Factor k(q).
2*q*(q - 1)*(q + 1)
Let s(r) be the second derivative of 8*r - 1/6*r**4 + 0 - 3*r**2 - 4/3*r**3. Let s(o) = 0. What is o?
-3, -1
Let a(q) = -q**2 - q. Let v be a(-2). Let d be 3/21 - (-3 - v). Solve -d*l**2 - 2/7 + 10/7*l = 0 for l.
1/4, 1
Let k(y) = y - 4. Let v be k(6). Let i(h) be the second derivative of 0*h**v + 0 + 1/6*h**3 - 1/12*h**4 - h. Factor i(b).
-b*(b - 1)
Factor 1/6*a**5 - 1/3*a + 0 - 1/6*a**4 + 5/6*a**2 - 1/2*a**3.
a*(a - 1)**3*(a + 2)/6
Let l be 0/(-2*(-2 - -3)). Let -1/5*i**2 + 0*i + l = 0. Calculate i.
0
Let o = 71 + -212/3. Factor 1/3*n**4 - 1/3*n - 2/3*n**2 - 1/3*n**5 + o + 2/3*n**3.
-(n - 1)**3*(n + 1)**2/3
Let c(v) be the third derivative of -v**8/12 + 38*v**7/105 - v**6/2 + v**5/15 + v**4/3 - 4*v**2. Suppose c(u) = 0. What is u?
-2/7, 0, 1
Let b(k) be the first derivative of -2*k**5/45 - 5*k**4/18 - 2*k**3/3 - 7*k**2/9 - 4*k/9 + 7. Factor b(v).
-2*(v + 1)**3*(v + 2)/9
Determine n, given that -3*n + 27*n**2 - 28*n**2 + 0 - 2 + 0 = 0.
-2, -1
Let d(v) be the first derivative of v**7/420 - v**6/240 - 3*v**2/2 - 2. Let s(c) be the second derivative of d(c). Factor s(q).
q**3*(q - 1)/2
Suppose -54*p**2 + 31*p - 3*p**4 + 21*p**3 - 24 + 27*p + 2*p = 0. What is p?
1, 2
Factor 0*b - 1/3*b**4 + 2/3*b**3 + 0 - 1/3*b**2.
-b**2*(b - 1)**2/3
Let y(p) = p**3 + 4*p**2. Let k be y(-4). Factor 4 + k*z**2 - 6*z - 3*z**2 + 5*z**2.
2*(z - 2)*(z - 1)
Suppose -d + 4 = -0*d. Let k(r) be the first derivative of 4/3*r**3 - 2/5*r**5 + 0*r**2 + 0*r**d + 1 - 2*r. Let k(p) = 0. Calculate p.
-1, 1
Let d be 4/18 - (-34)/9. Suppose 0*z = -4*z + 4*t + 28, 26 = 3*z - d*t. Find u, given that -u + z*u**3 - u**4 + 0*u**3 + 1 - u = 0.
-1, 1
Suppose 3*q + 2*r - 18 = -q, -5 = -2*q + 3*r. Let s be ((-8)/(-3))/(q/6). Factor a**2 + 4*a**s - 2*a**3 + a**4 - 4*a**4 + 0*a**3.
a**2*(a - 1)**2
Let t(y) = y + 1. Suppose 1 = 2*b - 1. Let v be t(b). Factor 9*d**v + d**3 - d - 9*d**2.
d*(d - 1)*(d + 1)
Let g(j) = 18*j**2 + 32*j + 16. Let a(y) = 17*y**2 + 32*y + 16. Let r(f) = -6*a(f) + 5*g(f). Factor r(v).
-4*(v + 2)*(3*v + 2)
Let y(m) be the second derivative of m**7/147 - 2*m**6/105 - 3*m**5/35 + 10*m**4/21 - 19*m**3/21 + 6*m**2/7 + 27*m. Factor y(z).
2*(z - 2)*(z - 1)**3*(z + 3)/7
Let b(q) be the third derivative of -q**7/105 - q**6/30 - 4*q**2. Determine l so that b(l) = 0.
-2, 0
Solve 0*k + 0 + 1/8*k**2 = 0 for k.
0
Factor 1/2*w**2 + 0 + 0*w**3 - 1/2*w**4 + 0*w.
-w**2*(w - 1)*(w + 1)/2
Let w(b) be the third derivative of b**5/270 - b**4/18 + b**3/3 + 2*b**2. Solve w(a) = 0.
3
Factor -8*c**3 - c**3 + 2*c**5 + 4*c**2 + 9*c**4 - 5*c**5 - c**2.
-3*c**2*(c - 1)**3
Factor 0 + 0*n + 2/15*n**3 + 0*n**2.
2*n**3/15
Let g = -171/2 + 87. Let z(c) be the first derivative of -c**2 - g*c**4 + 0*c + 2/5*c**5 + 2*c**3 + 2. Let z(q) = 0. What is q?
0, 1
Let i = 155/2 + -1549/20. Let h(j) be the second derivative of -1/20*j**5 + 0*j**4 - j + 0 - 1/84*j**7 - i*j**6 + 0*j**3 + 0*j**2. Factor h(g).
-g**3*(g + 1)*(g + 2)/2
What is p in -2/13 - 2/13*p**3 + 2/13*p**2 + 2/13*p = 0?
-1, 1
Let k(b) = b**4 - 5*b**3 - 6*b**2 + 7*b. Let g(u) = -u**3 - u**2 + u. Let a(q) = -35*g(q) + 5*k(q). What is n in a(n) = 0?
-1, 0
Let b(t) be the first derivative of 3*t**3 - 3 + 3/4*t**4 - 3*t - 6/5*t**5 - 3/2*t**2. Solve b(s) = 0.
-1, -1/2, 1
Let l(z) be the second derivative of z**2 + 3*z + 1/2*z**4 - 1/10*z**5 - z**3 + 0. Factor l(b).
-2*(b - 1)**3
Let i be 0 + -1 - (-5 + 1). Factor -5*a + a + a**2 - a + i*a.
a*(a - 2)
Factor 2*k**2 - 7*k**2 + 7*k**2.
2*k**2
Let a(h) be the first derivative of 2*h**6/3 - 12*h**5/5 + h**4 + 4*h**3 - 4*h**2 + 4. Factor a(p).
4*p*(p - 2)*(p - 1)**2*(p + 1)
Let 11/2*a**3 - 2*a - 8*a**2 + 9/2*a**4 + 0 = 0. Calculate a.
-2, -2/9, 0, 1
Let x(p) be the second derivative of -p - 1/24*p**3 - 1/8*p**2 + 0 + 1/80*p**5 + 1/48*p**4. Suppose x(n) = 0. Calculate n.
-1, 1
Suppose 3*r + 19 + 11 = 0. Let p = r - -12. Factor 2/3*k + 2/3*k**p + 0.
2*k*(k + 1)/3
Let w(v) be the second derivative of v**5/60 + v**4/12 + v**3/6 + 3*v**2/2 - 2*v. Let b(n) be the first derivative of w(n). Let b(d) = 0. Calculate d.
-1
Let n(f) = -30*f**3 - 25*f**2 + 125*f + 85. Let x(j) = 15*j**3 + 12*j**2 - 62*j - 42. Let a(w) = 2*n(w) + 5*x(w). Factor a(m).
5*(m - 2)*(m + 2)*(3*m + 2)
Let r = 4/47 - 1/564. Let y(o) be the third derivative of 0 - 7/240*o**5 + 0*o - 1/160*o**6 + 1/32*o**4 + r*o**3 - o**2 + 1/168*o**7. Factor y(q).
(q - 1)**2*(q + 1)*(5*q + 2)/4
Suppose 37*o = 45*o - 8. Factor -13/2*r - o - 11/2*r**2.
-(r + 1)*(11*r + 2)/2
Let h(g) = 9*g**3 - 4*g**2 + 5. Let n(v) = 4*v**3 - 2*v**2 + 2. Let x = 6 - 8. Let l(k) = x*h(k) + 5*n(k). Factor l(d).
2*d**2*(d - 1)
Suppose u + 2*d + d - 6 = 0, 0 = -4*u - 5*d + 17. Suppose v = u*v. Factor 3*l**2 + v*l**2 - l**2 + 4*l + 1 + 1.
2*(l + 1)**2
Find c such that 0 + 2*c**3 + 6/5*c**4 - 8/5*c**5 - 6/5*c**2 - 2/5*c = 0.
-1, -1/4, 0, 1
Let v(u) be the third derivative of 5/36*u**4 + 0*u + 0 + 1/15*u**5 + 1/9*u**3 - u**2. Factor v(o).
2*(2*o + 1)*(3*o + 1)/3
Let q(z) = -2*z**2 - 22*z. Let b(t) = -t**2 - 9*t. Let p be 12/(6/(-2) - -2). Let a(v) = p*b(v) + 5*q(v). Find o such that a(o) = 0.
0, 1
Suppose 8*r = 11*r - 9. Solve 1/2 + 1/2*q**4 - q**2 + 0*q**r + 0*q = 0 for q.
-1, 1
Let m be -1 + 3 + 45/(-24). Factor m*y + 1/4*y**2 - 3/8.
(y - 1)*(2*y + 3)/8
Find o, given that -1/5*o + 0 - 1/5*o**3 + 2/5*o**2 = 0.
0, 1
Suppose 32*y = 34*y - 10. Factor 5/2*z**4 + 1/2 + y*z**2 + 5*z**3 + 1/2*z**5 + 5/2*z.
(z + 1)**5/2
Suppose -10*r = -7*r - 6. What is j in 1/6*j**r - 1/6 - 1/6*j + 1/6*j**3 = 0?
-1, 1
Suppose 9 = 4*d - 5*z - 9, -2*d + z = -6. Let j(p) be the first derivative of -1/12*p**3 - p - 1/2*p**2 + d. Factor j(l).
-(l + 2)**2/4
Let i(n) be the third derivative of 0*n - 2/3*n**3 + 1/30*n**5 - 1/12*n**4 + 0 + 9*n**2. Let i(c) = 0. Calculate c.
-1, 2
Let t(k) = -k + 6. Let b be t(0). Solve 10 - b - 2*g - 4*g**2 + 2*g**2 = 0.
-2, 1
Let r = 2/39 - -35/78. Let x(c) be the first derivative of 7/4*c**2 + c**4 + 7/3*c**3 + 1 + r*c. Factor x(z).
(z + 1)*(2*z + 1)*(4*z + 1)/2
Let o be 36/(-198) + 502/2640. Let c(g) be the third derivative of 0*g + 0*g**3 + 0 - 1/30*g**5 + 2*g**2 + 1/24*g**4 + o*g**6. Factor c(y).
y*(y - 1)**2
Let c(p) = -p**3 + p**2. Suppose -4*f = 2*q + 20, q = 3*f + 11 + 4. Let d(i) = 3*i - 2 - 7*i**3 + 0 - i + 0*i + 7*i**2. Let m(n) = f*c(n) + d(n). Factor m(y).
-2*(y - 1)**2*(y + 1)
Determine f, given that 6/5*f - 3/5*f**2 - 3/5 = 0.
1
Let s be ((-328)/(-32) - 6) + -4. Find d such that 0 - 1/4*d**5 + 1/4*d**3 - 1/4*d**2 + s*d**4 + 0*d = 0.
-1, 0, 1
Let x(y) be the third derivative of 0*y**3 + 0*y**5 - 2*y**2 + 1/12*y**4 + 0*y - 1/60*y**6 + 0. Suppose x(l) = 0. What is l?
-1, 0, 1
Let o be 4/14*4/80. Let q(t) be the third derivative of 0 - 1/140*t**6 - 1/84*t**4 + 0*t - 1/735*t**7 + 2*t**2 - o*t**5 + 0*t**3. Factor q(s).
-2*s*(s + 1)**3/7
Let b(v) be the first derivative of -v**4/24 + v**3/4 - v**2/2 + v + 2. Let s(d) be the first derivative of b(d). Factor s(t).
-(t - 2)*(t - 1)/2
Let o be (-1)/(-2)*1/12. Let s(a) be the third derivative of o*a**4 - 1/60*a**5 + 0*a**3 + 0 + 2*a**2 - 1/120*a**6 + 0*a + 1/210*a**7. Solve s(j) = 0.
-1, 0, 1
Let g(c) = -2*c - 5. Let k be g(-5). Suppose -3 = u - 6. Factor x - 4*x**u + 5*x**5 - 3*x**k + x.
2*x*(x - 1)**2*(x + 1)**2
Let n(j) be the first derivative of -3*j**6/220 - j**5/55 - j**4/132 + 5*j**2 - 8. Let k(r) be the second derivative of n(r). Suppose k(h) = 0. What is h?
-1/3, 0
Suppose 13 = -4*p + 45. Let c be (1/2)/(p + -7). Factor -1/2*l**2 - 3/4*l**3 + 7/4*l - c.
-(l - 1)*(l + 2)*(3*l - 1)/4
Let w(l) = 9*l**4 + 5*l**3 + 5*l**2 - 5*l + 5. Let f(i) = -5*i**4 - 3*i**3 - 3*i**2 + 3*i - 3. Let m(v) = 5*f(v) + 3*w(v). Determine t so that m(t) = 0.
0
Factor -18*f**2 - 13*f**3 + 29*f**2 - 21*f**2 + 5*f**5 - 2*f**3.
5*f**2*(f - 2)*(f + 1)**2
Let h(l) be the second derivative of 1/3*l**3 + 2/5*l**2 - 7/30*l**4 + 0 - 3*l. Factor h(a).
-2*(a - 1)*(7*a + 2)/5
Let a(i) be the third derivative of -i**9/30240 + i**8/6720 - i**7/5040 + 7*i**4/24 + 8*i**2. Let d(z) be the second derivative of a(z). Factor d(f).
-f**2*(f - 1)**2/2
Let o(p) be the second derivative of p**7/63 - p**6/15 + p**5/15 - 2*p. Factor o(y).
2*y**3*(y - 2)*(y - 1)/3
Let t(r) be the