) be the second derivative of -2*u**7/35 - 2*u**6/15 - u**5/15 + 4*u**2 + 7*u. Let j(g) be the first derivative of o(g). Factor j(y).
-4*y**2*(y + 1)*(3*y + 1)
Let w(m) be the second derivative of 0*m**2 + 1/10*m**5 + 5*m + 0*m**3 + 0 + 4/15*m**6 + 0*m**4. Factor w(s).
2*s**3*(4*s + 1)
Let x(i) = -6*i**2 - 9*i + 5. Let g(w) = -1. Let h(o) = g(o) - x(o). Factor h(v).
3*(v + 2)*(2*v - 1)
Suppose 2 = -5*g - s, g - s + 2 = -2*s. Factor 0 + 1/2*n**2 + 1/2*n**4 + n**3 + g*n.
n**2*(n + 1)**2/2
Let j(d) be the third derivative of -d**5/240 - d**4/48 - 17*d**2. Factor j(g).
-g*(g + 2)/4
Let l(b) be the first derivative of -b**4/2 - 4*b**3/3 - b**2 - 11. Find r, given that l(r) = 0.
-1, 0
Let c(r) = -r - 7. Let b be c(-9). Factor 2*t**5 + 3*t**3 + b*t**5 + 3*t**3 + 6*t**3 + 12*t**4 + 4*t**2.
4*t**2*(t + 1)**3
Factor -2/7*g**2 + 4/7 + 2/7*g.
-2*(g - 2)*(g + 1)/7
Let z = -10 - -12. Factor 1/4 - 1/2*n**z + 0*n**3 + 0*n + 1/4*n**4.
(n - 1)**2*(n + 1)**2/4
Let w(q) be the first derivative of 2*q**3/15 - 2*q**2/5 + 3. Suppose w(o) = 0. Calculate o.
0, 2
Let z(g) be the third derivative of g**8/24 + g**7/21 - 3*g**6/20 - g**5/6 + g**4/6 + 29*g**2. Find v such that z(v) = 0.
-1, 0, 2/7, 1
Let b be (-10)/(-4)*(-9 - -11). Let z(t) be the first derivative of -t**3/3 + t**2/2 + 1. Let a(y) = -2*y**2 + 3*y. Let q(d) = b*z(d) - 2*a(d). Factor q(v).
-v*(v + 1)
Let r = 18 - 16. Suppose 0 = -r*w - w. Factor -1/2*x**4 + 0*x + 0 + w*x**2 - 1/2*x**3.
-x**3*(x + 1)/2
Let q be (-4)/3 + (-6)/(-18). Let m(k) = -k + 1. Let t be m(q). Factor t*c**3 + 3*c**2 - 10*c**2 + 5*c**2.
2*c**2*(c - 1)
Suppose n + 5 = 0, -5 = -5*h + 3*n - 6*n. Factor -1/3*b**3 + 0*b - 1/6*b**h - 1/6*b**2 + 0.
-b**2*(b + 1)**2/6
Let x(r) = 7*r + 2. Let v(g) = -2*g. Let f(s) = -6*v(s) - 2*x(s). Let d be f(-4). Factor 2*n - 4*n**4 + 0*n**2 - n**3 - n + 4*n**2 + 0*n**d.
-n*(n - 1)*(n + 1)*(4*n + 1)
Let w(y) be the first derivative of -3 + 2*y + 1/2*y**2 - 1/3*y**3. Factor w(j).
-(j - 2)*(j + 1)
Let i be 6*(-2 + (-32)/(-12)). Let x(d) be the second derivative of 0*d**2 - 1/3*d**3 + 0 + 3*d - 1/6*d**i + 1/10*d**5 + 1/15*d**6. Find g, given that x(g) = 0.
-1, 0, 1
Let t(c) be the second derivative of c**4/12 - 4*c**3/3 + 7*c**2/2 + 2*c. Let p be t(7). Solve 2/3*s + p - 4/3*s**2 - 8/3*s**4 - 14/3*s**3 = 0.
-1, 0, 1/4
Let j(t) be the first derivative of -2*t**3/15 + t**2/5 + 4*t/5 - 42. Factor j(a).
-2*(a - 2)*(a + 1)/5
Let q(o) be the first derivative of -3*o**5/20 - 9*o**4/16 - o**3/2 - 12. Solve q(k) = 0 for k.
-2, -1, 0
Let m = 21987/4 + -5462. Let i = -34 + m. Factor 9/4*s**3 + 9/4*s**2 + 0 + 3/4*s**4 + i*s.
3*s*(s + 1)**3/4
Let o(d) be the second derivative of 1/12*d**4 + 0 + 0*d**2 - d - 1/18*d**3 - 1/20*d**5 + 1/90*d**6. Factor o(r).
r*(r - 1)**3/3
Let c be 10/4*(-24)/20. Let f = c + 3. Factor 1/2*j**3 + 0 + 5/4*j**5 + 0*j + 7/4*j**4 + f*j**2.
j**3*(j + 1)*(5*j + 2)/4
Let j(v) = 65*v**3 + 235*v**2 + 90*v - 40. Let p(o) = -5*o**3 - 18*o**2 - 7*o + 3. Let k(g) = 3*j(g) + 40*p(g). Factor k(s).
-5*s*(s + 1)*(s + 2)
Let x(k) be the second derivative of -k**4/54 + k**3/27 + 10*k. Factor x(o).
-2*o*(o - 1)/9
Let d(u) be the second derivative of u**6/60 - u**5/8 + 7*u**4/24 - u**3/4 - 19*u. Solve d(h) = 0 for h.
0, 1, 3
Let y(x) = -4*x**2 + 2*x + 2*x + 0*x**2 - 2*x**3 - 2*x**4 - 3*x**4. Let v(n) = n**3 + n**2 - n. Let p(w) = -4*v(w) - y(w). Suppose p(o) = 0. What is o?
0, 2/5
Let n(g) be the second derivative of 2*g**7/7 - 13*g**6/10 + 33*g**5/20 - g**4/2 - 6*g. Determine h so that n(h) = 0.
0, 1/4, 1, 2
Let z(q) = -23*q**4 + 10*q**3 + 77*q**2 + 18*q - 18. Let g(h) = -h**4 - h**2 + h - 1. Let j(i) = -2*g(i) - z(i). Suppose j(l) = 0. What is l?
-1, 2/5, 2
Let w(y) = 2*y**4 - 12*y**3 + 10*y**2 - 2*y - 2. Let n(g) = 9*g**4 - 60*g**3 + 51*g**2 - 11*g - 11. Let q(d) = 2*n(d) - 11*w(d). Factor q(h).
-4*h**2*(h - 2)*(h - 1)
Let g(z) = -z**2 - 3*z + 4. Let m be g(-4). Suppose 0*c + c - 4 = m. Factor -6*q**5 + 3*q**3 + 3*q**c - 3*q**2 + 5*q**5 - 2*q**5.
-3*q**2*(q - 1)**2*(q + 1)
Let r = 130 + -253/2. Suppose -6*j + 4 = -20. Factor 0 + 0*s - s**2 - 5/2*s**j + r*s**3.
-s**2*(s - 1)*(5*s - 2)/2
Let b = -14 + 17. Let g be 35/15 + (-1)/b. Factor -1/3*k + 0 - 4/3*k**g.
-k*(4*k + 1)/3
Let k(s) be the first derivative of -1/8*s**2 - 1/48*s**4 + 1/12*s**3 + 3*s - 2. Let p(w) be the first derivative of k(w). Factor p(v).
-(v - 1)**2/4
Let b(j) be the second derivative of j**5/210 - j**4/84 - 2*j**2 + 3*j. Let g(r) be the first derivative of b(r). Factor g(m).
2*m*(m - 1)/7
Factor -2/3*p**3 + 2/9*p**4 + 2/3*p - 4/9 + 2/9*p**2.
2*(p - 2)*(p - 1)**2*(p + 1)/9
Let i = -184 + 187. Factor 18/5*y**i + 0 + 14/5*y**4 + 4/5*y**2 + 0*y.
2*y**2*(y + 1)*(7*y + 2)/5
Let r(l) be the first derivative of -2*l**5/35 + 8*l**4/7 - 64*l**3/7 + 256*l**2/7 - 512*l/7 + 12. Factor r(s).
-2*(s - 4)**4/7
Factor 4*j**4 - 2/5*j**3 + 0*j - 32/5*j**5 + 0*j**2 + 0.
-2*j**3*(2*j - 1)*(8*j - 1)/5
Let q(j) be the first derivative of j**6/30 - j**5/10 + 3*j - 3. Let o(m) be the first derivative of q(m). Determine d so that o(d) = 0.
0, 2
Factor 3*j**4 + 0*j**5 + 2*j**5 - 40 + 6*j**2 + j**5 + 31 + 15*j - 18*j**3.
3*(j - 1)**3*(j + 1)*(j + 3)
Let l(t) be the first derivative of 0*t**5 + 1/14*t**6 + 0*t**2 + 0*t**3 + 0*t + 2 - 3/28*t**4. Factor l(n).
3*n**3*(n - 1)*(n + 1)/7
Let z(a) be the first derivative of 1/900*a**6 + 0*a + 0*a**2 - 1 - 1/60*a**4 + 2/3*a**3 + 0*a**5. Let c(j) be the third derivative of z(j). Solve c(w) = 0.
-1, 1
Let f be (-116)/(-176) - (-7)/77. Factor 0*i + 0 + 3/4*i**2 - f*i**3.
-3*i**2*(i - 1)/4
Let j = 10 + -7. Factor 0*m + 0 + 2/7*m**j + 2/7*m**2.
2*m**2*(m + 1)/7
Suppose -10*x = -11*x + 2. Factor -2*t + 3*t**x - 4*t**2 - 2*t**3 + 3*t**2 + 2*t**2.
-2*t*(t - 1)**2
Suppose 2*q = -0 + 8. Factor -7*g**2 + 5*g**2 + q*g**2 - 2.
2*(g - 1)*(g + 1)
Let p(b) be the third derivative of -34/735*b**7 + 2/35*b**5 + 0 + 1/30*b**6 + 5/392*b**8 - 2/21*b**3 - 5/84*b**4 + 0*b + b**2. Solve p(z) = 0.
-2/5, -1/3, 1
Let i(k) = 2*k + k**3 - 3*k**3 - k**2 + k**3 - k. Let m(l) = -3*l**4 - 6*l**3 - 6*l**2 + 6*l. Let r(f) = -6*i(f) + m(f). Solve r(u) = 0.
0
Determine w so that w**4 + 6*w**3 - 8*w**2 + 6*w**3 + w**4 - 18*w**3 = 0.
-1, 0, 4
Let z(o) be the third derivative of -o**6/240 - 7*o**5/120 - o**4/6 + 4*o**3/3 - 6*o**2. Factor z(p).
-(p - 1)*(p + 4)**2/2
Let w(o) be the third derivative of 0 + 0*o**4 + 0*o**3 + 0*o**5 + 0*o + 3*o**2 - 1/60*o**6. Let w(q) = 0. Calculate q.
0
Let s(m) be the second derivative of -2*m + 0 + 1/20*m**5 + 3/160*m**6 + 0*m**3 - m**2 + 1/24*m**4. Let t(q) be the first derivative of s(q). Factor t(n).
n*(3*n + 2)**2/4
Let y be (-6)/33 + 46/11. Suppose 5*c - 5 = -y*x + 13, 5*c = 10. Solve -3*a**4 + a - x*a**2 - 2*a**3 + 5*a**4 + 2*a - a = 0 for a.
-1, 0, 1
Let j(c) be the third derivative of c**6/780 - c**4/156 - 17*c**2. Find p, given that j(p) = 0.
-1, 0, 1
Let d(f) = 5*f**3 + 11*f**2 - 4*f + 4. Let v(g) = -11*g**3 - 22*g**2 + 9*g - 9. Let u(p) = -9*d(p) - 4*v(p). Let u(y) = 0. What is y?
-11, 0
Let m = 348 - 344. Factor 0*c**3 - 2*c**2 + 0 + 2/3*c**m + 4/3*c.
2*c*(c - 1)**2*(c + 2)/3
Let k(c) = -c**3 + 4*c**2 + 7*c - 10. Let y be k(5). Find p, given that 2/3*p - 1/3*p**2 + y - 1/3*p**3 = 0.
-2, 0, 1
Let a = -45/7 - -163/21. Factor a - 10/3*l + 4/3*l**2.
2*(l - 2)*(2*l - 1)/3
Suppose 4*a = -3*l, -a - 2*a - 3*l = 0. Factor a - 1/3*t - 1/3*t**5 + 0*t**2 + 2/3*t**3 + 0*t**4.
-t*(t - 1)**2*(t + 1)**2/3
Let c be 3*(2 + -1) + -1*3. Let q(l) be the first derivative of 3 + l**2 + c*l - 2/3*l**3. Factor q(i).
-2*i*(i - 1)
Let z(o) be the first derivative of o**7/70 + o**6/40 - o**5/20 - o**4/8 + 2*o**2 + 2. Let f(s) be the second derivative of z(s). Suppose f(i) = 0. Calculate i.
-1, 0, 1
Let w(z) be the first derivative of z**3/9 - z**2/6 + 1. Factor w(x).
x*(x - 1)/3
Let g(k) be the first derivative of k**4/4 - 5*k**3/3 - 3. Let a be g(5). Let -2/5*l**4 + 0*l**2 + 0*l - 2/5*l**3 + a = 0. Calculate l.
-1, 0
Let l = 7 - 14. Let o = l - -10. Let d**2 - d**2 - 2*d**2 - 4*d + 6*d**3 - 2*d**o + 2 = 0. Calculate d.
-1, 1/2, 1
Let h(j) = j**3 - j**2 + j - 1. Let m(t) = -t**3 + 11*t**2 - 6*t + 6. Let q(s) = -6*h(s) - m(s). Factor q(i).
-5*i**2*(i + 1)
Determine f, given that 0 - 26/5*f**3 - 8/5*f - 24/5*f**2 - 12/5*f**4 - 2/5*f**5 = 0.
-2, -1, 0
Let