). Factor u(k).
2*k*(k - 1)*(k + 1)**3
Let y(h) = -h**3 + 3*h**2 + 14*h - 17. Let u be y(5). Determine g so that 18/5*g**2 + 2/5*g**4 + 2*g**u + 14/5*g + 4/5 = 0.
-2, -1
Let w(y) = 4*y**2 + 5*y + 1. Let h(b) = -7*b**2 - 9*b - 2. Let z(d) = -3*h(d) - 5*w(d). Suppose z(l) = 0. Calculate l.
-1
Suppose -3*j + 0*j - v + 57 = 0, -2*j + 38 = 5*v. Suppose -3*g + 0*l - 2*l - 4 = 0, -j = 3*g + 5*l. Solve 4/5*q + 0 + 2/5*q**g = 0.
-2, 0
Let o be 36/15*(-15)/(-6). Suppose 0 = o*c - 12. Determine a, given that 2/9*a**3 + 2/9*a**c + 0*a + 0 = 0.
-1, 0
Factor 20*h**2 - 2*h**3 + 16 + 4*h**3 - 6*h**3 - 188*h + 156*h.
-4*(h - 2)**2*(h - 1)
Let q(r) be the second derivative of 0 + 1/6*r**3 - r + 0*r**2 + 1/12*r**4. Solve q(v) = 0 for v.
-1, 0
Let u(r) be the third derivative of -r**7/420 - r**3/6 - 4*r**2. Let z(n) be the first derivative of u(n). Solve z(k) = 0.
0
Let t(b) be the second derivative of 2*b**6/105 - b**5/35 + b**4/84 + 5*b. Factor t(o).
o**2*(2*o - 1)**2/7
Let y(p) = -p**3 - p - 2. Let x(m) = 10*m**3 - 40*m**2 + 30*m - 20. Let l(o) = -x(o) + 5*y(o). Factor l(z).
-5*(z - 1)**2*(3*z - 2)
Let r(d) be the first derivative of -4*d**3/3 + 4*d**2 + 12*d + 9. Factor r(t).
-4*(t - 3)*(t + 1)
Let u(r) = 3*r - 18. Let t be u(6). Let p(h) be the second derivative of 0*h**2 - h + t*h**4 + 0 - 1/189*h**7 + 0*h**5 + 0*h**6 + 0*h**3. Factor p(d).
-2*d**5/9
Let z be (-13 - -15)*(-2)/(-4). Suppose 4*a = a + 6. Suppose -3*m + z + 9/4*m**a = 0. Calculate m.
2/3
Let i be 0 + 1 - (5 - 6). Let j be (i/(-5))/((-2)/2). Suppose j*n**2 + 0*n - 2/5*n**4 + 2/5*n**5 - 2/5*n**3 + 0 = 0. Calculate n.
-1, 0, 1
Let i be ((-12)/9)/(20/(-30)). Factor -2/3*w**i - 2*w**3 + 0 + 4/3*w.
-2*w*(w + 1)*(3*w - 2)/3
Let d(q) be the second derivative of -q**7/11340 - q**6/1620 - q**5/540 - q**4/4 - 3*q. Let p(j) be the third derivative of d(j). Factor p(y).
-2*(y + 1)**2/9
Let z(h) be the third derivative of 0 + 1/30*h**5 + 1/336*h**8 + 0*h**6 + 3*h**2 - 1/24*h**4 + 0*h**3 - 1/105*h**7 + 0*h. Suppose z(o) = 0. What is o?
-1, 0, 1
Let s(o) = 4*o**3 - 3*o**2 - 12*o + 11. Let q(b) = 12*b**3 - 10*b**2 - 36*b + 34. Let u(n) = 3*q(n) - 10*s(n). Factor u(h).
-4*(h - 1)**2*(h + 2)
Let t = 6 + -4. Let b be t/9 + 32/18. Find q such that -1/4*q**b - 1/4*q + 0 = 0.
-1, 0
Let z(m) be the first derivative of -4*m**3/3 + 10*m**2 + 18. Factor z(a).
-4*a*(a - 5)
Let o(w) be the second derivative of -w**4/20 + w**3 - 15*w**2/2 + 7*w. Solve o(l) = 0 for l.
5
Let c(d) be the second derivative of -1/20*d**4 - 6/5*d**2 + 5*d + 0 - 2/5*d**3. Find o such that c(o) = 0.
-2
Let v(c) be the second derivative of -9*c**7/14 - 12*c**6/5 - 39*c**5/20 - c**4/2 + 2*c. Let v(g) = 0. Calculate g.
-2, -1/3, 0
Factor 1/4*a**3 - 1/4*a - 1/4*a**2 + 1/4*a**4 + 0.
a*(a - 1)*(a + 1)**2/4
Let p(o) be the first derivative of -2 - 2/3*o**3 + o + 7/4*o**2. Solve p(n) = 0 for n.
-1/4, 2
Let b(u) = 3*u**3 + 13*u**2 - 5*u. Let a(v) = v**3. Let y(s) = -2*a(s) + b(s). Let l(p) = 6*p**2 - 2*p. Let o = 0 - -2. Let m(c) = o*y(c) - 5*l(c). Factor m(t).
2*t**2*(t - 2)
Let a(r) = -r**3 + 9*r**2 - 5*r - 11. Let m be a(8). Let w = -10 + m. Factor 4/3*i**w + 0*i + 2/3 - 2*i**2.
2*(i - 1)**2*(2*i + 1)/3
Find s such that 0 - 4/15*s + 2/5*s**2 = 0.
0, 2/3
Solve 4/5*n**3 + 0*n**2 + 0 - 4/5*n = 0 for n.
-1, 0, 1
Suppose 6 = i + 2. Let d be ((-8)/(-10))/(4/10). Find h, given that -5*h**3 - 1 - 17*h**3 + 8*h**i + 18*h**d - 2*h - 1 = 0.
-1/4, 1
Let i(g) = 3*g**4 + 6*g**3 + 3*g**2 - 11*g - 1. Let n(k) = 4*k**4 + 6*k**3 + 4*k**2 - 12*k - 2. Let a(h) = 6*i(h) - 5*n(h). Factor a(b).
-2*(b - 2)*(b - 1)**2*(b + 1)
Let q(a) be the third derivative of a**5/135 - a**4/27 + 29*a**2. What is w in q(w) = 0?
0, 2
Let l = -1101 - -1101. Factor 4/3 + l*r**2 - 2*r + 2/3*r**3.
2*(r - 1)**2*(r + 2)/3
Let x(n) = n**5 - n**3 - n**2 + n + 1. Let v(o) = -6*o**5 + 3*o**4 + 6*o**3 - 3*o - 3. Let k(f) = v(f) + 3*x(f). Factor k(a).
-3*a**2*(a - 1)**2*(a + 1)
Let g(i) be the second derivative of -i**7/98 - i**6/35 - 3*i**5/140 + 4*i. Factor g(t).
-3*t**3*(t + 1)**2/7
Suppose -3*j + 41 - 29 = 0. Factor -4/3 - 44/3*p**j - 64/3*p**2 - 76/3*p**3 - 10/3*p**5 - 26/3*p.
-2*(p + 1)**4*(5*p + 2)/3
Let o = 8 + -4. Suppose 0 = o*p - 9*p. Factor 0 - l + l**2 + p.
l*(l - 1)
Let i(u) = u - 4. Let m be i(6). Let y = 5 - m. Factor 5*f - f**2 - 4*f + 2*f - f - 3*f**y.
-f*(f + 1)*(3*f - 2)
Factor 6*f**2 - 2*f**2 + 0*f + 8*f.
4*f*(f + 2)
Let q be 153/(-27) - (4 - 10). Let o = -76/9 + 88/9. Let -4/3*c + q*c**2 + o = 0. What is c?
2
Let y(w) be the second derivative of -28/3*w**3 + 0 + 49/3*w**4 + w + 8/3*w**2 - 343/30*w**5. Determine j, given that y(j) = 0.
2/7
Let h be 2/(-2)*(-24)/6. Suppose h*f - 7*f = -6. Solve -4/3 - 10/3*u - 8/3*u**f - 2/3*u**3 = 0.
-2, -1
Suppose 4*a + 20 + 0 = -3*m, 0 = 4*m - 3*a - 15. Suppose 2*j - j - 2 = 0, 2*f - 4*j + 8 = m. Factor -2*o + 3*o**2 + 2*o + 3 + 6*o + f*o.
3*(o + 1)**2
Factor 3/7*u**2 + 30/7 + 33/7*u.
3*(u + 1)*(u + 10)/7
Let r(n) = -4*n**4 + 4*n**2 + 2*n. Let t(i) = -i**5 + i**4 + i**3 - i**2 - i. Let y(c) = -r(c) - 2*t(c). Factor y(f).
2*f**2*(f - 1)*(f + 1)**2
Let i(c) be the first derivative of -1/3*c**2 - 8/15*c**5 - c**4 - 2 - 8/9*c**3 - 1/9*c**6 + 0*c. Factor i(v).
-2*v*(v + 1)**4/3
Let s(q) be the third derivative of q**6/180 + q**5/45 - q**4/12 + 26*q**2. Factor s(p).
2*p*(p - 1)*(p + 3)/3
Let y = 221/79 - 52487/18960. Let b(j) be the third derivative of 1/160*j**6 + y*j**5 + 1/24*j**3 + 0 + 0*j - 4*j**2 + 5/96*j**4. Solve b(k) = 0 for k.
-1, -1/3
Let 2*k**2 - 3*k**4 + 2 + 16*k**3 - 14*k**2 - 3*k**4 = 0. Calculate k.
-1/3, 1
Let t(b) be the third derivative of -1/24*b**3 + 0*b + 0 + 3*b**2 - 1/160*b**6 + 1/240*b**5 + 1/32*b**4. Factor t(o).
-(o - 1)*(o + 1)*(3*o - 1)/4
Let d be -1*(8/(-60) + (-86)/30). Let o(m) be the third derivative of m**2 - 1/24*m**4 + 1/48*m**5 + 0 - 1/24*m**d + 0*m. What is n in o(n) = 0?
-1/5, 1
Let b(t) = -t**2 + t + 1. Let f(k) = -k**3 + 10*k**2 - 7*k - 12. Let y(p) = -6*b(p) - f(p). Suppose y(s) = 0. Calculate s.
-1, 2, 3
Factor -y**4 - 6 - 2*y**2 + 4 + 2 + 3*y**3.
-y**2*(y - 2)*(y - 1)
Let a(d) = -d. Let o be a(-3). Suppose -u - j = o, 2*j + 0*j = u - 12. Factor 2*r**4 + u*r**4 - 2*r**4.
2*r**4
Let b(p) = 28*p**2 + 22*p + 4. Let m(w) be the third derivative of -w**5/60 + 2*w**2. Let r(s) = -2*b(s) + 4*m(s). Factor r(l).
-4*(3*l + 1)*(5*l + 2)
Let o(k) be the third derivative of -4*k**5/105 - 2*k**4/21 - 2*k**3/21 + 22*k**2. Factor o(x).
-4*(2*x + 1)**2/7
Let n be 3/(-6) - (-100)/8. Suppose -v - 3*v = -n. Find a, given that 3/2*a**4 + 0 + v*a**3 + 0*a**2 + 0*a = 0.
-2, 0
Let z = -154 + 1849/12. Let b(n) be the third derivative of -1/60*n**5 + 0*n**3 + 4*n**2 + 0 + 0*n - z*n**4. Suppose b(f) = 0. Calculate f.
-2, 0
Suppose -3*n + 12 = -6. Suppose 3*h = n*h. Suppose 0 + 4/7*x**2 + 2*x**3 + h*x = 0. Calculate x.
-2/7, 0
Let d be -5 + (4 - (-28)/12). Factor -2/3*g**2 - d*g - 2/3.
-2*(g + 1)**2/3
Let k(n) = n**3 + 5*n**2 + n + 5. Let p be 0 - 2 - (6 - 3). Let z be k(p). Determine h, given that -1 + h**4 + 2*h - 2*h**3 + z + 0*h = 0.
-1, 1
Let u = -15 - -17. Let o(s) be the second derivative of 0*s**4 - 2*s + 0*s**u + 1/50*s**5 - 1/15*s**3 + 0. Factor o(z).
2*z*(z - 1)*(z + 1)/5
Suppose -4*d + 7 = -13. Let z(r) be the second derivative of -1/20*r**d + 0*r**2 + 1/30*r**6 + 0 + 2*r + 0*r**3 + 0*r**4. Factor z(i).
i**3*(i - 1)
Let b(o) be the third derivative of o**5/330 + o**4/22 - 18*o**2. Find h such that b(h) = 0.
-6, 0
Let c(n) = -n**3 - 10*n**2 - n - 8. Let j be c(-10). Let i(a) be the first derivative of 0*a**j + 0*a**3 + 2 + 1/4*a**4 + 0*a. Factor i(x).
x**3
Let n(y) be the first derivative of -y**4/8 - 19*y**3/3 - 361*y**2/4 + 20. Determine j, given that n(j) = 0.
-19, 0
Let v(x) be the third derivative of x**6/540 - 26*x**2. Let v(b) = 0. Calculate b.
0
Let q = 689/20 - 137/4. Factor p - q - 4/5*p**2.
-(p - 1)*(4*p - 1)/5
Let t = 1 + 1. Suppose 2*v + i = 4*v, i = -t*v + 4. Factor p**2 + p - v - p**3 - p + p.
-(p - 1)**2*(p + 1)
Suppose -3*z + 27 = -3*y, z - 4*z + 15 = y. Let p**2 - 2*p - 3 - 2 + z = 0. What is p?
1
Solve -4/5*q**3 + 4/5*q**2 + 1/5*q**4 + 0 + 0*q = 0 for q.
0, 2
Suppose 2*l - 8*l = 0. Find x, given that 2*x**3 + l + 4/9*x + 22/9*x**2 = 0.
-1, -2/9, 0
Let m(w) be the first derivative of 25/14*w**4 - 10/21*w**3