 = 4*h. Determine k, given that h + 2/5*k**3 + 0*k**2 + 0*k = 0.
0
Let d(g) = 20*g**2 + 11*g - 8. Let p(w) = -13*w**2 - 7*w + 5. Let y(j) = 5*d(j) + 8*p(j). Factor y(h).
-h*(4*h + 1)
Let y(q) = -3*q - 16. Let f(w) = 4*w + 24. Let a(k) = 5*f(k) + 7*y(k). Let x be a(6). Suppose p**2 + p - 3*p**x + p**2 = 0. What is p?
0, 1
Let a(v) be the first derivative of -1/3*v**6 + v**2 - 4 + 0*v + 0*v**4 - 4/5*v**5 + 4/3*v**3. Solve a(k) = 0 for k.
-1, 0, 1
Let i(l) be the first derivative of -4*l**3/15 - 3*l**2 + 16*l/5 + 18. Factor i(b).
-2*(b + 8)*(2*b - 1)/5
Factor -2/15*n + 4/5 - 2/15*n**2.
-2*(n - 2)*(n + 3)/15
Let m = -10222/7 - -1462. Find o such that 0 - m*o**3 + 4/7*o**2 + 0*o = 0.
0, 1/3
Let k = -454/5 + 91. Determine n so that 1/5*n + 0 + k*n**3 + 2/5*n**2 = 0.
-1, 0
Solve l**4 + 0*l + 2*l - 2*l**3 + 2*l**2 - 3*l**4 = 0 for l.
-1, 0, 1
Let r(x) = x + 14. Let v be r(-9). Let g(q) be the third derivative of 0*q**3 + 1/72*q**4 - 2*q**2 + 0*q + 0 - 1/90*q**v + 1/360*q**6. Factor g(n).
n*(n - 1)**2/3
Let w = -6 + 10. Suppose v = -p + w, -p - 13 = -3*v - 5*p. Factor -2*y**v + 4*y**4 - 5*y**4 - 4*y**2 + 3*y**2.
-y**2*(y + 1)**2
Let c(k) be the first derivative of k**5/50 - k**3/5 + 2*k**2/5 + 4*k - 2. Let x(i) be the first derivative of c(i). Find p, given that x(p) = 0.
-2, 1
Factor 1/6 + 1/2*j**2 - 1/2*j - 1/6*j**3.
-(j - 1)**3/6
Let t(a) be the third derivative of -a**6/120 + a**5/3 - 19*a**4/24 + a**3/2 + 2*a**2. Let k be t(19). Let 0 + 5/3*v**k - v**2 - 2/3*v = 0. What is v?
-2/5, 0, 1
Solve -135*m**2 - 3/2*m**4 + 300*m + 24*m**3 - 375/2 = 0.
1, 5
Let a(q) = 5*q**2 + 9*q - 6. Let p(j) = -10*j + 27*j + 2 + 9*j**2 - 13. Let y(h) = 11*a(h) - 6*p(h). Factor y(l).
l*(l - 3)
Suppose 2 = -r + 7. Let g(b) = b + 3. Let y be g(r). Factor y*k**2 + 1 + k**3 - 4*k + 11*k - 17*k**3.
-(k - 1)*(4*k + 1)**2
Factor 2*a**3 + 0 - 3*a**3 + 2 + 2 - 3*a**2.
-(a - 1)*(a + 2)**2
Suppose -11*n + 5*n + 12 = 0. Factor -2/5*r + 2/5 - 2/5*r**n + 2/5*r**3.
2*(r - 1)**2*(r + 1)/5
Let u(o) be the second derivative of -o + 0 + 3/14*o**7 + 0*o**3 - 1/3*o**4 + 4/5*o**5 - 7/10*o**6 + 0*o**2. Factor u(m).
m**2*(m - 1)*(3*m - 2)**2
Suppose -b - 14 = 4*p - 0, -2*b = -4*p - 20. Suppose 0 = 2*i - 6 - 0. Find c such that 2*c**3 - 2*c - c**i + 1 + 3*c**b + 5*c + 0 = 0.
-1
Let o = 1/145 - -23/29. Let r(f) be the first derivative of -2/15*f**3 - 1 - o*f - 3/5*f**2. Solve r(z) = 0.
-2, -1
Find a, given that 4/7*a**2 - 2/7*a - 2/7*a**3 + 0 = 0.
0, 1
Let f = 1 + 4. Let k(d) = -d**5 - d**4 - 4*d**3 - 2*d. Let a(l) = -2*l**5 - l**4 - 9*l**3 - 5*l. Let w(p) = f*k(p) - 2*a(p). Factor w(i).
-i**3*(i + 1)*(i + 2)
Let u(t) be the second derivative of -1/3*t**3 + 1/5*t**5 + 0 - t - t**2 - 1/21*t**7 + 1/3*t**4 - 1/15*t**6. Suppose u(p) = 0. Calculate p.
-1, 1
Let y(i) be the second derivative of 0 - 9/2*i**3 - 1/2*i**4 + 27/20*i**5 + 3*i**2 - 4*i. Factor y(v).
3*(v - 1)*(v + 1)*(9*v - 2)
Let f = 19 - 13. Suppose f*c = 3*c. Factor -1/4*h**3 + 1/4*h**2 + c*h + 0.
-h**2*(h - 1)/4
Suppose 0 = 42*y - 77*y + 175. Suppose 0 + 0*p**2 + 4/11*p**4 + 0*p - 14/11*p**y + 0*p**3 = 0. What is p?
0, 2/7
Let m(b) be the second derivative of b**6/180 - b**4/12 + b**3/6 - 4*b. Let s(g) be the second derivative of m(g). Factor s(u).
2*(u - 1)*(u + 1)
Let z(q) be the first derivative of 5*q**6/6 - 7*q**5 + 45*q**4/2 - 100*q**3/3 + 20*q**2 - 4. Factor z(c).
5*c*(c - 2)**3*(c - 1)
Let i = 6 + -13. Let q be ((-2)/6)/(7/i). Solve -q - 2/3*h - 1/3*h**2 = 0.
-1
Let h(k) be the second derivative of -7/10*k**5 + 5/6*k**4 - 2*k + 2/3*k**3 + 0 + 0*k**2. Suppose h(f) = 0. Calculate f.
-2/7, 0, 1
Factor 0 - 2/9*b**4 - 2/9*b - 2/3*b**3 - 2/3*b**2.
-2*b*(b + 1)**3/9
What is p in -3 + 5*p**2 - 2*p**2 - 2*p + 3*p**3 - p = 0?
-1, 1
Let a(j) be the second derivative of -j**4/18 + 4*j**3/3 - 12*j**2 - j. Factor a(y).
-2*(y - 6)**2/3
Let z be ((-24)/20)/((-2)/5). Factor -10 - 3*o + 3*o**z - 4 + 11 + 3*o**2.
3*(o - 1)*(o + 1)**2
Let g(s) be the first derivative of 2/5*s**2 - 1/10*s**4 + 3*s + 1/75*s**6 - 1/15*s**3 + 1/50*s**5 - 4. Let l(o) be the first derivative of g(o). Factor l(x).
2*(x - 1)**2*(x + 1)*(x + 2)/5
Suppose v**4 + 3*v**5 - 3*v**3 + 2*v**4 + 0*v**4 - 3*v**3 = 0. What is v?
-2, 0, 1
Let c be -6 + 0 - (0 - 0). Let x(n) = -n**3 - 7*n**2 - 8*n - 8. Let b be x(c). What is l in -2*l - 2 + 4*l**2 + 2*l**3 - b*l**2 + 2*l**2 = 0?
-1, 1
Let s = -9 - -10. Let h = 4 - s. Factor -81*a**h + 2 - 6 - 81*a**2 - 27*a + 1.
-3*(3*a + 1)**3
Let w(i) = 15*i**2 + 21*i + 6. Let k(v) = -8*v**2 - 11*v - 3. Let y(q) = 9*k(q) + 5*w(q). Factor y(x).
3*(x + 1)**2
Suppose 5*m = -w + 13, -m - 2*m + 21 = 5*w. Let c(s) be the first derivative of 1/3*s**2 - 8/9*s**3 + 1/2*s**4 + w + 0*s. Factor c(g).
2*g*(g - 1)*(3*g - 1)/3
Suppose 4*c = -5*o - 39 - 21, 5*o = -c - 75. Let h = -10 - o. Let n(g) = g**2 - 1. Let r(q) = -7*q**2 - 4*q + 2. Let l(k) = h*n(k) + r(k). Factor l(i).
-(i + 2)**2
Let r = -7 + 10. Factor -4 + 6*j + 4 - r*j + 6*j**2 + 3*j**3.
3*j*(j + 1)**2
Factor -32*l + 20*l + l**2 + 13*l.
l*(l + 1)
Let p(h) be the first derivative of -3*h**4/16 + 3*h**3/4 - 3*h**2/4 + 12. Factor p(t).
-3*t*(t - 2)*(t - 1)/4
Let w be ((-38)/19)/(1/(-2)). Let j(n) be the first derivative of 6/5*n + 3/20*n**w - 3 - 3/10*n**2 - 2/5*n**3. Let j(y) = 0. Calculate y.
-1, 1, 2
Let f be 6/4 + 65/10. Let c be (-44)/(-18) - f/4. Factor -c + 2*b - 14/9*b**2.
-2*(b - 1)*(7*b - 2)/9
Suppose -2*v = 5*q, q = -3*q - 3*v. Find g, given that 0*g**3 + 0 + 0*g - 2/11*g**4 + q*g**2 = 0.
0
Suppose -4*m + 2 = -o, 5*m + 0 = 5. Let j(s) be the second derivative of 1/3*s**o - s + 8/9*s**4 + 0 - 8/9*s**3. Determine z so that j(z) = 0.
1/4
Let a(l) = -l - 1. Let b(v) = v**2 - 22*v + 77. Let h(t) = -4*a(t) + b(t). Let h(k) = 0. Calculate k.
9
Let x(y) = y**5 - y**4 + y**3 - y + 1. Let q(u) = 0*u - 6*u**4 + 2 + 11*u**3 - 5*u**3 + 4*u**2 - 2*u - 2*u**5 + 0*u. Let h(d) = q(d) - 2*x(d). Factor h(o).
-4*o**2*(o - 1)*(o + 1)**2
Let j(o) be the second derivative of -3*o**5/4 - o**4/4 + 8*o. Suppose j(k) = 0. Calculate k.
-1/5, 0
Let x = 73 + -647/9. Factor x*r**2 + 8/9 + 16/9*r + 2/9*r**3.
2*(r + 1)*(r + 2)**2/9
Factor -5*j**3 - 24*j**2 - 84/5*j - 16/5.
-(j + 4)*(5*j + 2)**2/5
Let f(g) = g**2 + 2*g + 4. Let z be f(-3). Factor -6*t**2 + z*t**2 + 2 - 3*t**2.
-2*(t - 1)*(t + 1)
Let p = 525/4 - 191. Let u = p - -60. Find x such that 1/2*x**3 + 0*x**2 + u*x**4 + 0*x + 0 = 0.
-2, 0
Let b(p) be the second derivative of 1/14*p**7 + 1/2*p**4 - 3/2*p**2 + 4*p - 1/10*p**6 + 0 + 1/2*p**3 - 3/10*p**5. Solve b(z) = 0.
-1, 1
Determine b, given that -6*b**4 - 44*b**3 + 0 - 88/3*b**2 + 18*b**5 - 16/3*b = 0.
-2/3, -1/3, 0, 2
Factor -40*y - 6*y**3 - 14*y**3 - 3*y**3 - 2*y**3 + 110*y**2.
-5*y*(y - 4)*(5*y - 2)
Suppose 3*r = 2*x - 1, 0 = -2*x + 3*x - 2*r. Let j be (-1)/(-3)*(x + 4). Factor -1/2*n**j - 1/2*n**3 + 0*n + 0.
-n**2*(n + 1)/2
Let m be ((-1)/(-2))/(12/96) - 2. Factor 0 - h + 3/2*h**m.
h*(3*h - 2)/2
Let l(u) = 49*u**3 - 113*u**2 - 48*u. Let r(h) = 12*h**3 - 28*h**2 - 12*h. Let b(p) = 2*l(p) - 9*r(p). Factor b(g).
-2*g*(g - 3)*(5*g + 2)
Let n(z) be the first derivative of z**4/20 + 4*z**3/5 + 24*z**2/5 + 64*z/5 + 4. Suppose n(m) = 0. What is m?
-4
Let f = 239/3 - 79. Let i(p) be the second derivative of 2*p**2 + 0 + f*p**3 + 1/12*p**4 + p. Factor i(w).
(w + 2)**2
Suppose -59*x**5 + 55*x**5 + 8*x**2 + 16*x**4 - 20*x**3 + 0*x**2 = 0. Calculate x.
0, 1, 2
Let j(s) be the third derivative of -s**8/336 + 11*s**7/525 - 11*s**6/200 + s**5/15 - s**4/30 + 32*s**2. Determine u, given that j(u) = 0.
0, 2/5, 1, 2
Let s = -13 + 7. Let q be (2 + 1)/(s/(-4)). Factor -32*w + 130*w**2 + 32*w**q + 8 + 15*w - 55*w.
2*(9*w - 2)**2
Let b be ((-3)/(-54))/((-8)/(-12)). Let i(w) be the second derivative of -w - 1/12*w**3 - 1/40*w**5 + 0*w**2 + 0 + b*w**4. Suppose i(p) = 0. Calculate p.
0, 1
Let b(y) = -11*y**4 + 10*y**3 + 5*y**2 + y + 17. Let g(h) = 5*h**4 - 5*h**3 - 3*h**2 - h - 8. Let i(s) = 6*b(s) + 13*g(s). Factor i(j).
-(j + 1)**3*(j + 2)
Suppose 5*w = -2*m + 16, m + 2*w + 0*w - 7 = 0. Determine k so that 2*k + k - m*k**2 - 7*k + k = 0.
-1, 0
Factor 0*v + 4/3*v**3 + 0 + 1/3*v**4 + 0*v**2.
v**3*(v + 4)/3
Let f(v) be the first derivative of -2*v**6/3 - 4*v**5/5 + 2*v**4 + 8*v**3/3 - 2*v**2 - 4*v + 3. Solve f(d) = 0.
-1, 1
Factor -i**5 - 6*