11. Let g be b(-10). Let x be m(g). Factor x*h**5 + 0*h**5 + h - 5*h**5 - 2*h**4 + 2*h**2 + h**5.
-h*(h - 1)*(h + 1)**3
Let v be 3/(-5) + 312/20. Suppose -2*s + 5*s - v = 0. Factor -m**5 - 4*m + m**4 + 2*m**2 + 0*m - 3*m**4 + s*m.
-m*(m - 1)*(m + 1)**3
Let b(s) = 2*s**4 + s**3 - 6*s**2 - 5*s - 5. Let l(w) = -w**4 + 5*w**2 + 4*w + 4. Let a(u) = 4*b(u) + 5*l(u). Factor a(r).
r**2*(r + 1)*(3*r + 1)
Let x be 3/(-12) + (-51)/(-12). Determine v so that 0*v + 2*v - v**2 - x*v - 1 = 0.
-1
Let i(k) be the third derivative of -k**7/126 + k**6/45 - k**5/180 - k**4/36 - 6*k**2. Factor i(w).
-w*(w - 1)**2*(5*w + 2)/3
Let u = -386 - -391. Factor 0*x + 0*x**2 + 0 - 4/3*x**3 - 4/3*x**4 - 1/3*x**u.
-x**3*(x + 2)**2/3
Let n(j) = -3*j**2 + 10*j - 7. Let m(a) = a**2 - 3*a + 2. Let k(v) = -14*m(v) - 4*n(v). Suppose k(w) = 0. Calculate w.
0, 1
Let g(z) = 3*z**2 + 6. Suppose 0 = -y - 2, -1 = 5*k - 3*y - 12. Let n(c) = -1. Let w(h) = k*g(h) + 6*n(h). Determine r, given that w(r) = 0.
0
Let w(n) be the second derivative of -n**5/15 + 5*n**4/18 - 4*n**3/9 + n**2/3 + 2*n. Factor w(p).
-2*(p - 1)**2*(2*p - 1)/3
Let q(d) = 5*d - 27. Let w be q(6). Let b(a) be the third derivative of 0 - 1/90*a**5 - 1/12*a**4 + 0*a - 3*a**2 - 2/9*a**w. What is x in b(x) = 0?
-2, -1
Factor -23*p**3 - 2 - 4*p**2 + 3*p + 24*p**3 + 2*p.
(p - 2)*(p - 1)**2
Suppose 0 = 5*w + 38 - 48. Let 0*d - 2/3*d**w + 0 + 7/3*d**3 - 5/3*d**4 = 0. What is d?
0, 2/5, 1
Let w(i) = -i**3 + 13*i**2 - 10*i - 15. Let n be w(12). Let k be 29/n - 14/63. Suppose 0 + 2*b**2 - 2/3*b**k - 4/3*b = 0. What is b?
0, 1, 2
Let m(r) be the second derivative of -1/21*r**7 + 0*r**4 + 2/15*r**6 + 0*r**3 - 2*r + 0*r**2 - 1/10*r**5 + 0. Factor m(i).
-2*i**3*(i - 1)**2
Let k(c) = 3*c - 4. Let t be k(3). Suppose -5*q - 20 = g, q = -t*g + 3*q + 8. Factor -24*y**2 + y**3 - 11*y**3 + g - 4 - 18*y.
-2*(y + 1)**2*(5*y + 2)
Let 5/7*x**2 - 2/7*x + 16/7*x**3 + 9/7*x**4 + 0 = 0. Calculate x.
-1, 0, 2/9
Let y = -997 + 4989/5. Let -y - 2/5*o - 2/5*o**4 + 6/5*o**2 + 2/5*o**3 = 0. Calculate o.
-1, 1, 2
Let i = -54 + 271/5. Suppose 0 = -2*f + 5 + 3. Factor -4/5*g**f + 0 + i*g**5 - 4/5*g**2 + 1/5*g + 6/5*g**3.
g*(g - 1)**4/5
Let i(b) be the first derivative of b**3/3 - 7*b**2/2 + 4*b + 5. Let o be i(7). Suppose 12*h**2 - 18*h**3 - 10/3*h + 1/3 + 9*h**o = 0. What is h?
1/3, 1
Let t(v) = -v**5 - 4 + 0*v**4 - 4*v**4 - 2 - v**3 + 4*v**2 - 6*v - 4*v**3. Let l(a) = a**2 - a - 1. Let m(s) = 6*l(s) - t(s). Factor m(f).
f**2*(f + 1)**2*(f + 2)
Let h = -4/17 - -29/51. Factor 1/3*s**2 + 0 + h*s**3 + 0*s.
s**2*(s + 1)/3
Let q = -4 + 7. Suppose 9 - 23*p + 81*p**q - 86*p**2 + 15 - 13*p + 32*p**2 = 0. Calculate p.
-2/3, 2/3
Let n(h) = -2*h**2 + 4*h - 7. Let q(t) = 6*t**2 - 11*t + 22. Let m(v) = -7*n(v) - 2*q(v). Let z(i) = -i**2 + 6*i - 4. Let f(g) = 4*m(g) + 5*z(g). Factor f(r).
3*r*(r + 2)
Let z(a) = -a**3 - a**2 + a - 1. Let p(y) = -3*y**4 + 9*y**3 - 3*y + 3. Let x(i) = -p(i) - 3*z(i). Determine s, given that x(s) = 0.
0, 1
Let l(b) = 5*b - 12. Let q(o) = -14*o + 36. Let n(i) = -17*l(i) - 6*q(i). Let v be n(-12). Find h such that v + 0*h + 2/3*h**3 - 4/3*h**2 = 0.
0, 2
Let k(y) = 2*y**3 - 2*y**2 - 4*y + 4. Let q(d) = 0*d + 0*d - d + 1. Let l(p) = -k(p) + 2*q(p). Determine n so that l(n) = 0.
-1, 1
Let k(u) = u**3 + 14*u**2 + 39*u - 10. Let f be k(-10). Suppose 2/3*a**3 + 2/3*a**2 + f - 4/3*a = 0. What is a?
-2, 0, 1
Let g(a) = -2*a**4 - 8*a**3 - 6*a**2 + 4. Let o(v) = -2*v**4 - 9*v**3 - 7*v**2 + 5. Let j(t) = 5*g(t) - 4*o(t). Suppose j(k) = 0. What is k?
-1, 0
Factor 9/5*a + 0 + 3/5*a**2.
3*a*(a + 3)/5
Let z(n) be the third derivative of -n**5/120 - 29*n**2. Factor z(t).
-t**2/2
Let g(s) be the second derivative of -s**8/168 - 2*s**7/105 - s**6/60 - s**2/2 + 2*s. Let y(w) be the first derivative of g(w). Suppose y(h) = 0. What is h?
-1, 0
Let u(l) be the first derivative of l**9/189 + 3*l**8/140 + l**7/35 + l**6/90 + 5*l**3/3 + 3. Let q(h) be the third derivative of u(h). Let q(w) = 0. What is w?
-1, -1/4, 0
Let n(p) be the third derivative of -1/180*p**5 + 1/18*p**3 + 0*p + 0 + 2*p**2 + 0*p**4. Factor n(c).
-(c - 1)*(c + 1)/3
Factor 6/7*s + 2/7*s**2 + 4/7.
2*(s + 1)*(s + 2)/7
Let m = -509 - -6621/13. Find y, given that m + 2/13*y**2 + 6/13*y = 0.
-2, -1
Let k(p) be the second derivative of 0*p**3 - p - 1/36*p**4 + 0 + 1/6*p**2. Suppose k(o) = 0. What is o?
-1, 1
Factor -1/5 - 3/10*b**2 - 1/2*b.
-(b + 1)*(3*b + 2)/10
Let l(k) be the second derivative of -k**4/3 - 4*k**3 - 18*k**2 + 27*k. Factor l(f).
-4*(f + 3)**2
Let -a + 0 - 1/6*a**4 + 5/6*a**2 + 1/3*a**3 = 0. Calculate a.
-2, 0, 1, 3
Let j = 19 - 15. Let f(b) = 6*b**4 - b**3 - b**2 - 4*b + 5. Let l(x) = -5*x**4 + x**3 + x**2 + 3*x - 4. Let t(d) = j*f(d) + 5*l(d). Factor t(q).
-q*(q - 1)**2*(q + 1)
Let p(x) be the third derivative of x**7/70 + x**6/5 + 6*x**5/5 + 4*x**4 + 8*x**3 + 35*x**2. Factor p(z).
3*(z + 2)**4
Let b be 2/(4 + (-33)/9). Suppose 0 = 3*j + 4*g - 22, j - g + 2*g = b. Factor 2/3*m**j + 2/3 + 4/3*m.
2*(m + 1)**2/3
Let u(v) = -v**4 - 2*v**2 + 3*v. Let l(y) = 4*y**4 + 10*y**2 - 14*y. Let d(o) = -3*l(o) - 14*u(o). Factor d(w).
2*w**2*(w - 1)*(w + 1)
Let h(a) be the third derivative of -a**5/15 + 2*a**3/3 + 8*a**2. Let h(s) = 0. What is s?
-1, 1
Factor 34/25*b + 4/25 + 6/5*b**2.
2*(b + 1)*(15*b + 2)/25
Let k(y) = -y**3 - 3*y**2 + 3*y + 10. Let s be k(-2). Factor -1/4*t**2 + s + 0*t.
-t**2/4
Let a(h) be the first derivative of h**4/28 - h**3/21 + 9. Suppose a(t) = 0. What is t?
0, 1
Let i(d) be the first derivative of 5*d**3/3 + 5*d**2/2 - 26. Factor i(y).
5*y*(y + 1)
Let o(z) = -z**2 - 14*z - 10. Let h be o(-13). Determine u, given that u**3 - 3*u**4 + 0*u**2 + 5*u**h + 0*u**2 = 0.
0, 2
Let t(r) be the first derivative of -r**6/24 - r**5/4 - 9*r**4/16 - 7*r**3/12 - r**2/4 + 29. Find p, given that t(p) = 0.
-2, -1, 0
Let g(m) be the second derivative of -9*m**5/5 - 4*m**4 + 22*m**3/3 - 4*m**2 - 13*m + 2. Find d, given that g(d) = 0.
-2, 1/3
Let n = -6/11 + 45/22. Factor 1/2*s - n*s**2 + 3/2*s**3 - 1/2*s**4 + 0.
-s*(s - 1)**3/2
Let h = 91/15 - 27/5. Factor 1/3*j**2 + h - j.
(j - 2)*(j - 1)/3
Let v(u) be the second derivative of u**7/14 + 3*u**6/10 + 3*u**5/10 - u**4/2 - 3*u**3/2 - 3*u**2/2 + 3*u. Factor v(o).
3*(o - 1)*(o + 1)**4
Let b(k) be the second derivative of k**4/12 + k**3/6 - 7*k. Factor b(m).
m*(m + 1)
Suppose 0 = -g - 3*g + 24. Suppose h + 20 = g*h. Let -2*d + 4*d + h*d**2 - 6*d**2 = 0. Calculate d.
0, 1
Suppose -2/7*q**3 + 0 - 6/7*q**2 + 8/7*q = 0. Calculate q.
-4, 0, 1
Let k be (-15)/(-9) - 3/(-9). Find b such that 0*b + 0 + 2/5*b**k = 0.
0
Suppose 2 = -3*z + 17. Suppose 10 = -2*c + 3*m - m, -z*c + m = 5. Suppose 2/5*a**2 + c - 2/5*a = 0. Calculate a.
0, 1
Let n(j) be the second derivative of 3/10*j**5 + 0 - 1/10*j**6 + 0*j**2 + 0*j**3 + 0*j**4 + 6*j. Find m such that n(m) = 0.
0, 2
Let u be 5*(3 - 48/20). Let c = -5 + 9. What is k in 4*k**3 - 2*k**5 - 8*k**c + 51*k**5 - 20*k**4 + 0*k**u = 0?
0, 2/7
Let g = 11931/16390 - 1/1490. Solve -g*n**2 - 4/11 - 2/11*n**3 - 10/11*n = 0.
-2, -1
Let i = 12260/27 - 454. Let s(m) be the first derivative of 2/9*m**2 + 0*m + 1 - i*m**3 + 2/45*m**5 - 1/9*m**4. Factor s(g).
2*g*(g - 2)*(g - 1)*(g + 1)/9
Factor 0 + 8/3*w**2 + 4/3*w + 4/3*w**3.
4*w*(w + 1)**2/3
Let f(z) be the third derivative of z**6/72 + 7*z**5/36 + 55*z**4/72 + 25*z**3/18 + 47*z**2. Factor f(i).
5*(i + 1)**2*(i + 5)/3
Let w(l) be the first derivative of 2*l**3/33 - 18*l**2/11 + 162*l/11 + 31. Factor w(m).
2*(m - 9)**2/11
Suppose 10 = 14*f - 9*f. Let -2/7*q**3 + 0 - 8/7*q + 8/7*q**f = 0. Calculate q.
0, 2
Factor -10/23*v**2 + 6/23*v + 2/23*v**4 + 2/23*v**3 + 0.
2*v*(v - 1)**2*(v + 3)/23
Let v(s) be the second derivative of -s**4/2 - 21*s**3/4 - 15*s**2/4 - 17*s. Factor v(x).
-3*(x + 5)*(4*x + 1)/2
Let l(a) be the second derivative of a**4/36 + 7*a**3/18 - 29*a. Factor l(v).
v*(v + 7)/3
Let p(b) be the second derivative of b**7/8820 - b**6/1260 - b**5/140 - 5*b**4/12 + b. Let f(w) be the third derivative of p(w). Factor f(o).
2*(o - 3)*(o + 1)/7
Let a(p) be the third derivative of p**7/280 + p**6/40 + p**5/80 - 3*p**4/16 + 16*p**2. Suppose a(m) = 0. What is m?
-3, -2, 0, 1
Let u(n) be the third derivative of -n**6/36 + n**5/5 + 11*n**4/12 + 10*n**3/9 - 15*n**2. What is r in u(r) = 0?
