14)/12. Factor 1/4*h - 1/4*h**3 - 1/4 + k*h**2.
-(h - 1)**2*(h + 1)/4
Suppose -2*x + 12 = 2*u, -4*u - x + 12 = -0*x. Determine h so that 5*h**2 - 2*h**3 + 0*h**3 - 4*h**u + 2*h**4 - h**4 = 0.
0, 1
Let i(h) be the third derivative of -3*h**8/616 - h**7/385 + 17*h**6/660 + 7*h**5/330 - 2*h**4/33 - 4*h**3/33 + 4*h**2. Determine s so that i(s) = 0.
-1, -2/3, 1
Let m(f) be the first derivative of -f**5/20 + f**4/12 + f - 3. Let l(v) be the first derivative of m(v). Factor l(r).
-r**2*(r - 1)
Find p, given that -2*p + 3*p**5 + 2*p**3 - 9*p**4 - 3*p**3 + 0*p**2 + 5*p**2 + 4*p**4 = 0.
-1, 0, 2/3, 1
Let y be (3/14)/(-9*(-8)/240). Let i(v) be the first derivative of -8/21*v**3 - 1/14*v**4 - 4 - y*v**2 - 4/7*v. Factor i(w).
-2*(w + 1)**2*(w + 2)/7
Let c = -172/133 - -30/19. Factor 0 + c*m**5 - 6/7*m**3 + 0*m - 4/7*m**2 + 0*m**4.
2*m**2*(m - 2)*(m + 1)**2/7
Suppose 18 + 192 = -3*a + 5*v, 2*a + 141 = 3*v. Let s be (-6)/a*(-20)/(-4). Factor -6/5*q + 4/5 + s*q**2.
2*(q - 2)*(q - 1)/5
Let 6/7*o**2 + 0 + 0*o + 9/7*o**3 - 3/7*o**5 + 0*o**4 = 0. Calculate o.
-1, 0, 2
Let m(p) be the first derivative of -p**8/504 + 2*p**7/315 - p**5/45 + p**4/36 + 2*p**2 + 3. Let r(d) be the second derivative of m(d). Factor r(v).
-2*v*(v - 1)**3*(v + 1)/3
Let l(t) be the third derivative of -t**5/240 + t**4/12 - t**3/2 + 2*t**2 + 11*t. Factor l(k).
-(k - 6)*(k - 2)/4
Let s(l) be the third derivative of l**8/504 + 2*l**7/315 - l**6/60 - 2*l**5/45 + l**4/9 + 27*l**2. Solve s(i) = 0.
-2, 0, 1
Let l = -162 - -164. Factor 0*c - 2/5*c**l + 2/5.
-2*(c - 1)*(c + 1)/5
Let z(u) be the second derivative of -u**4/12 + u**3/12 + u**2/4 + 4*u. Solve z(t) = 0.
-1/2, 1
Let f(a) be the first derivative of 0*a**3 - 1/5*a**2 - 3 + 1/10*a**4 + 0*a. Let f(w) = 0. What is w?
-1, 0, 1
Suppose 13*l = 30 + 9. Factor -5*q**l + 25/4*q**4 + 5*q - 1 - 21/4*q**2.
(q - 1)*(q + 1)*(5*q - 2)**2/4
Determine y so that y**3 - 4/3*y - 1/3*y**4 + 0*y**2 + 0 = 0.
-1, 0, 2
Let f(i) = 16*i**4 + 43*i**3 - 47*i**2 - 19*i. Let x(l) = -8*l**4 - 21*l**3 + 23*l**2 + 9*l. Let d(c) = 6*f(c) + 14*x(c). Factor d(y).
-4*y*(y - 1)*(y + 3)*(4*y + 1)
Let s(q) = 12*q - 81. Let z be s(7). Let 2/11*x**4 + 2/11 + 12/11*x**2 - 8/11*x - 8/11*x**z = 0. What is x?
1
Let f be (-12)/(-40)*(-36)/(-27). Let q(v) be the first derivative of 0*v - 4 + 2/3*v**3 - 1/2*v**4 + v**2 - f*v**5. Determine y, given that q(y) = 0.
-1, 0, 1
Let c = 5 + -1. Suppose -j + c = 2*g, -2*g + 2*j = -0*j - 4. Factor -2*u + 4*u**g - 4*u**2 + 2*u**2.
2*u*(u - 1)
Let r(m) = 5*m - 5*m + m. Let z(b) = -3*b**2 + 3*b. Let o be 10/4*(-6 - -4). Let q(v) = o*r(v) + z(v). Determine u, given that q(u) = 0.
-2/3, 0
Let i(c) = -6*c + 34. Let d be i(5). Solve 0*k**2 + 0 + 0*k - 1/2*k**5 + 0*k**d + 1/2*k**3 = 0 for k.
-1, 0, 1
Let j(g) be the second derivative of -1/6*g**3 - 1/15*g**6 - 1/2*g**2 + 1/4*g**4 + 5*g + 0 + 1/20*g**5. Determine t so that j(t) = 0.
-1, -1/2, 1
Let f = -2 - 2. Let w be f/(-2) - 1 - -3. Solve 6*q**w - 9*q**4 + q + q**5 + 6*q**3 - 4*q**2 - q**4 = 0.
0, 1
Let q(u) be the second derivative of -5*u**7/252 + u**5/12 - 5*u**3/36 + 16*u. Factor q(m).
-5*m*(m - 1)**2*(m + 1)**2/6
Let o = -11 - -11. What is t in o - 3/4*t**2 - 3/2*t = 0?
-2, 0
Let c(x) be the first derivative of -3*x**2 + 3/2*x**4 + 3*x - 3/5*x**5 + 2 + 0*x**3. Factor c(j).
-3*(j - 1)**3*(j + 1)
Factor -18/5*q**2 - 24/5*q + 3/5*q**4 - 9/5 + 0*q**3.
3*(q - 3)*(q + 1)**3/5
Let w(c) be the second derivative of -1/18*c**4 + 1/30*c**5 + 0 + 1/3*c**2 + c - 1/9*c**3. Find f, given that w(f) = 0.
-1, 1
Let v be -4 - ((-558)/(-21))/(-2). Let n = 281/28 - v. Factor 0*o + 9/4*o**4 - 9/4*o**3 - n*o**5 + 0 + 3/4*o**2.
-3*o**2*(o - 1)**3/4
Let j = 86/5 + -154/9. Let q(y) be the second derivative of -4/15*y**5 - 1/9*y**3 + 5/18*y**4 + 0*y**2 + j*y**6 + 0 - y. Factor q(n).
2*n*(n - 1)*(2*n - 1)**2/3
Let z(a) be the first derivative of -3*a**4/8 + 2*a**3 + 15*a**2/4 - 62. Factor z(g).
-3*g*(g - 5)*(g + 1)/2
Let a be 4 + (3 - (-47)/(-7)). Let -a - 2/7*x**2 - 4/7*x = 0. Calculate x.
-1
Factor -73*s**2 + 92*s**3 - 67*s**3 + 50*s + 208*s**2.
5*s*(s + 5)*(5*s + 2)
Let z(a) be the second derivative of 1/12*a**4 - 3*a + 0 - 2/3*a**3 + 2*a**2. Find c, given that z(c) = 0.
2
Let f be 6/(-4) - (-85)/51. Find l such that 0 - 1/6*l**3 - f*l**2 + 1/6*l**4 + 1/6*l = 0.
-1, 0, 1
Let q(r) be the second derivative of 0*r**2 + 0 - 1/12*r**3 + r + 1/16*r**4. Suppose q(c) = 0. Calculate c.
0, 2/3
Let z(y) be the second derivative of -y**7/126 + y**6/90 - 12*y. Factor z(i).
-i**4*(i - 1)/3
Let s(n) = 10*n**2 - 24*n + 36. Let y(m) = -21*m**2 + 48*m - 72. Let l(q) = 13*s(q) + 6*y(q). Factor l(v).
4*(v - 3)**2
Determine v so that 35*v - 2*v**4 + 14*v**3 - 36*v**2 - 7 + 5*v - 9 = 0.
1, 2
Let a be 2/(-7) + (-4)/(-14). Factor -k**2 + a*k**2 - k**2.
-2*k**2
Let x be (-12)/10*(-4)/8. What is d in 2/5*d - 7/5*d**3 - x*d**2 + 3/5*d**4 + 0 + d**5 = 0?
-1, 0, 2/5, 1
Let c(l) be the third derivative of l**8/6720 + l**7/1680 + l**6/1440 - l**3/2 - 4*l**2. Let k(w) be the first derivative of c(w). Factor k(u).
u**2*(u + 1)**2/4
Let x(y) be the first derivative of -y**4/20 + 2*y**3/5 - 6*y**2/5 + 8*y/5 - 1. Factor x(n).
-(n - 2)**3/5
Let p be (-3)/(-2) - (-2)/4. Let -3*q**p + 2 + 5*q - 3 - q + q**3 - q = 0. Calculate q.
1
Determine n, given that 19*n**2 + n**2 - 5*n**3 + 0*n**2 + 5*n - 10 - 10 = 0.
-1, 1, 4
Let u = -209/20 + 56/5. Let -3/2*s**3 - 3/4 + 3/2*s + u*s**4 + 0*s**2 = 0. What is s?
-1, 1
Suppose -4*t + 4*t**3 - 2*t**2 - 5*t**2 + 7*t**2 = 0. Calculate t.
-1, 0, 1
Let 9*i + 3/2*i**3 - 3 - 27/4*i**2 = 0. What is i?
1/2, 2
Suppose 3*q = -3*j + 2*j - 47, 0 = 4*q + 5*j + 81. Let x be -2 + (-12)/q*3. Find m such that 2/7*m**2 - x*m + 2/7 = 0.
1
Factor 2/9*n**2 - 2/3*n**3 + 2/3*n - 4/9 + 2/9*n**4.
2*(n - 2)*(n - 1)**2*(n + 1)/9
Factor 4/7 - 6/7*r + 2/7*r**2.
2*(r - 2)*(r - 1)/7
Let d(h) = h**2. Let k(b) = b**4 - b**3 - 7*b**2 + b. Let m(c) = 6*d(c) + k(c). Suppose m(f) = 0. Calculate f.
-1, 0, 1
Suppose -2*u + 6 - 2 = 2*k, 3*u - 5 = -4*k. Let m = u + -1. What is f in -f - f**2 + 0*f - f**m + f**2 = 0?
-1, 0
Let m = 123 - 120. Find o such that -1/2 + 1/4*o**4 - 3/4*o + 3/4*o**m + 1/4*o**2 = 0.
-2, -1, 1
Let w(q) be the second derivative of -q**6/30 - 3*q**5/40 + q**4/8 + q**3/6 - 2*q. Factor w(c).
-c*(c - 1)*(c + 2)*(2*c + 1)/2
Factor -g**2 + 10*g - 12*g + 4 - g**2.
-2*(g - 1)*(g + 2)
Suppose -3*m - 5*v + 33 = -20, 0 = -5*m + 2*v + 47. Factor x**5 + x**4 + 11 - x**3 - x**2 - m.
x**2*(x - 1)*(x + 1)**2
Find u, given that 1/2*u**3 - 1/4*u**2 + 0 - 1/4*u**4 + 0*u = 0.
0, 1
Let b be (-6)/((-11)/(33/6)). Solve 0*f + 106/9*f**b + 14/9*f**5 + 62/9*f**2 - 8/9 + 22/3*f**4 = 0 for f.
-2, -1, 2/7
Let c(f) = 2*f**2 - 6*f + 2. Let i(v) = 4*v**2 - 12*v + 3. Let m(s) = -5*c(s) + 2*i(s). Find z such that m(z) = 0.
1, 2
Let i(h) be the first derivative of 0*h**5 + 1/60*h**6 - 2 + 1/4*h**2 + 0*h**3 - 1/12*h**4 + h. Let f(w) be the first derivative of i(w). Solve f(t) = 0 for t.
-1, 1
Suppose 1/7*u**2 + 25/7 + 10/7*u = 0. What is u?
-5
Factor 23*z - 12*z + 39*z - 6*z + 4 + 121*z**2.
(11*z + 2)**2
Let f = -10 + 14. Let b = f - 1. Solve 0*j + 0 + 0*j**b + 1/4*j**4 - 1/4*j**2 = 0 for j.
-1, 0, 1
Suppose -4*w + 5*q = -32, -18 = -2*w + 2*q + q. Suppose -13 = -g + 5*a, 0 = w*g - 2*a + 3*a - 7. Factor 0*y - 2/7*y**2 - 2/7*y**g + 0.
-2*y**2*(y + 1)/7
Suppose -3 = -f - 0. Let d be 29/2 - (-2)/4. Suppose -d*r**f - 4*r + 7/2*r**4 + 0 + 18*r**2 = 0. What is r?
0, 2/7, 2
Let m(g) = -36*g**3 + 99*g**2 - 90*g + 27. Let s(y) = 24*y**3 - 66*y**2 + 60*y - 18. Let b(q) = -5*m(q) - 7*s(q). Factor b(c).
3*(c - 1)**2*(4*c - 3)
Let l(u) be the third derivative of 7*u**6/120 + 13*u**5/60 - 23*u**4/24 + u**3/2 - 7*u**2. Factor l(z).
(z - 1)*(z + 3)*(7*z - 1)
Let i(v) be the third derivative of 0 + 0*v**3 - 8*v**2 + 1/3*v**4 + 1/30*v**6 + 1/5*v**5 + 0*v. Factor i(a).
4*a*(a + 1)*(a + 2)
Let h(j) be the first derivative of -1/3*j - 3 - 1/9*j**3 - 1/3*j**2. Solve h(f) = 0 for f.
-1
Let l(a) be the second derivative of a**7/21 + 7*a**6/45 - a**5/30 - 7*a**4/18 - 2*a**3/9 - 15*a. Solve l(y) = 0 for y.
-2, -1, -1/3, 0, 1
Let q be (-36)/117*(-78)/12. Factor 4/3*w + q + 2/9*w**2.
2*(w + 3)**2/9
Let n(t) be the first derivative of -3*t**5/5 + 3*t**4 - 2*t**3 - 6*t**2 + 9*t + 23. Determine b so that 