1)**2*(5*y + 2)
Find y such that 1/4*y**2 + 1/2 - 3/4*y = 0.
1, 2
Let f be 0/4 - (-2)/24. Let j(q) be the third derivative of 0 + 0*q - 1/24*q**6 - 7/60*q**5 - f*q**4 + 0*q**3 - 2*q**2. Factor j(g).
-g*(g + 1)*(5*g + 2)
Let -2/7*m**2 + 2/7*m + 4/7 = 0. What is m?
-1, 2
Let x(s) = -2*s - 6. Let l be x(-4). What is o in o**l + 4 - 7 - o + 3 = 0?
0, 1
Suppose -u = 2 - 4. Let f(g) be the third derivative of -1/105*g**7 + 1/6*g**4 - 1/30*g**6 + 1/3*g**3 + 0*g**5 + 0*g - g**u + 0. Factor f(o).
-2*(o - 1)*(o + 1)**3
Factor 15*k**2 - 15*k + 17*k**3 - 14*k**3 + 5 - 8*k**3.
-5*(k - 1)**3
Let o(t) be the first derivative of t**7/735 - t**6/210 + t**5/210 - t**2 - 6. Let g(q) be the second derivative of o(q). Determine s, given that g(s) = 0.
0, 1
Let u(k) be the first derivative of -2*k**3/33 - 5*k**2/11 - 8*k/11 + 4. Factor u(p).
-2*(p + 1)*(p + 4)/11
Let f = 89 - 89. Factor -36/5*x**2 + f - 12/5*x - 39/5*x**3 - 18/5*x**4 - 3/5*x**5.
-3*x*(x + 1)**2*(x + 2)**2/5
Factor 3*m**2 + 0*m + 2*m**2 - 5*m.
5*m*(m - 1)
Let o = 134 - 400/3. Factor o*r + 2/3*r**2 - 4/3.
2*(r - 1)*(r + 2)/3
Let l(i) be the first derivative of -i**3/5 + 3*i**2/5 + 9*i/5 - 12. Factor l(f).
-3*(f - 3)*(f + 1)/5
Let g(a) = -3*a - 1. Let f be g(-1). Let -1/3*l**f + 0*l + 1/3 = 0. Calculate l.
-1, 1
Let u(a) be the third derivative of -a**5/240 - a**4/32 - a**3/12 + a**2. Let u(s) = 0. What is s?
-2, -1
Let i(m) be the third derivative of -m**6/20 + m**5/6 - m**4/12 - m**3/3 + 9*m**2. Suppose i(a) = 0. What is a?
-1/3, 1
Let h(a) = 2*a**2 - 4*a. Let m(k) = -3*k**2 + 5*k. Let t(x) = -4*h(x) - 3*m(x). Factor t(u).
u*(u + 1)
Let m(q) = q - 4. Let v be m(4). Factor -6/5*z**3 + v*z + 0 - 4/5*z**2 - 2/5*z**4.
-2*z**2*(z + 1)*(z + 2)/5
Let o(m) = -m + 2. Let k be o(0). Solve 1/3*n**k + 2/3 + n = 0 for n.
-2, -1
Determine m, given that -12 - 4*m**2 - 24*m + 1 - 11 - 10 = 0.
-4, -2
Let d(c) be the first derivative of -c**4 - 2*c + 3 - 4/3*c**3 - 1/3*c**6 + 3*c**2 + 6/5*c**5. Suppose d(j) = 0. Calculate j.
-1, 1
Suppose 0 = -5*a + 5*v - 5, a - 5*a = -5*v + 9. Solve -u**a + 2*u**3 + 2 - 2*u + 3 - 1 - 3 = 0.
-1, 1
Let r = 731/10 - 73. Let l(q) be the first derivative of 1/5*q**2 + r*q**4 + 3 + 0*q - 4/15*q**3. Factor l(h).
2*h*(h - 1)**2/5
Let w(l) = l**3 + 11*l**2 - l - 7. Let a be w(-11). Factor -1 - 9 - a*j**2 + 4 + j**2 - 9*j.
-3*(j + 1)*(j + 2)
Let y(o) = 2*o**3 + 24*o**2 - 53*o + 5. Let w(b) = b**3 - b + 1. Let g(n) = 5*w(n) - y(n). Suppose g(x) = 0. What is x?
0, 4
Let o = -318 - -318. Factor 4/9*z**2 + 0 - 2/9*z**3 + o*z.
-2*z**2*(z - 2)/9
Let r be ((-42)/8 - -5)*-2. Let l be (4 - 4)*(-2)/(-4). Factor -r*h + l - 1/2*h**2.
-h*(h + 1)/2
Let c be ((-36)/24)/((-6)/16). Factor -3 + 4*g + 9 + 3*g - 3*g**2 - c*g.
-3*(g - 2)*(g + 1)
Let c(x) be the first derivative of -x**5/5 - x**4/4 + x**3 + x**2/2 - 2*x - 23. Factor c(b).
-(b - 1)**2*(b + 1)*(b + 2)
Factor 4/17*r - 6/17 + 2/17*r**2.
2*(r - 1)*(r + 3)/17
Let d(w) = w**3 + 9*w**2 - 2*w - 6. Let o be d(-9). Suppose -4*u - 3*t = -0 - 3, -5*t - o = u. Factor 5/2*q**2 + 2 - 25/2*q**u + 8*q.
-(q - 1)*(5*q + 2)**2/2
Let o(v) be the third derivative of v**5/12 + 35*v**4/24 + 42*v**2. Factor o(t).
5*t*(t + 7)
Let s = 32/105 - -1/35. Let h(d) = -d**3 + 2*d**2 + 2*d + 1. Let c be h(-1). Let -1/3*g**5 + 0*g**c + 0*g + s*g**3 + 0 + 0*g**4 = 0. What is g?
-1, 0, 1
Let z = -4/43 - -227/129. Let q(w) be the first derivative of z*w**3 - 1 + w**2 + 0*w. Suppose q(d) = 0. What is d?
-2/5, 0
Let x be ((-2)/3)/(10/(-45)). Factor 1/3*d**x + 2/3*d**2 - 4/3*d**4 + 0*d + 0 - d**5.
-d**2*(d + 1)**2*(3*d - 2)/3
Solve 6*y**4 - 22*y**3 + 4 + 39*y**2 - 18*y - 12*y**2 + 3*y**2 = 0 for y.
2/3, 1
Let y be -1*(-9)/(-6)*(-1)/3. Factor 1/4*h**2 + y*h + 1/4.
(h + 1)**2/4
Let k(h) = -36*h**4 - 15*h**3 + 15*h**2 + 15*h + 21. Let r(d) = 7*d**4 + 3*d**3 - 3*d**2 - 3*d - 4. Let n(p) = 4*k(p) + 21*r(p). Factor n(x).
3*x*(x - 1)*(x + 1)**2
Let f be (1/(-4))/((-4)/24). Factor 0*b + 3/2*b**4 + 1/2*b**2 + 0 + 1/2*b**5 + f*b**3.
b**2*(b + 1)**3/2
Let j(b) be the third derivative of b**8/84 - 2*b**7/21 + 7*b**6/30 - b**5/5 - 6*b**2 + 3*b. Solve j(y) = 0.
0, 1, 3
Let m(t) be the first derivative of -t**4/4 + 2*t**3/3 - 9. Factor m(g).
-g**2*(g - 2)
Let m(p) be the first derivative of -3*p**2 - 9*p - 1/3*p**3 - 2. Let m(f) = 0. Calculate f.
-3
Let d be (2/18)/((-15)/(-9)). Let p(j) be the third derivative of 0 + 1/9*j**3 + 7/360*j**6 - 4*j**2 + 1/24*j**4 + 0*j - d*j**5. Factor p(u).
(u - 1)**2*(7*u + 2)/3
Suppose -19 = -3*r + 4*p, -3*r + 7*r - 24 = 4*p. Suppose 0 - 4/7*j**r + 4/7*j**3 + 0*j + 4/7*j**4 - 4/7*j**2 = 0. What is j?
-1, 0, 1
Let a(u) = -u**3 - 3*u**2 + 4*u - 2. Let v be a(-4). Let p = 1 - v. Determine m so that p*m + 3*m**2 - m**3 - 4*m**3 + 1 + 6*m**3 = 0.
-1
Let m(o) = -2*o**2 - 2*o - 1. Let x be m(-1). Let g(y) = 5*y**3 + 9*y**2 - 9*y - 5. Let q(f) = -f**3 - f**2 + f + 1. Let i(j) = x*g(j) - 6*q(j). Factor i(d).
(d - 1)**3
Suppose -38*s = -35*s - 9. Factor 4/11*u**s + 0*u**2 - 4/11*u - 2/11*u**4 + 2/11.
-2*(u - 1)**3*(u + 1)/11
Let p(o) be the third derivative of -o**6/480 - o**5/60 - 5*o**4/96 - o**3/12 + 3*o**2. Suppose p(g) = 0. Calculate g.
-2, -1
Let t(g) = -g + 1. Let l be t(1). Let a(y) be the first derivative of -2/5*y**5 + 2/3*y**3 + l*y + 1/3*y**6 + 2 - 1/2*y**4 + 0*y**2. Factor a(v).
2*v**2*(v - 1)**2*(v + 1)
Let u(o) be the third derivative of -o**8/6720 - o**7/840 - o**6/360 - o**4/8 - o**2. Let i(p) be the second derivative of u(p). Let i(q) = 0. What is q?
-2, -1, 0
Let c(u) be the first derivative of u**4/18 - 2*u**3/9 + 2*u**2/9 - 10. Factor c(k).
2*k*(k - 2)*(k - 1)/9
Let l(m) be the second derivative of m**6/15 + m**5/4 + m**4/6 - 12*m. Factor l(g).
g**2*(g + 2)*(2*g + 1)
Let z(f) be the second derivative of f**6/5 + 9*f**5/20 + f**4/4 - 26*f. Suppose z(m) = 0. What is m?
-1, -1/2, 0
Suppose 3*k = -0*k + 4*l + 107, 3*k - 3*l = 108. Factor 37*a - 2*a**5 - k*a - 2*a**4.
-2*a**4*(a + 1)
Let x be 48/(-60) + 26/20. Determine i so that 3/4*i - x + 5/4*i**2 = 0.
-1, 2/5
Let b be 140/30 - (-4)/(-6). Let i(z) be the third derivative of 0 + 0*z - 1/24*z**b - 1/6*z**3 + 3*z**2 - 1/240*z**5. Factor i(m).
-(m + 2)**2/4
Let s be (0 - 3 - -3)/1. Factor 4/5*v**4 + 2/5*v**5 - 2/5*v - 4/5*v**2 + s*v**3 + 0.
2*v*(v - 1)*(v + 1)**3/5
Let p(x) be the first derivative of 0*x + 0*x**4 - 2/15*x**5 - 1/6*x**2 + 2/9*x**3 + 4 + 1/18*x**6. Factor p(b).
b*(b - 1)**3*(b + 1)/3
Let v(o) be the third derivative of -o**8/1344 + o**6/480 - 14*o**2. What is p in v(p) = 0?
-1, 0, 1
Let a(w) be the first derivative of 4*w**5/15 + 2*w**4/3 - 4*w**2/3 - 4*w/3 - 3. Determine k so that a(k) = 0.
-1, 1
Factor -5*i**2 - 20/3*i**3 + 5/3*i + 0.
-5*i*(i + 1)*(4*i - 1)/3
Suppose -4/11*n**2 + 0 + 0*n + 2/11*n**3 = 0. What is n?
0, 2
Let y(z) be the second derivative of 2*z**6/15 + 2*z**5/5 - z**4 - 16*z**3/3 - 8*z**2 + 17*z. Solve y(q) = 0.
-2, -1, 2
Let t be 4/(-18) + 235/45. Let v = t - 1. What is n in 0*n**2 - 2/5*n**5 + 4/5*n**3 + 0 + 0*n**v - 2/5*n = 0?
-1, 0, 1
Let j = -13 - -15. Suppose 3*q = -j*q. Factor 2/5*y**2 + 2/5*y + q.
2*y*(y + 1)/5
Let f(q) be the second derivative of q**8/5880 - q**7/2940 - q**6/1260 + q**5/420 + q**3/3 - q. Let o(n) be the second derivative of f(n). Factor o(y).
2*y*(y - 1)**2*(y + 1)/7
Let v(t) = -2*t**2 + 6*t - 2. Let a(m) = -4*m + 2*m**2 - 2*m - 4 + 5 - m**2. Let f(o) = -5*a(o) - 4*v(o). What is w in f(w) = 0?
-1
Let a = -30/11 + 292/99. Determine i so that 0 - a*i**2 + 0*i = 0.
0
Factor t**3 + 0*t**4 + 5*t**2 + 3*t + 6*t**4 - 7*t**4.
-t*(t - 3)*(t + 1)**2
Suppose -3*b + 5*v = 0, -5*v = -0*b - 4*b. Factor 3/5*z**2 - 1/5*z**3 + b - 2/5*z.
-z*(z - 2)*(z - 1)/5
Let u be ((-25)/20)/((-1)/(-4)). Let l = u + 8. Determine r, given that l + 2*r**2 - 4*r - 1 + 8*r = 0.
-1
Let v(u) = -u**2 - 10*u + 8. Let j be v(-12). Let t = 10 - j. Suppose -2*g**3 + g + 18*g**2 - t*g**2 - 4 - 11*g = 0. Calculate g.
-2, -1
Let 3/5*m**2 - 3/5*m - 6/5 = 0. Calculate m.
-1, 2
Let x be (4 - (-44)/(-10))*-50. Let o be ((-4)/x)/((-12)/30). Factor -j - o*j**4 + 0*j**2 + 1/2 + j**3.
-(j - 1)**3*(j + 1)/2
Suppose -7 = -3*f + 5. Let s(i) = i**3 - 5*i**2 + 3*i + 4. Let k be s(f). Solve -1/2*d**2 + k + 1/4*d - 1/4*d**3 + 1/2*d**4 = 0.
-1, 0, 1/2, 1
Let y = 29 - 25. Suppose -q + y*f = -3*q - 12, -q = -4*f - 