*2/4
Suppose 4*w = -n + 6, 5*w - w - 16 = 4*n. Let o be (6/21)/(15/21). Factor -6/5*q**w - o - 6/5*q - 2/5*q**3.
-2*(q + 1)**3/5
Let h(o) = -o**3 - 4*o**2 - 4*o - 7. Let q be h(-3). Let c be (q/18)/((-19)/57). Suppose 0*j**2 + 0 + 0*j**3 + 0*j - c*j**5 + 0*j**4 = 0. What is j?
0
Factor -4*z + 5*z**3 - 3*z + 4*z + 8*z - 10*z**2.
5*z*(z - 1)**2
Let v be (-16)/(-5) - 1/5. Let u(w) be the first derivative of -2/3*w + 1/3*w**2 - 3 - 1/6*w**4 + 2/9*w**v. Suppose u(k) = 0. Calculate k.
-1, 1
Let b(u) be the second derivative of -u**6/150 - 3*u**5/100 - u**4/30 - 4*u. Factor b(p).
-p**2*(p + 1)*(p + 2)/5
Let b be ((-94)/4)/(3/60). Let x be 1/(-3) + b/(-24). Factor 0*q + q**2 - 49/4*q**5 + 0 - 8*q**3 + x*q**4.
-q**2*(q - 1)*(7*q - 2)**2/4
Let -2*a + 2*a**3 + 1/5 + 24/5*a**2 - 5*a**4 = 0. What is a?
-1, 1/5, 1
Let 24*z**3 - 42*z**3 + 2*z**4 + 24*z**3 = 0. What is z?
-3, 0
Let t(j) be the first derivative of -2*j**5/5 - j**4 + 2*j**3/3 + 2*j**2 - 24. Factor t(a).
-2*a*(a - 1)*(a + 1)*(a + 2)
Let a(v) be the third derivative of -v**7/735 - v**6/21 - 24*v**5/35 - 36*v**4/7 - 144*v**3/7 - 5*v**2 + 3*v. Factor a(g).
-2*(g + 2)*(g + 6)**3/7
Let l(u) be the third derivative of -u**2 + 0*u**4 + 0*u**3 - 1/90*u**5 + 0*u + 1/504*u**8 - 1/105*u**7 + 0 + 1/60*u**6. Determine d so that l(d) = 0.
0, 1
Let t(p) be the third derivative of p**6/90 + 7*p**5/30 - p**4/3 - 11*p**3/9 + 6*p**2. Solve t(y) = 0.
-11, -1/2, 1
Suppose -3*m + 3*l = -0*l + 6, 0 = 2*l. Let h(g) = -5*g**2 + 5. Let f(y) = -16*y**2 + 16. Let c(v) = m*f(v) + 7*h(v). Factor c(n).
-3*(n - 1)*(n + 1)
Let q(p) be the first derivative of 1/10*p**5 + 0*p**2 + 1/2*p - 2 + 0*p**4 - 1/3*p**3. Factor q(k).
(k - 1)**2*(k + 1)**2/2
Determine k, given that 2/5*k**2 + 0 - 9/5*k**3 + 0*k = 0.
0, 2/9
Let o(k) be the third derivative of 0*k**3 - 1/108*k**4 - 1/270*k**5 + 0*k + 0 - 5*k**2. Factor o(r).
-2*r*(r + 1)/9
Let j(p) be the third derivative of -p**8/20160 - p**7/5040 - p**5/10 - 3*p**2. Let k(t) be the third derivative of j(t). Factor k(y).
-y*(y + 1)
Let i(r) be the first derivative of r**3/24 - 3*r**2/16 - r/2 + 1. Find y such that i(y) = 0.
-1, 4
Let u be (-3)/(-9) - 29/78. Let w = 59/182 + u. Factor 2/7*r**4 - 2/7*r**2 - 2/7*r + 0 + w*r**3.
2*r*(r - 1)*(r + 1)**2/7
Let f = 9 + -6. Factor -15*k + 6 - 5*k**2 - f*k**3 + 16*k**2 + k**2.
-3*(k - 2)*(k - 1)**2
Let v = 19/40 + -3/8. Let g(a) be the second derivative of 0 - a + 2/21*a**7 + 0*a**2 + v*a**5 + 1/12*a**4 - 7/30*a**6 + 0*a**3. Factor g(i).
i**2*(i - 1)**2*(4*i + 1)
Let m(w) be the third derivative of w**5/60 + w**4/24 - w**3/3 + 4*w**2. What is g in m(g) = 0?
-2, 1
Let m = 318 + -2222/7. Factor -m*s + 2/7*s**3 + 2/7*s**2 + 0.
2*s*(s - 1)*(s + 2)/7
Determine a, given that 8 - 3*a - 3*a**2 - 11*a**2 - 3*a**4 + 13*a**3 - a = 0.
-2/3, 1, 2
Let b(f) be the third derivative of -f**7/12600 + f**4/8 + 2*f**2. Let j(y) be the second derivative of b(y). Factor j(r).
-r**2/5
Let g(x) = -3*x**3 + 45*x**2 - 122*x + 80. Let h(m) = -m**3 + m. Let o(f) = -g(f) - 2*h(f). Factor o(k).
5*(k - 4)**2*(k - 1)
Factor 0*c + 0 - 3/2*c**2 - 3/2*c**3.
-3*c**2*(c + 1)/2
Let d(z) = -3*z**3 + 3*z**2 - 21*z. Let n(a) = -a**2 + 2*a + 2*a**3 + 8*a - a**3. Let x(v) = 4*d(v) + 9*n(v). Factor x(b).
-3*b*(b - 2)*(b + 1)
Let c(m) be the third derivative of m**5/10 - 5*m**4/12 + 2*m**3/3 + 10*m**2. Factor c(y).
2*(y - 1)*(3*y - 2)
Let m be ((-32)/64)/(2 + (-7)/2). Let 0 - m*s - 1/3*s**3 + 2/3*s**2 = 0. What is s?
0, 1
Factor 12*n**4 - 2*n**5 - 25*n**3 + 8*n**4 - 2*n**2 - 3*n**5 + 12*n**2.
-5*n**2*(n - 2)*(n - 1)**2
Let b(y) = 2*y**3 + 70*y**2 + 48*y - 10. Let s(q) = -q**3 - 23*q**2 - 16*q + 3. Let x(k) = -3*b(k) - 10*s(k). Solve x(o) = 0 for o.
-4, -1, 0
Factor -2*a**4 + 4/3*a**2 + 2*a - 2/3*a**5 + 2/3 - 4/3*a**3.
-2*(a - 1)*(a + 1)**4/3
Let a(l) be the second derivative of l**7/980 - 11*l**6/2520 + l**5/210 + l**4/12 + 4*l. Let o(k) be the third derivative of a(k). Determine i so that o(i) = 0.
2/9, 1
Let v(m) = -17*m**2 - 11*m - 5. Let l(x) = 6*x**2 + 4*x + 2. Let z(f) = -11*l(f) - 4*v(f). Factor z(j).
2*(j - 1)*(j + 1)
Suppose 12 = 3*q - 6*q. Let x = -2 - q. Factor -1/4 + 1/4*v**x + 0*v.
(v - 1)*(v + 1)/4
Let u = -2/73 - -81/292. Factor 0*h**3 + u*h**2 - 1/4*h**4 + 0*h + 0.
-h**2*(h - 1)*(h + 1)/4
Suppose 12/5*k**2 - 12/5*k**3 + 0 + 0*k - 9/5*k**4 = 0. What is k?
-2, 0, 2/3
Suppose -g - 10 = -m, -5*g - 2*m - 20 = 2. Let x be 2/g - (-63)/27. Factor 6/7*k**3 - 8/7*k - 2/7*k**5 - 4/7*k**4 + 8/7*k**x + 0.
-2*k*(k - 1)**2*(k + 2)**2/7
Suppose -21*o - 9 = -51. Let y(w) = -w**3 - w**2. Let s be y(-1). Factor 0 - 2/5*q**3 + s*q + 2/5*q**o.
-2*q**2*(q - 1)/5
Let s(d) = -d**5 + 1. Let g(r) = 6*r**5 + 6*r**4 + 12*r**3 + 8*r**2 - 5. Let c(o) = g(o) + 5*s(o). Factor c(m).
m**2*(m + 2)**3
Let g be (-4)/(-6) - (-141)/(-9). Let y be 3/15 - 27/g. Let -8 - 4*a**3 + 2*a**3 + y*a**2 + 0*a**3 + 4*a**2 = 0. Calculate a.
-1, 2
Let r(l) = 5*l**2 + 2*l - 1. Let z be r(-2). Let i be z/4 + (-4)/(-16). Factor -1/2*x**3 + 0*x + 0*x**2 + 0 - 1/2*x**i.
-x**3*(x + 1)/2
Let y(c) be the third derivative of c**7/12600 - c**6/1800 + c**4/24 - 2*c**2. Let a(s) be the second derivative of y(s). Factor a(b).
b*(b - 2)/5
Let 25 - 11*u**2 - 30*u + 6*u**2 - 70 = 0. Calculate u.
-3
Factor 0 + 3/4*j**5 + 39/4*j**3 + 3*j - 9/2*j**4 - 9*j**2.
3*j*(j - 2)**2*(j - 1)**2/4
Let o(j) be the first derivative of j**4 + 8*j**3/3 + 2*j**2 + 21. Factor o(t).
4*t*(t + 1)**2
Let x(w) be the first derivative of w**2 - w - 1/3*w**3 + 4. Determine b, given that x(b) = 0.
1
Suppose -5*r + 4*r + 4 = 0. Let y be (2/(-3))/(-4 + 2). Factor 0*k - 1/3*k**2 + 0*k**3 + y*k**r + 0.
k**2*(k - 1)*(k + 1)/3
Let w = 8009/4 - 2050. Let v = 49 + w. Factor 3/4*h**2 + v*h - 1/4*h**3 - 1/4*h**4 + 1/2.
-(h - 2)*(h + 1)**3/4
Suppose 32/7*y - 4/7*y**2 - 64/7 = 0. Calculate y.
4
Let r = 16 + -8. Determine m so that r*m**2 + 4*m**4 + 2*m**5 + 6*m**3 + 2*m**4 - 6*m**2 = 0.
-1, 0
Let a(p) be the third derivative of 3*p**5/4 + 175*p**4/12 - 40*p**3/3 + 5*p**2 - 6*p. Factor a(t).
5*(t + 8)*(9*t - 2)
Let v(h) = h**2 + 79*h + 3. Let f be v(0). Factor -4/11*i + 0*i**2 + 4/11*i**f + 2/11*i**4 - 2/11.
2*(i - 1)*(i + 1)**3/11
Let g(j) be the third derivative of 0 - 1/105*j**7 + 3*j**2 + 0*j - 1/12*j**4 + 1/30*j**5 + 1/60*j**6 + 0*j**3. Factor g(a).
-2*a*(a - 1)**2*(a + 1)
Let r = 565 + -563. Let 7/5*t**r + 3*t + 9/5 + 1/5*t**3 = 0. What is t?
-3, -1
Suppose 4*h - 11 = 1. Determine l so that -26*l**3 + 23*l**h - 12*l**2 + l - 13*l = 0.
-2, 0
Let q(n) = 2*n**2 + n - 1. Suppose 4*f = f, -v = f - 1. Let x be q(v). Factor -21*m**4 - 56*m**3 - 8*m**x + 1 - 1 - 77*m**4.
-2*m**2*(7*m + 2)**2
Let b(d) = d**2 + 2*d. Let z(v) = -2*v**2 - 4*v. Let a(n) = 7*b(n) + 3*z(n). Factor a(j).
j*(j + 2)
Let u = 0 - 2. Let n be (u/(-16))/((-5)/(-20)). Factor -1/2*j - 1/2*j**2 + 1/2*j**3 + n.
(j - 1)**2*(j + 1)/2
Let v(b) be the first derivative of -b**5/10 + b**4/4 - b**2/2 + b/2 - 6. Determine d so that v(d) = 0.
-1, 1
Let q(j) be the third derivative of j**5/160 - j**3/16 - 48*j**2. Factor q(z).
3*(z - 1)*(z + 1)/8
Factor 3/5 - 9/5*x**2 - 6/5*x.
-3*(x + 1)*(3*x - 1)/5
Suppose 2*j = -5*v + 11, 3*v + j + 4*j + 1 = 0. Suppose 4/7*g**5 + 0*g + 16/7*g**2 + 0*g**v - 12/7*g**4 + 0 = 0. What is g?
-1, 0, 2
Let g be 196/48 + (-5 - -1). Let y(f) be the first derivative of -2/9*f**3 + 1/6*f**2 + 1 + g*f**4 + 0*f. Suppose y(u) = 0. What is u?
0, 1
Factor 253 - 7*i**3 - 6*i**3 + 3*i**3 + 105*i**2 - 193 + 175*i.
-5*(i - 12)*(i + 1)*(2*i + 1)
Factor 0 + 6/5*b**3 - 1/5*b**4 + 4/5*b - 9/5*b**2.
-b*(b - 4)*(b - 1)**2/5
Factor -14*o**4 + 30*o**3 - 65*o + 30 + 2*o**4 + 20*o**2 - 3*o**5 + 2*o**4 - 2*o**5.
-5*(o - 1)**3*(o + 2)*(o + 3)
Solve 0*w + 0 + 1/2*w**3 + 0*w**2 - 1/4*w**4 = 0.
0, 2
Let g be 58/18 + (-14)/63. Let b(u) be the third derivative of 0 - 1/15*u**g + 1/60*u**4 + 0*u + 3*u**2 + 1/150*u**5 - 1/300*u**6. Solve b(v) = 0.
-1, 1
Let w(i) be the first derivative of 0*i**2 - 3/20*i**4 + 0*i + 1 - 1/5*i**3. Find x, given that w(x) = 0.
-1, 0
Let a be 3/(-7)*(-302)/453. Factor 0 - 1/7*y - 1/7*y**3 + a*y**2.
-y*(y - 1)**2/7
Let y = 10 - 8. Solve -2*d**y + 0*d**2 + d**2 + 1 = 0 for d.
-1, 1
Factor -135*n + 35*n**3 - 11*n**2 + 56*n**2 + 10*n**4 - 270 + 2*n**4 - 7*n**4.
5*(n - 2)*(n + 3)**3
Let t be (6/18)/(2/3). So