- 1)*(k + 2)/5
Suppose -y = -0*y + 56. Let r = y - -394/7. Factor -2/7*n**3 + 0 + r*n**2 + 0*n.
-2*n**2*(n - 1)/7
Let z be 16/10 + 6/(-6) - -3. Determine k, given that z*k**3 - 2/5 - 6*k**2 + 14/5*k = 0.
1/3, 1
Let z = -95 + 289/3. Find o, given that -2/3*o**2 - 2*o**3 + z*o + 0 = 0.
-1, 0, 2/3
Let g(s) be the second derivative of -s**6/45 - s**5/15 + s**4/18 + 2*s**3/9 + s. Determine n, given that g(n) = 0.
-2, -1, 0, 1
Suppose -19 = -5*d + 16. Let r be (3/d)/(69/230). Find t such that -6/7*t**5 - r*t**4 + 2/7*t**2 + 0*t - 2/7*t**3 + 0 = 0.
-1, 0, 1/3
Factor -2/3*l**2 + 1/3*l - 2/3*l**3 + 1/3*l**4 + 1/3*l**5 + 1/3.
(l - 1)**2*(l + 1)**3/3
Let n(b) be the second derivative of -b**7/56 - b**6/60 + b**5/8 + b**4/4 - b**3/6 - b. Let l(a) be the second derivative of n(a). Solve l(k) = 0 for k.
-1, -2/5, 1
Let z be 1/(-4) - (-143)/156. Factor 4/3*p**3 + z*p**2 + 2/3*p**4 + 0*p + 0.
2*p**2*(p + 1)**2/3
Let g(a) be the second derivative of a**5/4 - 5*a**4/4 + 31*a. Determine v so that g(v) = 0.
0, 3
Let w(b) be the first derivative of -2*b**3/9 + 2*b**2/3 - 13. Factor w(x).
-2*x*(x - 2)/3
Let p = 6/11 + -7/33. Let g(a) be the first derivative of -p*a**2 + 1/3*a**4 + 0*a + 0*a**3 - 1/9*a**6 + 4 + 0*a**5. Suppose g(y) = 0. Calculate y.
-1, 0, 1
Let t(d) = 8*d**2 - d + 1. Let o be t(2). Suppose -5*z + 0*z = 3*r - o, -2*z + 14 = 2*r. Find l such that 2/7*l**r + 0*l**3 + 0 + 0*l - 2/7*l**4 = 0.
-1, 0, 1
Let l(q) be the third derivative of -q**7/720 - q**6/720 + q**4/6 - 2*q**2. Let g(m) be the second derivative of l(m). Solve g(t) = 0.
-2/7, 0
Let h(c) = c**2 + 3. Let r(w) = 3*w**2 - w + 9. Let b(l) = -11*h(l) + 4*r(l). Let a(u) = 2*u**2 - 9*u + 7. Let m(f) = -4*a(f) + 9*b(f). Factor m(q).
(q - 1)*(q + 1)
Let r be 1*(-6134)/1810 + 3. Let h = 2/181 - r. Factor 2/5*j**2 - 2/5*j**4 + h*j**3 - 2/5*j**5 + 0 + 0*j.
-2*j**2*(j - 1)*(j + 1)**2/5
Let q(z) be the third derivative of 0*z - 7/60*z**4 - 1/75*z**5 - 2/15*z**3 + z**2 + 0 + 1/100*z**6. Factor q(w).
2*(w - 2)*(w + 1)*(3*w + 1)/5
Let h be ((-2)/(-5))/(5/150). Solve -h*z**3 - 3*z**2 + 11*z**3 + z**2 = 0.
-2, 0
Let g(t) be the third derivative of t**8/756 + 2*t**7/945 - t**6/54 - t**5/135 + 4*t**4/27 - 8*t**3/27 + 23*t**2. Factor g(j).
4*(j - 1)**3*(j + 2)**2/9
Suppose -7*y + 36 = -y. Let m(k) be the second derivative of 0 + 0*k**5 + 1/15*k**y - k + k**2 - 1/3*k**4 + 0*k**3. Determine u so that m(u) = 0.
-1, 1
Let z(m) be the third derivative of m**6/80 - m**5/15 + m**4/12 - 32*m**2. Factor z(p).
p*(p - 2)*(3*p - 2)/2
Let h(z) = 8*z**3 - 96*z**2 - 80*z + 60. Let o(b) = -b**3 + b**2 + 1. Let n(r) = h(r) - 12*o(r). Suppose n(t) = 0. Calculate t.
-1, 2/5, 6
Let j(z) = -z**2 - 6*z + 1. Suppose 2*f + u = -9, -4*u + 2*u - 24 = 5*f. Let g be j(f). Factor -1 + g - 4*t**2 + 2*t**2 + 2*t**4.
2*t**2*(t - 1)*(t + 1)
Let k(a) = 8*a**3 - 5*a**2 - 3*a. Let x(o) = -2*o**3 + o**2 + o. Let t(d) = -6*k(d) - 22*x(d). Factor t(f).
-4*f*(f - 1)**2
Solve 0 + 5/4*l**2 - 1/4*l = 0.
0, 1/5
Suppose -2*l = -10, 4*s - l = 2*l + 1. Suppose -q + 3*c - 11 = -3, -15 = -3*q - s*c. Let -1 + 3 - q - 3*t**3 + 9*t + 5 = 0. What is t?
-1, 2
Let k(o) be the first derivative of -o**4/72 + o**2/12 - 5*o - 4. Let j(l) be the first derivative of k(l). Determine t, given that j(t) = 0.
-1, 1
Let w(o) be the second derivative of -1/12*o**3 - 3*o + 0 + 1/24*o**4 + 0*o**2. Factor w(v).
v*(v - 1)/2
Let y(f) = 3*f**2 + 2*f - 5. Let v(r) = -24*r**2 - 15*r + 39. Let l(a) = 4*v(a) + 33*y(a). Factor l(s).
3*(s - 1)*(s + 3)
Suppose -2*x + 5*x - 700 = 4*w, 0 = -x. Let u be (-190)/w + 2/(-7). Factor u*b + 0 - 2/5*b**2.
-2*b*(b - 2)/5
Let g(q) = q + 4. Let r be g(4). Suppose 4 = -f + r. Factor -f*o**2 + 2*o**2 + o**2.
-o**2
Let d(r) be the third derivative of r**8/2016 - r**7/1260 - r**6/144 - r**5/120 - 49*r**2. Let d(p) = 0. Calculate p.
-1, 0, 3
Factor 3/2*o + 9*o**2 - 3/2.
3*(2*o + 1)*(3*o - 1)/2
Factor -2*z - 6*z**2 + 0 + 7/2*z**4 + 9/2*z**3.
z*(z - 1)*(z + 2)*(7*z + 2)/2
Let z be (1/4)/((-4)/(-16)). Suppose z - 3 = -q. Determine h, given that h**4 - 8 - h**q + 8 = 0.
-1, 0, 1
Let x(r) = 2*r**2 - 8*r + 2. Let w be x(4). Let v(i) be the first derivative of 0*i + 1/11*i**w - 2 + 2/33*i**3. Factor v(b).
2*b*(b + 1)/11
Let l(y) be the second derivative of -y**4/54 - 2*y**3/27 - y**2/9 - 6*y. Let l(x) = 0. What is x?
-1
Let n(s) = 4 - 5 + 2. Let c(v) = 2*v**2 + 2*v - 7. Let j(a) = a**2 + a - 1. Let d(l) = -2*c(l) + 2*j(l). Let x(t) = d(t) - 12*n(t). Factor x(r).
-2*r*(r + 1)
Let l(y) be the second derivative of y**4/18 + 16*y**3/9 + 64*y**2/3 - 2*y. Factor l(u).
2*(u + 8)**2/3
Let f(c) be the third derivative of 3*c**2 + 0*c + 0*c**6 + 0*c**4 - 1/15*c**5 + 0 + 1/3*c**3 + 1/105*c**7. Solve f(w) = 0.
-1, 1
Let u = 17 + -15. Suppose -z = -i - 3, 3 = z - 0*z + 3*i. Factor -u*g**z - g**2 + g**3 - g - g**2 + 0*g**2.
-g*(g + 1)**2
Let y be ((-4)/(-10))/((-1)/(-5)). Let g(x) = 3*x**5 - 2*x**4 + 6*x**2 + x - 4. Let w(k) = k**5 + k**3 + k**2 - 1. Let r(o) = y*w(o) - g(o). Factor r(v).
-(v - 2)*(v - 1)**2*(v + 1)**2
What is l in -3/7*l**5 - 30/7*l**2 - 30/7*l**3 - 15/7*l**4 - 15/7*l - 3/7 = 0?
-1
Determine q so that -3593*q**4 + 32*q + 36*q**3 + 16*q + 3597*q**4 + 80*q**2 = 0.
-6, -2, -1, 0
Let y = 57 + -54. Find c such that -5/2*c + 1 + 1/2*c**y + 3/2*c**2 - 1/2*c**4 = 0.
-2, 1
Let a(m) be the first derivative of -3/20*m**5 + 0*m - 1/2*m**4 + 7 - 1/4*m**2 - 7/12*m**3. Solve a(t) = 0 for t.
-1, -2/3, 0
Let n(j) be the second derivative of 0 + 1/48*j**4 + 0*j**2 - 4*j - 1/24*j**3. Factor n(i).
i*(i - 1)/4
Let f(h) be the third derivative of h**6/36 - h**5/15 + h**4/15 - 2*h**3/3 + 2*h**2. Let z(g) be the first derivative of f(g). Determine x, given that z(x) = 0.
2/5
Let b be ((-32)/(-140))/(2/5). Let x = b - -13/14. Factor 0 - x*z**3 + 0*z + 3*z**2.
-3*z**2*(z - 2)/2
Factor 15*w**3 - 13*w**3 + 6*w**5 + 8*w**4 - 3*w**5 + 3*w**5.
2*w**3*(w + 1)*(3*w + 1)
Suppose -5*w = -3*w - 4. Let u(a) be the first derivative of w - 14/9*a**3 + 5/3*a**2 + 4/3*a. Factor u(s).
-2*(s - 1)*(7*s + 2)/3
Suppose -12*i = -67 + 19. Factor 0 + 0*k + k**3 - 1/2*k**2 - 1/2*k**i.
-k**2*(k - 1)**2/2
Let p = -839923/225 - -3733. Let r = 679/450 - p. Factor -r - 9*c - 15/2*c**2.
-3*(c + 1)*(5*c + 1)/2
Let g be (-4)/(-1) - (-11)/(44/(-8)). Suppose -9/7*p - 3/7*p**g - 6/7 = 0. Calculate p.
-2, -1
Let a be (14/(-4) - -3)*-8. What is p in 12*p + 3*p - p + 10*p**2 + a = 0?
-1, -2/5
Let f(r) be the third derivative of -r**6/660 + r**5/110 + r**4/132 - r**3/11 + 13*r**2. What is s in f(s) = 0?
-1, 1, 3
Let y be (-5)/(-3) - 2/(-6). Let s be y/4 - (-11)/(-22). What is a in s*a**3 + 4/3*a - 2*a**2 + 2/3*a**4 + 0 = 0?
-2, 0, 1
Let j = -1 - -1. Let z = 73/3 + -24. Find t, given that 1/3*t**2 - z*t**3 + 0 + j*t = 0.
0, 1
Let y(x) be the first derivative of 0*x - 1/2*x**2 - 4 - 1/3*x**3. Factor y(w).
-w*(w + 1)
Let m(u) be the second derivative of u**7/14 + u**6/6 + 7*u**5/60 + u**4/36 + 22*u. Factor m(w).
w**2*(w + 1)*(3*w + 1)**2/3
Let w(v) be the first derivative of -v**4/38 - 26*v**3/19 - 507*v**2/19 - 4394*v/19 + 38. Suppose w(c) = 0. Calculate c.
-13
Let a = 169 - 167. Solve -16/3 - 1/3*q**a - 8/3*q = 0.
-4
Let m(o) = o**2 - 2*o - 2. Let w be m(4). Factor -5*c + w + 3*c**3 - 2*c - 2*c.
3*(c - 1)**2*(c + 2)
Let l(v) = -v**2 + v + 3. Let s be l(0). Suppose 3*c = s + 9. Let y(i) = i + 1. Let w(p) = -p**2 - 6*p - 5. Let m(b) = c*y(b) + w(b). Factor m(x).
-(x + 1)**2
Suppose 2*r - 35 = j, -3*r - 2*j + 70 = -0*j. Let u be 45/r - 1/4. Factor 4*y**2 + 0*y**u - 3*y**2 - 1 - 5*y - 5*y**2.
-(y + 1)*(4*y + 1)
Let d(c) be the first derivative of -c**6/360 + c**4/72 - 2*c**2 + 5. Let g(w) be the second derivative of d(w). Determine j so that g(j) = 0.
-1, 0, 1
Let l(q) be the first derivative of -3*q**4/4 + 3*q**3 - 3*q**2 + 7. Factor l(h).
-3*h*(h - 2)*(h - 1)
Let d = 29 - 69. Let b be 2*1 - d/(-24). Suppose 0 + 0*m + b*m**2 + 4/3*m**3 = 0. Calculate m.
-1/4, 0
Suppose 7*z = -15*z. Factor 4/9*s**3 + 2/9*s**2 + 0 + z*s + 2/9*s**4.
2*s**2*(s + 1)**2/9
Let s(a) be the third derivative of a**9/7560 + a**8/1680 - a**6/180 - a**5/60 + a**4/24 - 3*a**2. Let n(z) be the second derivative of s(z). Factor n(m).
2*(m - 1)*(m + 1)**3
Let x = -12 - -21. Let b(y) = -13*y**4 + 9*y**3 + 9. Let d(a) = 6*a**4 - 4*a**3 - 4. Let i(k) = x*d(k) 