4
Let s(h) = 6*h**3 + 22*h**2 - 84*h + 76. Let t(z) = 2*z**3 - z**2 - z + 1. Let q(p) = s(p) - 4*t(p). Factor q(f).
-2*(f - 9)*(f - 2)**2
Let l(i) be the second derivative of i**8/16800 + i**7/1050 + i**6/150 + 2*i**5/75 - i**4/12 + 2*i. Let w(v) be the third derivative of l(v). Factor w(t).
2*(t + 2)**3/5
Let j be -4 + 0 - 3232/(-40). Let k = 77 - j. Factor -k*x**3 + 0*x + 0 + 2/5*x**2.
-x**2*(x - 2)/5
Suppose 0*z + 2*z = -z. Solve z + 1/4*c**5 + 1/4*c**4 - 1/4*c**2 + 0*c - 1/4*c**3 = 0.
-1, 0, 1
Let s = -12 - -15. Suppose -n - 4 = -3, 0 = 4*a + s*n - 5. Factor 0*h - 2/5*h**a + 2/5.
-2*(h - 1)*(h + 1)/5
Let w(u) be the third derivative of 1/42*u**7 - 1/30*u**5 + 0*u**4 - 6*u**2 + 0*u + 0 - 1/40*u**6 + 0*u**3. Factor w(h).
h**2*(h - 1)*(5*h + 2)
Let o be ((-3)/2)/(21/(-28)). Suppose u + 5*a = 13, -o - 6 = -4*a. Factor 2*l**u - 3*l**3 - 3*l**4 - 2*l**3.
-3*l**3*(l + 1)
Let w(i) = -4*i**2 - 2*i - 3. Let v(p) = p**2 + p + 1. Let q(f) = -15*v(f) - 5*w(f). Factor q(l).
5*l*(l - 1)
Let s(m) be the second derivative of -m**5/10 - m**4/18 + 2*m**3/9 + 7*m. Solve s(x) = 0.
-1, 0, 2/3
Let d(k) = -k**2 - 7*k - 6. Let l be d(-4). Let h(v) be the first derivative of 6/5*v**5 - 4/3*v**l + 0*v**3 + 1/2*v**4 + 1 + 0*v + 0*v**2. Factor h(c).
-2*c**3*(c - 1)*(4*c + 1)
Let q(h) be the third derivative of h**7/840 - h**6/96 + 3*h**5/80 - 7*h**4/96 + h**3/12 + 9*h**2. Solve q(w) = 0.
1, 2
Factor -33*d**3 - 5*d + 57*d**3 - 29*d**3 - 3*d**2 - 7*d**2.
-5*d*(d + 1)**2
Determine x, given that 15/4*x**2 + 3/4*x + 9/4*x**3 - 3/4 = 0.
-1, 1/3
Let f(t) be the third derivative of 1/6*t**3 - 1/8*t**5 - 1/4*t**4 + 1/40*t**6 + 0 + 0*t + 3*t**2. Let q(a) be the first derivative of f(a). Factor q(y).
3*(y - 2)*(3*y + 1)
Let s = -1 - -7. Let n = -4 + s. Factor 2*l**2 - l - 5*l**4 - l**n + 4*l**4 + l**3.
-l*(l - 1)**2*(l + 1)
Suppose 5*u + 5*t - 23 = 3*t, 5*t - 20 = 0. Let y = 7 - 3. Factor 2/7*n - 2/7*n**y - 2/7*n**u + 2/7*n**2 + 0.
-2*n*(n - 1)*(n + 1)**2/7
Factor 8/3*a**3 + 8/3*a - 2/3 - 4*a**2 - 2/3*a**4.
-2*(a - 1)**4/3
Let o(f) = -f**2 - f. Let v(m) = m - 2. Let h be v(5). Let k(z) = -z**3 - 3*z**2 - 2*z. Let c(l) = h*k(l) - 6*o(l). Determine n so that c(n) = 0.
-1, 0
Let y = 129 - 126. Factor -18/5 - 32/5*r**2 - 57/5*r - r**y.
-(r + 3)**2*(5*r + 2)/5
Let d(y) be the second derivative of y**5/210 - y**4/84 + y**2/2 + 2*y. Let g(h) be the first derivative of d(h). Factor g(w).
2*w*(w - 1)/7
Suppose -b - 17 = -4*m - m, b = m - 1. Factor 3*r**2 + 1 + 2*r**2 - 5*r**2 - r**2 + r - r**b.
-(r - 1)*(r + 1)**2
Let q(z) be the first derivative of -2*z**6/3 + 16*z**5/5 + 2*z**4 - 32*z**3/3 - 2*z**2 + 16*z + 39. Find t such that q(t) = 0.
-1, 1, 4
Let -2/5*y - 3/5*y**2 - 1/10 - 1/10*y**4 - 2/5*y**3 = 0. What is y?
-1
Let q be 1 + 4/(-8) - 1/6. Factor -q*f + 1/3*f**2 + 0.
f*(f - 1)/3
Let c(w) be the third derivative of 3*w**6/280 - 11*w**5/140 + 3*w**4/14 - 2*w**3/7 + 2*w**2. Suppose c(g) = 0. Calculate g.
2/3, 1, 2
Find x such that 10/17*x**3 - 2*x**2 + 32/17*x - 8/17 = 0.
2/5, 1, 2
Determine r so that 16*r - 11 - 3*r - 13*r**2 - 4*r**3 + 15 = 0.
-4, -1/4, 1
Let b = 4433 - 17559/4. Let t = -43 + b. Factor 1/4 + t*m**2 + 1/2*m.
(m + 1)**2/4
Let a = -4 - -4. Suppose h + a*h = 5. Factor 0*g - 2*g - 4*g**4 + 2*g**h + 0*g + 4*g**2.
2*g*(g - 1)**3*(g + 1)
Let 0 + 2*i + 23/2*i**3 + 7/2*i**4 + 10*i**2 = 0. Calculate i.
-2, -1, -2/7, 0
Suppose -128 + 4*v - 12*v**3 - 4*v**2 + 128 + 8*v**5 + 4*v**4 = 0. Calculate v.
-1, 0, 1/2, 1
Let o be (-38)/(-88) + (-26)/143. Solve 0*y**2 + 1/4*y**3 - o*y**5 + 0*y**4 + 0*y + 0 = 0.
-1, 0, 1
Let q = 784/9 + -87. Let t(o) be the third derivative of 0*o + 4/9*o**3 - o**2 + 0 + 1/90*o**5 - q*o**4. Factor t(l).
2*(l - 2)**2/3
Let z = -180/7 + 26. Factor z*o**2 + 2/7*o**3 - 2/7 - 2/7*o.
2*(o - 1)*(o + 1)**2/7
Suppose -2/5*z**3 + 26/5*z**2 + 4/5*z - 16/5 - 2/5*z**5 - 2*z**4 = 0. Calculate z.
-4, -2, -1, 1
Suppose -4*g + 23 = 3. Let c(x) = x - 3. Let a be c(g). Factor a - u**2 + 4*u - 5*u**2 + 5*u**2 + 3*u**2.
2*(u + 1)**2
Suppose 5*n + 15 = -5*b, -13*b + 12*b - 9 = 3*n. Factor 1/3*a**2 + b - 1/3*a.
a*(a - 1)/3
Let l(y) be the first derivative of -y**7/280 - y**6/160 + y**5/80 + y**4/32 - 3*y**2/2 + 4. Let s(u) be the second derivative of l(u). Factor s(r).
-3*r*(r - 1)*(r + 1)**2/4
Let i(u) be the third derivative of u**7/1260 - u**6/720 - u**5/120 + u**4/144 + u**3/18 - 25*u**2. Solve i(n) = 0 for n.
-1, 1, 2
Let w(v) = 50*v**4 - 35*v**3 + 13*v**2 + 5*v. Let l(m) = 50*m**4 - 36*m**3 + 12*m**2 + 4*m. Let i(n) = 5*l(n) - 4*w(n). Factor i(j).
2*j**2*(5*j - 2)**2
Let u(x) = -x - 4*x + 0*x + 3*x. Let k be u(-1). Determine a so that 9*a + 3 - 3 - 1 + 3*a**3 + 4 + 9*a**k = 0.
-1
Let t(q) = q + 7. Let l be t(-5). Suppose -2 = l*n, -2*b - 2*n = -5*b + 2. What is r in 2/5*r**3 + 2/5*r**5 - 4/5*r**4 + b*r + 0 + 0*r**2 = 0?
0, 1
Let j(d) = -d + 3. Let v(h) = 2*h - 8. Let r(z) = 8*j(z) + 3*v(z). Let x be r(-1). Factor 2/5*a - 1/5*a**4 + a**x + 3/5*a**3 + 0 - 1/5*a**5.
-a*(a - 2)*(a + 1)**3/5
Let w(d) be the first derivative of -5*d**6/6 + 7*d**5/5 + 2*d**4 - 4*d**3/3 - 4. Determine b, given that w(b) = 0.
-1, 0, 2/5, 2
Let o(j) be the first derivative of 0*j + 1/36*j**4 - j**2 - 7/135*j**5 - 1 + 2/27*j**3. Let f(u) be the second derivative of o(u). Factor f(r).
-2*(2*r - 1)*(7*r + 2)/9
Factor -18*v**2 + 3*v**3 + 0*v + 43*v - 16*v.
3*v*(v - 3)**2
Factor 0*d + 8/3*d**3 + 0*d**4 + 0 + 0*d**2 - 2/3*d**5.
-2*d**3*(d - 2)*(d + 2)/3
Let w(d) be the third derivative of d**9/6048 - d**8/1680 - d**7/1680 + d**6/360 - d**3/2 - d**2. Let m(y) be the first derivative of w(y). Factor m(c).
c**2*(c - 2)*(c - 1)*(c + 1)/2
Suppose -j - 5*z - 4 = 0, 5*z = -3*j + 8*j - 10. Find g such that -j + 4*g + g**2 + g**2 - 2*g - 3*g**2 = 0.
1
Let x be (-6*2/(-30))/((-13)/(-5)). Factor -10/13*j**3 - x*j**4 + 2/13*j**2 + 2/13*j**5 + 8/13 + 16/13*j.
2*(j - 2)**2*(j + 1)**3/13
Let z = -21 - -43. Let s = -20 + z. Factor 2*l + 3/4*l**s + 1.
(l + 2)*(3*l + 2)/4
Let m be (1/(-4) + 0)/((-23)/69). Solve -1/4*g**3 - m*g - 3/4*g**2 - 1/4 = 0 for g.
-1
Suppose 0*d - 13 = d. Let k be d/(-15) + (-4)/6. Factor k*h - 1/5*h**2 + 0.
-h*(h - 1)/5
Let w = 14 + 3. Suppose -23 = -f + w. Find q such that 36*q**3 + f*q**2 + q + 13*q**3 - 12*q**2 + 3*q = 0.
-2/7, 0
Let p(t) be the first derivative of -t**5/180 + t**4/72 + t**3/9 + 4*t**2 + 6. Let n(s) be the second derivative of p(s). Solve n(k) = 0.
-1, 2
Let p(k) = 9*k - 6. Let l be p(4). Let s be 22/l - 8/24. Factor s*y - 2/5*y**2 + 0 + 2/5*y**4 - 2/5*y**3.
2*y*(y - 1)**2*(y + 1)/5
Let r(m) be the first derivative of m**6/30 + m**5/10 + m**4/12 + 2*m - 2. Let h(q) be the first derivative of r(q). Determine u, given that h(u) = 0.
-1, 0
Let j(h) be the second derivative of 0 + 1/2*h**5 + 3/2*h**4 - h**2 + h**3 - 2*h. Determine x so that j(x) = 0.
-1, 1/5
Let j be 12/18*(-6)/(-4). Let w = j + 3. Factor -25*g - 2*g**4 + 25*g - 6*g**3 - w*g**2.
-2*g**2*(g + 1)*(g + 2)
Suppose -5*u = -3*o - 209, -5*u + 7 = -13. Let w = 316/5 + o. Solve -w*q - 1/5*q**3 + 0 - 2/5*q**2 = 0 for q.
-1, 0
Determine q so that 209/4*q**3 - 245/4*q**2 + 3 - 4*q + 1281/4*q**4 - 441/4*q**5 = 0.
-1/3, 2/7, 3
Let q(g) = -g**3 - 6*g**2 - 5*g + 5. Let y be q(-5). Suppose -t - 4*h = -7*h - 1, -y*h = 4*t - 21. What is w in w**3 + 4*w + t*w**2 + w**3 - 2*w = 0?
-1, 0
Let s = 38027/5 - 7539. Let o = -66 + s. Let 12/5*i**2 - 24/5*i + 16/5 - o*i**3 = 0. What is i?
2
Let t(y) be the second derivative of y**6/40 - 3*y**5/80 - y**4/4 + y**3/2 + 7*y. Determine p, given that t(p) = 0.
-2, 0, 1, 2
Let o(k) be the third derivative of -k**5/420 - 2*k**2 + 25. Determine n so that o(n) = 0.
0
Suppose 0 = 2*j - 5*y + 2*y - 19, 0 = -5*j + y + 15. Suppose 4*g - 2 = s, 0*s + 5*s - 9 = g. Suppose j + s + 2*k**2 - 6 = 0. What is k?
-1, 1
Factor 3/2*q**4 + 0 + 1/2*q**2 - 1/2*q**5 - 3/2*q**3 + 0*q.
-q**2*(q - 1)**3/2
Let y(z) = z**5 - z**3 - z**2 - 1. Let t(b) = -12*b**5 + 4*b**4 + 20*b**3 - 12*b**2 + 8*b + 8. Let k(m) = -t(m) - 8*y(m). Let k(u) = 0. Calculate u.
-2, 0, 1
Let h(l) = l**2 + 3*l - 1. Let a be h(-4). Find v, given that a*v**4 + 2*v**3 + 4*v**3 - 2*v**3 - 5*v**3 = 0.
0, 1/3
Let r(c) be the third derivative of -c**7/105 + 2*c**6/5 - 36*c**5/5 + 72*c**4 - 432*c**3 - 17*c**2. Let r(q) = 0. What is q?
6
Let t be (-660)/(-840