*n**3 + 24*n**2 + 22*n + 10. Let t(v) = -2*h(v) + l(v). Factor t(w).
2*(w + 1)*(w + 2)*(3*w + 2)
Let x = 8 + -6. Suppose -2*f = -g - x, -3*f + 3*g = f. Factor 2*o**2 + 2*o + 0*o**2 - f*o**2 + 3*o**2.
2*o*(o + 1)
Let q(i) be the third derivative of -i**8/336 + i**7/210 + i**6/40 - i**5/12 + i**4/12 + 14*i**2. Let q(o) = 0. What is o?
-2, 0, 1
Let r = -18 + 50. Let g = 34 - r. Factor 2/3*y**g + 2/3 + 4/3*y.
2*(y + 1)**2/3
Factor 0*z + 2/9*z**2 + 0 - 20/9*z**3.
-2*z**2*(10*z - 1)/9
Factor 1/6*n**2 + 0*n - 1/6*n**3 - 1/6*n**4 + 0 + 1/6*n**5.
n**2*(n - 1)**2*(n + 1)/6
Let w be (1/3)/((-1)/(-6)). Suppose 2*n - 7*n + 33 = 4*u, 23 = 5*n - u. Factor 2*a**n + a**4 - 3*a + 2*a**3 + w*a**2 + 2*a**4 - a**5 + 1 - 6*a**4.
(a - 1)**4*(a + 1)
Let r(m) = -4*m**4 + 2*m**3 - 2*m - 2. Let t(j) = j**5 - j**4 - j**2 - j - 1. Let x(c) = r(c) - 2*t(c). Suppose x(u) = 0. What is u?
-1, 0, 1
Let j(s) be the second derivative of s**7/42 - s**6/10 + 3*s**5/20 - s**4/12 - 3*s. What is w in j(w) = 0?
0, 1
Let y(z) be the third derivative of 1/48*z**4 + 0*z**3 - 1/240*z**6 + 0 + 0*z + 4*z**2 + 0*z**5. Let y(k) = 0. Calculate k.
-1, 0, 1
Let l(b) be the first derivative of -1/15*b**3 + 3 - 2*b - 1/30*b**4 + 0*b**2. Let m(y) be the first derivative of l(y). Find h such that m(h) = 0.
-1, 0
Let f(v) be the first derivative of v**3 + 3*v**2 + 12. Let f(y) = 0. Calculate y.
-2, 0
Let v(g) be the third derivative of -4*g**2 + 0*g + 0 + 0*g**5 + 0*g**4 - 1/20*g**6 + 0*g**3 + 1/14*g**7. Factor v(j).
3*j**3*(5*j - 2)
Let s(y) be the third derivative of 0 + 6*y**2 - 1/30*y**5 + 0*y - 1/2*y**4 - 3*y**3. Factor s(u).
-2*(u + 3)**2
Let m(v) be the third derivative of -v**7/168 - 13*v**6/480 + 7*v**5/30 - 5*v**4/24 + 2*v**2 - 8. Find u such that m(u) = 0.
-5, 0, 2/5, 2
Let r(z) be the second derivative of -z**5/60 + z**4/36 + z**3/18 - z**2/6 + 4*z. Let r(p) = 0. Calculate p.
-1, 1
Let w = -11/8 + 3/2. Let p(h) be the first derivative of -1/16*h**4 - w*h**2 + 1/6*h**3 + 0*h - 1. Factor p(t).
-t*(t - 1)**2/4
Let j(q) be the second derivative of -q**9/1512 - q**8/210 - q**7/70 - q**6/45 - q**5/60 + q**3/6 + 2*q. Let z(l) be the second derivative of j(l). Factor z(k).
-2*k*(k + 1)**4
Let s(k) = 4*k**3 + 12*k**2 + 8*k + 20. Let w(z) = 1. Let t(f) = -s(f) + 20*w(f). Factor t(b).
-4*b*(b + 1)*(b + 2)
Let q(z) = -2*z**2 - 2*z + 1. Let j(u) = -5*u**2 - 6*u + 3. Let p(v) = 3*j(v) - 8*q(v). Determine w, given that p(w) = 0.
1
Let c(j) be the third derivative of 3*j**5/80 - j**4/32 - j**3/12 - 20*j**2. Let c(h) = 0. Calculate h.
-1/3, 2/3
Let q = 1 + 1. Let i = -4 + 6. Factor 2*p**4 - 6*p**i + 2*p**2 + 0*p**2 - q*p**3 + 2*p**2 + 2*p**5.
2*p**2*(p - 1)*(p + 1)**2
Let l(y) be the first derivative of 0*y**2 - 2/15*y**3 - 3 - 1/4*y**4 + 0*y. Let l(s) = 0. Calculate s.
-2/5, 0
Let z(n) = n - 9. Let f be z(5). Let y = f + 7. Factor 11*v**5 - 7*v**5 - 24*v**4 + 4*v**2 + 6*v**y + 10*v**5.
2*v**2*(v - 1)**2*(7*v + 2)
Let p be (9 - (-30)/(-4))/((-2)/(-10)). Solve p*z**2 + 15/2*z**3 + 15/4*z**4 + 3/4 + 15/4*z + 3/4*z**5 = 0.
-1
Suppose 6*d**3 + 3*d**3 - 8*d**2 - d**3 - 4*d**3 = 0. Calculate d.
0, 2
Find y such that 4/3*y - 4/3 - 1/3*y**2 = 0.
2
Suppose 0*p**2 + 0*p + 0*p**3 + 2/17*p**5 + 0 - 2/17*p**4 = 0. What is p?
0, 1
Let c(y) = 12*y**4 + 56*y**3 + 59*y**2 + 20*y - 17. Let a(z) = 4*z**4 + 19*z**3 + 20*z**2 + 7*z - 6. Let x(n) = 11*a(n) - 4*c(n). Let x(p) = 0. Calculate p.
-2, -1, 1/4
Let f = 14 + -9. Factor -10*s**2 - 6*s + f*s + 2*s**4 + 5*s - 2*s**5 - s**3 + 7*s**3.
-2*s*(s - 1)**3*(s + 2)
Let w(i) = -15*i**4 - 10*i**3 + 40*i**2 - 10*i - 25. Let t(q) = -5*q**4 - 3*q**3 + 13*q**2 - 3*q - 8. Let v(s) = -10*t(s) + 3*w(s). Factor v(x).
5*(x - 1)**2*(x + 1)**2
Determine k, given that 3/2*k**2 + 3/4*k**3 - 6 - 3*k = 0.
-2, 2
Let k(p) be the second derivative of 3*p**5/140 - 3*p**4/28 + 6*p**2/7 + 12*p. Factor k(s).
3*(s - 2)**2*(s + 1)/7
Let d(x) be the third derivative of -x**8/20160 + x**7/2520 - x**6/720 - x**5/12 - x**2. Let w(b) be the third derivative of d(b). Factor w(i).
-(i - 1)**2
Let o(g) be the third derivative of g**6/120 + g**5/15 + 5*g**4/24 + g**3/3 + 22*g**2. Factor o(q).
(q + 1)**2*(q + 2)
Let m(v) be the third derivative of v**7/3150 + v**6/300 - v**4/8 + 9*v**2. Let j(x) be the second derivative of m(x). Suppose j(t) = 0. Calculate t.
-3, 0
Let y be -1 + (172/30)/1. Let j = y + 3/5. Factor -1/3*c**5 - 16*c - 32/3*c**3 - 56/3*c**2 - j - 3*c**4.
-(c + 1)*(c + 2)**4/3
Let u = 1 - 1. Let x(i) be the third derivative of -2*i**2 + 0*i**4 + 0*i**5 + 1/315*i**7 + 0 - 1/180*i**6 + 0*i**3 + u*i. Solve x(g) = 0.
0, 1
Let a(m) be the second derivative of -m**7/2100 - m**6/225 - m**5/75 - m**3/3 + m. Let z(o) be the second derivative of a(o). Solve z(v) = 0.
-2, 0
Let s(i) be the second derivative of i**6/150 - i**5/20 + 2*i**4/15 - 2*i**3/15 + 5*i. Factor s(g).
g*(g - 2)**2*(g - 1)/5
Let y(x) be the first derivative of -6*x**5/25 - 7*x**4/10 - 2*x**3/3 - x**2/5 - 2. Factor y(i).
-2*i*(i + 1)**2*(3*i + 1)/5
Suppose 0 = -4*i - 0*i + 8. Let w = 83/190 + 6/95. Factor 0 - w*k + 1/2*k**i.
k*(k - 1)/2
Suppose -2*i + 2*n = 2, 6*n - 1 = 5*i + 2*n. Let x be (5 - i) + (-4)/6. Let 0 - 2/3*u**3 - 4/3*u**2 + x*u**4 + u**5 - 1/3*u = 0. Calculate u.
-1, -1/3, 0, 1
Let n(a) be the first derivative of 81*a**4/7 + 48*a**3/7 + 8*a**2/7 + 5. Determine g so that n(g) = 0.
-2/9, 0
Let s(z) be the first derivative of z**4/4 + z**3/3 - 5*z**2/2 + 3*z + 10. Solve s(r) = 0 for r.
-3, 1
Let x(s) be the first derivative of -s**4/6 + s**3 - 2*s**2 - s - 7. Let m(d) be the first derivative of x(d). Factor m(w).
-2*(w - 2)*(w - 1)
Let t be 3 + 2/2 + -1. Factor 2*x - 5*x + 7*x**3 - 4*x**t.
3*x*(x - 1)*(x + 1)
Let m(k) be the first derivative of k**3/3 + k**2/2 + 1. Let s be m(-2). Factor -5*o**2 + 3*o**2 + 7*o - s - 3*o.
-2*(o - 1)**2
Let d(b) be the first derivative of 0*b**2 - 3/5*b**5 - 3/4*b**4 + 0*b + b**3 + 1/2*b**6 + 2. Suppose d(q) = 0. Calculate q.
-1, 0, 1
Suppose -5*i = 2*a - 75, 5*i = -3*a - 2*a + 195. Let z be 1/2*a/30. Determine n so that 8/3*n**2 - 8/3*n + 0 - z*n**3 = 0.
0, 2
Let r(m) be the first derivative of 5 + 0*m + 0*m**2 - 1/3*m**3 + 1/4*m**4. Find k such that r(k) = 0.
0, 1
Let c be 306/756 + 5/(-6) + 1. Factor c*l**5 - 8/7*l**2 + 8/7*l**3 - 4/7 - 12/7*l + 12/7*l**4.
4*(l - 1)*(l + 1)**4/7
Suppose 2*h + 4*v + 0*v - 68 = 0, -v = -3*h + 116. Let k be 1170/567 - (-4)/(-14). Factor 268/9*r**2 + h*r**3 + 6*r**5 + 104/9*r + 24*r**4 + k.
2*(r + 1)**2*(3*r + 2)**3/9
Let b = 1 + 2. Suppose -5*x - 5*g = -20, -b*x - 3 + 15 = 4*g. Factor -x*d + d**2 + 3 + 2*d - 2.
(d - 1)**2
Let s = -9 + 7. Let j = -2 - s. Factor 0 + j*v - 2/5*v**2.
-2*v**2/5
Factor -2/3 + j**2 - 1/3*j - 1/3*j**4 + 1/3*j**3.
-(j - 2)*(j - 1)*(j + 1)**2/3
Suppose 6*z = 8*z - 4. Factor -a**z + 5*a**2 + 6*a - a**2.
3*a*(a + 2)
Let b(v) be the first derivative of -3*v**5/5 + v**4/4 + 3*v**3 - 9*v**2/2 + 2*v - 20. Factor b(k).
-(k - 1)**2*(k + 2)*(3*k - 1)
Suppose 41 = 5*p - 29. Suppose 0 = -p*j + 16*j. Determine f so that 0*f + 1/2*f**4 - 1/2*f**2 + j*f**3 + 0 = 0.
-1, 0, 1
Let o be 2/((-6)/(-9)) + -1. Let l be (1/(-1))/((-1)/o). Factor 0 - 1/2*h**l + 0*h.
-h**2/2
Let j(y) = -26*y + 2. Let o be j(-1). Let d be (12/(-21))/((-24)/o). Solve 4/3 + d*n**2 - 2*n = 0 for n.
1, 2
Solve 21*k**2 + 17*k**2 + 4 - 42*k**2 = 0 for k.
-1, 1
Let r = 13 - 5. Suppose x = -3*x + r. Factor -1 + 1 + 3*d**x + 2*d.
d*(3*d + 2)
Factor -2/9*f**3 + 0*f + 0 + 2/3*f**2.
-2*f**2*(f - 3)/9
Let x = 55 - 55. Determine o so that -o**4 - 1/2*o**2 + 0*o + 5/4*o**3 + 1/4*o**5 + x = 0.
0, 1, 2
Let s(i) = -i**2 - i. Let r(z) = -z**2 - 7*z + 6. Let w(g) = r(g) - 2*s(g). Suppose w(x) = 0. What is x?
2, 3
Let y(f) be the third derivative of f**9/9072 + f**8/5040 - f**7/2520 - f**6/1080 + f**3/2 - 2*f**2. Let v(g) be the first derivative of y(g). Factor v(r).
r**2*(r - 1)*(r + 1)**2/3
Factor 1/5*n**2 - 1/5 - 1/5*n**3 + 1/5*n.
-(n - 1)**2*(n + 1)/5
Factor 1/6*x**3 + 0 + 1/2*x**2 + 1/3*x.
x*(x + 1)*(x + 2)/6
Let a(f) be the second derivative of f**6/2 - 4*f**5 + 145*f**4/12 - 50*f**3/3 + 10*f**2 + 21*f. Factor a(d).
5*(d - 2)**2*(d - 1)*(3*d - 1)
Let k(x) be the first derivative of -x**5/10 + 7*x**4/8 - 3*x**3 + 5*x**2 - 4*x + 53. Factor k(b).
-(b - 2)**3*(b - 1)/2
Let t(f) be the second derivative