Let o(g) = -2*g**5 + g**4 + 2*g**3 + g + 1. Let u(j) = -5*o(j) + 5*t(j). Factor u(x).
5*x**2*(x - 1)**2*(x + 1)
Let t = -2/331 + 1007/2317. Determine l, given that -3/7*l**5 + 0*l - 6/7*l**2 + t*l**3 + 6/7*l**4 + 0 = 0.
-1, 0, 1, 2
Let c be 2/(-3) + (-12)/(-9). Let t(w) = -w**2 + 2*w + 39. Let m be t(-5). Suppose d**3 + 1/3*d**m + 0 - c*d**5 - 1/3*d - 1/3*d**2 = 0. What is d?
-1, -1/2, 0, 1
Let f be 0 + 0 - 23/(575/(-10)). Factor -f*p**5 - 1/5*p**2 - p**4 + 0*p - 4/5*p**3 + 0.
-p**2*(p + 1)**2*(2*p + 1)/5
Factor 39*a**2 + 28*a**2 + 14*a**2 + 763*a + 3*a**3 - 34*a + 2187.
3*(a + 9)**3
Let f be ((-29)/9 - -3)/(2/(-6)). Let l(t) be the first derivative of -4 + 0*t + 0*t**2 - 1/2*t**4 - f*t**3. Factor l(m).
-2*m**2*(m + 1)
Let o(w) = w**2 + w + 1. Let k be 1/(((-12)/(-9))/4). Let a be k/4 + (-2)/(-8). Let d(n) = n**2 + 2*n + 2. Let s(h) = a*d(h) - 2*o(h). Factor s(j).
-j**2
Factor 7*p**2 + 2*p**2 - 17*p**3 - p**2 - 19*p**3.
-4*p**2*(9*p - 2)
Suppose 23 + 21 = 11*z. Factor 0 + 0*h**3 + 1/3*h**z - 4/3*h**2 + 0*h.
h**2*(h - 2)*(h + 2)/3
Find g such that 4/7*g**5 + 0 + 12/7*g**4 + 8/7*g**3 + 0*g + 0*g**2 = 0.
-2, -1, 0
Let x be 0/(-1) + (-2 - -1*4). Let k(y) be the first derivative of 0*y**2 + x + 2/3*y**3 - 7/4*y**4 + 0*y. Factor k(h).
-h**2*(7*h - 2)
Let q(c) be the third derivative of -c**7/210 + c**6/96 + 7*c**5/240 - c**4/48 - 13*c**2. Factor q(t).
-t*(t - 2)*(t + 1)*(4*t - 1)/4
Let m be (0/(-3) + -4)*(1 + -2). Let n(s) be the first derivative of 2/27*s**3 + 1 - 2/9*s - 1/18*s**m + 1/9*s**2. Suppose n(v) = 0. Calculate v.
-1, 1
Let l(m) = 2*m + 14. Let t be l(-6). Find u such that 3*u**t + 9 + 5*u - 17*u + 0 = 0.
1, 3
Let o = 51 - 152/3. Let r(z) be the first derivative of -1 + 6/5*z**5 + 0*z - 3/2*z**4 + 2/3*z**3 - o*z**6 + 0*z**2. Let r(t) = 0. Calculate t.
0, 1
Factor 1/4*i**2 - 3 - 2*i + 1/4*i**3.
(i - 3)*(i + 2)**2/4
Let t(s) be the first derivative of 9*s**4/28 - 5*s**3/7 + 3*s**2/7 + 1. Suppose t(a) = 0. What is a?
0, 2/3, 1
Let c(z) be the second derivative of 3*z**7/1400 - 2*z**6/225 + z**5/120 + z**4/60 - z**3/6 + z. Let p(u) be the second derivative of c(u). Factor p(m).
(m - 1)**2*(9*m + 2)/5
Suppose 64 - 336*k + 0*k**5 + 300*k**2 + 5*k**5 + 361*k**3 + 4*k**5 + 102*k**4 = 0. Calculate k.
-4, 1/3
Let h(u) = 6*u**2 + 41*u + 96. Let x(c) be the first derivative of -2*c**3/3 - 7*c**2 - 32*c + 5. Let s(m) = 2*h(m) + 7*x(m). Suppose s(o) = 0. What is o?
-4
Factor -20*w**2 - 2/3*w**3 - 2000/3 - 200*w.
-2*(w + 10)**3/3
Let n(h) be the second derivative of -h**7/21 - h**6/5 - 3*h**5/10 - h**4/6 - 11*h. Solve n(p) = 0.
-1, 0
Determine f, given that 2*f**2 + 12*f**3 + f**2 - 3*f**2 + 9*f**4 + 3*f**2 = 0.
-1, -1/3, 0
Let a(t) = -t**3 + t**2 + t + 1. Let q(v) = 0*v**4 + 2 + v**4 + 5*v - 3*v + 0*v**4 + 2*v**2 - v**3. Let w(i) = -2*a(i) + q(i). Factor w(p).
p**3*(p + 1)
Let r(a) be the first derivative of 1 + 0*a**3 - 1/5*a**5 + 0*a**2 - 1/4*a**4 + 0*a. Factor r(p).
-p**3*(p + 1)
Let f(g) be the first derivative of -2 - 2/3*g**3 - g**2 + 0*g. Factor f(m).
-2*m*(m + 1)
Suppose 4*f = 3*f. Suppose f*c - 2 = -c. Factor -z**2 + z**3 + 0*z**3 - c*z**3.
-z**2*(z + 1)
Let b(z) = z**3 + z**2 + 1. Suppose -2*y + 10 = -4*y. Let n(d) = -4*d**3 - 4*d**2 - d - 6. Let w(i) = y*b(i) - n(i). Factor w(a).
-(a - 1)*(a + 1)**2
Let a(o) be the third derivative of 0*o**3 + 0*o**4 + 0*o**5 + 0 + 0*o + 3*o**2 + 1/180*o**6. Factor a(y).
2*y**3/3
Let n be (21/(-8) + 3)/(1/2). Factor 3/4*l**2 + 0 + 3/2*l**3 + 0*l + n*l**4.
3*l**2*(l + 1)**2/4
Let i(t) be the second derivative of 5*t**4/24 + 5*t**3/12 - 5*t**2/2 + 4*t. Factor i(g).
5*(g - 1)*(g + 2)/2
Let t(f) be the second derivative of f**8/112 - 3*f**6/40 - f**5/10 - 3*f**2/2 + 8*f. Let p(w) be the first derivative of t(w). Suppose p(k) = 0. What is k?
-1, 0, 2
Let s(h) = -h**2 + 17*h + 38. Let f be s(19). Let r(b) be the second derivative of 2*b + 0 + 1/30*b**6 + 0*b**4 - 1/20*b**5 + f*b**2 + 0*b**3. Factor r(g).
g**3*(g - 1)
Let z(q) be the second derivative of -q**5/60 - 2*q**4/9 - 7*q**3/6 - 3*q**2 - 28*q. Suppose z(o) = 0. Calculate o.
-3, -2
Let h(g) be the third derivative of -g**8/112 + g**7/42 + g**6/120 - g**5/12 + g**4/12 + 6*g**2. Let h(n) = 0. Calculate n.
-1, 0, 2/3, 1
Suppose x = 2, -5*x = -4*i - 2*x + 26. Let l = 8 - i. Suppose 1/3*o + l - 1/3*o**4 + o**3 - o**2 = 0. What is o?
0, 1
Let k be (10 + 1045/(-99))/((-10)/12). Determine x, given that 0*x + 2/3 - k*x**2 = 0.
-1, 1
Let u(z) be the first derivative of 5*z**4 + 45*z**3/2 + 125*z**2/4 + 15*z - 47. Factor u(i).
5*(i + 1)*(i + 2)*(8*i + 3)/2
Let j(y) = -17*y**4 - 19*y**3 - 13*y**2 + 11*y. Let b(n) = 9*n**4 + 10*n**3 + 7*n**2 - 6*n. Let f(q) = -11*b(q) - 6*j(q). Factor f(s).
s**2*(s + 1)*(3*s + 1)
Let s be ((-8)/5)/(8/(-20)). Factor s*u**3 - 2*u**3 + 7*u**3 - 6*u**2.
3*u**2*(3*u - 2)
Let t = 6 - 1. Let x(k) be the second derivative of 0*k**2 + 0 - 1/50*k**t + 1/15*k**3 + 1/30*k**4 - 3*k - 1/75*k**6. Factor x(h).
-2*h*(h - 1)*(h + 1)**2/5
Let r(k) be the third derivative of -k**10/25200 + k**9/3780 - k**8/3360 - k**7/1260 + k**5/15 + 2*k**2. Let n(b) be the third derivative of r(b). Factor n(x).
-2*x*(x - 2)*(x - 1)*(3*x + 1)
Let m be ((-7)/21)/(1/6). Let j be (-1 - m)*3 - 3. Factor -2/9 + 2/9*t**2 + j*t.
2*(t - 1)*(t + 1)/9
Let o(u) be the third derivative of -u**5/270 - u**4/54 - u**3/27 - u**2. Factor o(m).
-2*(m + 1)**2/9
Let r = 17 - 14. Let o**2 + 0 - 1/4*o**r - o = 0. What is o?
0, 2
Suppose -3/4*s**2 + 1/4*s**3 + 1/2*s + 0 = 0. What is s?
0, 1, 2
Let p(x) be the second derivative of -x**8/1176 + x**7/245 - x**6/210 + 2*x**2 - 4*x. Let i(u) be the first derivative of p(u). What is v in i(v) = 0?
0, 1, 2
Let b(a) = -a**3 - 37*a**2 - 185*a + 33. Let z be b(-31). What is d in 4 - 2*d + 1/4*d**z = 0?
4
Suppose 0 = -4*t - 11 + 27. Suppose -l - 2 = 0, -4*a + l + 2 = t*l. Factor 4*x**3 - 4 - 3*x**2 + 5*x**a + 2*x**4 + 4.
2*x**2*(x + 1)**2
Let g(n) be the second derivative of -n**5/110 + 2*n**4/33 - n**3/11 - 12*n. Determine w, given that g(w) = 0.
0, 1, 3
Let p(l) be the second derivative of -3*l**5/100 + 2*l**4/5 - l**3/2 - 15*l**2 + l + 2. Factor p(u).
-3*(u - 5)**2*(u + 2)/5
Let d(y) = -6*y**3 - 2*y**2 + 5*y + 1. Let u(r) = -7*r**3 - 3*r**2 + 6*r + 2. Let h(x) = 6*d(x) - 5*u(x). Factor h(l).
-(l - 2)**2*(l + 1)
Let r(p) be the second derivative of p**6/5 + p**5/5 - 5*p**4/18 - 2*p**3/9 + 11*p. What is l in r(l) = 0?
-1, -1/3, 0, 2/3
Suppose 10*n = 9*n + 3. Let p(w) be the second derivative of 0*w**4 - w + 1/30*w**5 - 1/9*w**n + 0*w**2 + 0. Factor p(o).
2*o*(o - 1)*(o + 1)/3
Suppose 22 = 2*i - 4*v, -2*i + 5*i + 5*v = 0. Let u be (-1)/2*0/1. Factor 0*q**3 - 4/7*q**4 + u + 4/7*q**2 + 2/7*q - 2/7*q**i.
-2*q*(q - 1)*(q + 1)**3/7
Let r(l) be the third derivative of 16*l**7/105 - 2*l**6/15 - 7*l**5/30 - l**4/12 - 17*l**2. Factor r(z).
2*z*(z - 1)*(4*z + 1)**2
Let g be (-2 - 4/(-6))/(52/(-78)). Factor 2/5*m - 1/5 - 1/5*m**g.
-(m - 1)**2/5
Let r(i) = -i**2 - i + 12. Let a be r(-4). Find f, given that -1/4*f**2 + a + 1/2*f = 0.
0, 2
Let s(m) be the third derivative of m**8/10080 - m**7/1260 + m**6/360 - m**5/20 + 9*m**2. Let z(x) be the third derivative of s(x). Find j, given that z(j) = 0.
1
Let p = 42 - 39. Let l(u) be the third derivative of 0*u - 2*u**2 + 0*u**4 + 0 - 1/90*u**5 + 1/9*u**p. Suppose l(g) = 0. Calculate g.
-1, 1
Let 0*p**2 + 0*p**3 + 0 - 2/15*p**4 - 2/15*p**5 + 0*p = 0. What is p?
-1, 0
Let b(f) be the first derivative of 2*f**3/33 + 8*f**2/11 + 32*f/11 + 20. Factor b(i).
2*(i + 4)**2/11
Let c(h) be the second derivative of -h**4/48 - h**3/8 - h**2/4 + 13*h. Factor c(o).
-(o + 1)*(o + 2)/4
Let q(o) = -5*o**5 - 9*o**4 - 7*o**3 + o**2 + 6*o - 1. Let g(s) = 6*s**5 + 10*s**4 + 8*s**3 - 6*s + 2. Let k(w) = -3*g(w) - 4*q(w). Factor k(y).
2*(y - 1)*(y + 1)**4
Let a = -192 - -300. Let u be ((-8)/a)/((-2)/12). What is q in 0 + 2/9*q + 2/9*q**3 - u*q**2 = 0?
0, 1
Let b(w) = 3*w**3 + 2*w**2 - 2*w + 1. Let n be b(1). Let u = -3 + 3. Solve -1/4*o**n + 1/2*o**2 - 1/4 + 0*o + u*o**3 = 0 for o.
-1, 1
Suppose -9*n - 15 = -14*n. Factor 0 - 8/3*w**2 - 2/3*w**n - 8/3*w.
-2*w*(w + 2)**2/3
Let k(v) = -3*v**4 + 4*v**3 + 13*v**2 - 2*v + 4. Let n(s) = 21*s**4 - 27*s**3 - 90*s**2 + 15*s - 27. Let r(h) = 27*k(h) + 4*n(h). Determine c so that r(c) = 0.
-2, 0, 1
Let n 