et u(j) = 0 + 5 + 1 + 2*j**2 - 1 + 2*j. Let t(y) = -2 + y**2 - 3*y - 2*y**2 + 2*y. Let i(c) = 5*t(c) + 2*u(c). Factor i(l).
-l*(l + 1)
Find p such that -12*p - 7*p + 5*p + 0*p**2 + p**2 + 49 = 0.
7
Let o(t) = -4*t**3 - 16*t**2 + 12*t + 24. Let p(c) = -3*c**3 - 15*c**2 + 11*c + 23. Let a(m) = -5*o(m) + 6*p(m). Factor a(s).
2*(s - 3)**2*(s + 1)
Let q(x) = 15*x**3 - 25*x**2 - 15*x + 25. Let o(k) = -8*k**3 + 13*k**2 + 8*k - 13. Let u(l) = 5*o(l) + 3*q(l). Let u(i) = 0. What is i?
-1, 1, 2
Let r(z) be the third derivative of -z**5/360 - z**4/72 + 7*z**2. Find i, given that r(i) = 0.
-2, 0
Let g(b) = -b**2 + 6*b + 7. Let v be g(5). Suppose -v*p = -10*p. Determine c, given that p + 0*c + 2/11*c**5 + 2/11*c**2 + 6/11*c**3 + 6/11*c**4 = 0.
-1, 0
Let p be (-12)/(-10)*5/2. Suppose 0*g = 2*g + f - 1, -p*g - 4*f = 11. Find o such that o - 2*o**g + 4*o**4 + o**5 + 2*o**2 - 1 - 3*o**4 - 2*o**4 = 0.
-1, 1
Let w = -6 - -9. Let x**2 - 6*x + 4*x - w*x**2 + 4*x = 0. Calculate x.
0, 1
Let b be 11*((-82)/40 - -2). Let q = b + 4/5. Factor q*i**2 + 1/4 + 1/2*i.
(i + 1)**2/4
Determine b, given that -121/5 - 1/5*b**2 - 22/5*b = 0.
-11
Suppose -5*p - 20 = 5*k, 4*k + 9 + 1 = -p. Let i = p - -6. Solve 0 + 0*c - 2/3*c**i - 2/3*c**2 + 4/3*c**3 = 0.
0, 1
Factor 13*r**2 + 8 - 8*r**2 - 19*r - 21*r + 13*r**2.
2*(r - 2)*(9*r - 2)
Let q(g) be the third derivative of -g**7/525 + g**6/50 - 3*g**5/50 - 11*g**2. Factor q(y).
-2*y**2*(y - 3)**2/5
Factor -2*l - l + l + 2*l**2 - 4.
2*(l - 2)*(l + 1)
Factor -2/17*o**3 + 0*o + 0 + 0*o**2 + 2/17*o**4.
2*o**3*(o - 1)/17
Let t = 69 - 206/3. Factor 1/3 + 0*l - t*l**2.
-(l - 1)*(l + 1)/3
Let a be ((-2)/18)/(5/(-10)). Solve 2/9 - a*b**2 - 2/9*b**3 + 2/9*b = 0 for b.
-1, 1
Let n(k) be the second derivative of 0 + 1/42*k**3 + 1/42*k**4 - 7*k - 1/7*k**2 - 1/140*k**5. Factor n(j).
-(j - 2)*(j - 1)*(j + 1)/7
Let f(x) be the first derivative of -x**8/5880 + x**7/1470 - x**6/1260 + x**3/3 + 1. Let r(d) be the third derivative of f(d). Solve r(j) = 0 for j.
0, 1
Let c be (572/(-91))/(4/(-14)). Suppose 0 = h + 2*j + 4, 5*h - j = 3*j + c. Factor 1/2*n**h - 3/2*n + 0.
n*(n - 3)/2
Let p(g) = 21*g**3 - 42*g**2 + 6*g - 15. Let n(z) = 3*z**3 - 6*z**2 + z - 2. Let j(o) = -2*o - 6. Let u be j(-4). Let i(x) = u*p(x) - 15*n(x). Factor i(w).
-3*w*(w - 1)**2
Let p be (-2)/(-10) + (-108)/15. Let t(v) = 2*v + 17. Let m be t(p). Determine w so that -6/5*w + 0*w**2 + 2/5*w**m + 4/5 = 0.
-2, 1
Let v = -9 + 9. Let k(g) be the second derivative of -1/60*g**5 + v - 5/18*g**3 + 1/9*g**4 + 2*g + 1/3*g**2. Find r such that k(r) = 0.
1, 2
Factor 5 + 25/2*x**2 + 35/2*x.
5*(x + 1)*(5*x + 2)/2
Let a(w) be the first derivative of 5/7*w**4 - 20/21*w**3 - 4/7*w - 10/7*w**2 + 24/35*w**5 + 2. Solve a(b) = 0.
-1, -1/2, -1/3, 1
Let x = -19 - -21. Let m(u) be the second derivative of -1/30*u**4 + 1/15*u**3 - 2*u + 0 + 0*u**x. Suppose m(n) = 0. What is n?
0, 1
Suppose 0 = -2*k + 4*y - 288, 3*k + 474 = y + 52. Let g be (4/10)/((-42)/k). Suppose 0 - 1/3*t - 2/3*t**4 + 2/3*t**2 + g*t**3 - t**5 = 0. What is t?
-1, 0, 1/3, 1
Let 2*i**2 + 4/3*i - 2/3*i**4 + 0 + 0*i**3 = 0. What is i?
-1, 0, 2
Let r(f) be the first derivative of f**3/27 + f**2/9 + f/9 - 8. Factor r(a).
(a + 1)**2/9
Let b = -54 - -32. Let d = -15 - b. Let q**2 + d*q**4 - 3*q**2 - q**4 + 4*q**3 = 0. What is q?
-1, 0, 1/3
Let h = -6 - -9. Factor 2 - 13*w**h - 5*w**4 + 0*w**2 + w + 2*w**2 - 5*w**2 - 6*w**2.
-(w + 1)**3*(5*w - 2)
Let y(f) be the first derivative of -2*f**5/5 + f**4 - 2*f**2 + 2*f + 6. Determine d so that y(d) = 0.
-1, 1
Suppose a - 4*z = 3, a + 2*z + z = 10. Determine q, given that -4*q + 2*q**3 - 2 + a*q + q**2 - 7*q**2 + 3*q = 0.
1
Let x be 8/(-44) + 35/11. Suppose x*j - 8 = -j. Determine w, given that 2/3*w**j - 2/3 + 2/3*w - 2/3*w**3 = 0.
-1, 1
Solve 0 + 3/4*t**4 + 3/4*t**5 - 3/4*t**3 + 0*t - 3/4*t**2 = 0 for t.
-1, 0, 1
Let q be (2/(-4)*6)/(-1). Let p be ((-12)/(-45))/(2/q). Factor -2/5*b - 4/5 + p*b**2.
2*(b - 2)*(b + 1)/5
Let b(o) be the first derivative of 2*o**5/25 + 3*o**4/5 + 6*o**3/5 - 1. Determine x, given that b(x) = 0.
-3, 0
Suppose -4*y - 2*w = -4*w - 22, y - 5*w = 28. Factor 0*n + 1/4*n**2 + 0 + 0*n**y - 1/4*n**4.
-n**2*(n - 1)*(n + 1)/4
Let l(f) be the first derivative of -2*f**6/15 - 2*f**5/25 + f**4/10 + 7. Suppose l(m) = 0. What is m?
-1, 0, 1/2
Factor -3*r**2 - 3 - 1 + 2*r**2 + 4*r.
-(r - 2)**2
Let -31*d**4 - 35*d**4 - 60*d**2 + 12*d + 99*d**3 - 46*d**5 + 61*d**5 = 0. What is d?
0, 2/5, 1, 2
Let q(r) be the first derivative of -r**7/210 + r**6/45 - 7*r**3/3 - 10. Let i(g) be the third derivative of q(g). Factor i(w).
-4*w**2*(w - 2)
Let m(o) = -o**2 + 6*o - 3. Let w be m(5). Let -q**3 - q**2 - 1 - 4*q + 0*q**3 + q - 2*q**w = 0. What is q?
-1
Let c(i) = -i**2 - i. Let v(n) = 4*n**2 + 5*n. Let j(k) = -32*k**2 - 41*k. Let d(m) = 6*j(m) + 51*v(m). Let g(t) = 9*c(t) + d(t). What is b in g(b) = 0?
0
Let d(v) be the second derivative of 1/90*v**6 - 3*v + 0 + 1/20*v**5 + 1/12*v**4 + 1/18*v**3 + 0*v**2. Factor d(g).
g*(g + 1)**3/3
Let k(s) be the second derivative of s**6/10 - 3*s**5/10 + s**4/4 + 6*s. Solve k(l) = 0.
0, 1
Suppose -3*j**2 + 7*j**2 + 3*j**4 - 9*j**3 - 4*j**2 + 12*j = 0. What is j?
-1, 0, 2
Let m(q) = q**2 - q. Let l be (-35)/(-14)*2*1. Let v(h) = 6*h**2 - 5*h. Let d(c) = l*m(c) - v(c). Factor d(r).
-r**2
Let p = -164/3 - -55. Suppose -p*y**4 - 1/6*y**5 + 0 + 1/6*y + 0*y**3 + 1/3*y**2 = 0. Calculate y.
-1, 0, 1
Factor 0 + 6/7*d**3 + 0*d + 0*d**4 + 4/7*d**2 - 2/7*d**5.
-2*d**2*(d - 2)*(d + 1)**2/7
Let i = -151/3 + 51. Determine w, given that 0 + 2/3*w - i*w**2 = 0.
0, 1
Let i be (11190/(-36))/((-6)/4). Let r = i - 207. Factor r*w**3 + 4/9 + 8/9*w**2 + 10/9*w.
2*(w + 1)**2*(w + 2)/9
Factor -24 + 8*b - 2/3*b**2.
-2*(b - 6)**2/3
Let n(x) = -x**5 + x**4 - x**3 - x**2 - x + 1. Let b(v) = -v**5 + v**4 + 8*v**3 - 4*v**2 - v + 1. Let y(c) = b(c) + 2*n(c). Factor y(i).
-3*(i - 1)**3*(i + 1)**2
Let z(a) be the second derivative of a**7/7140 - a**6/1020 - a**5/1020 + a**4/68 + 2*a**3/3 + 7*a. Let h(f) be the second derivative of z(f). Factor h(p).
2*(p - 3)*(p - 1)*(p + 1)/17
Let i(c) be the third derivative of 1/60*c**5 + 0*c + 5*c**2 - 1/24*c**4 - 1/6*c**3 + 1/120*c**6 + 0. Solve i(p) = 0.
-1, 1
Let m(v) = -v + 4. Let u be m(0). Suppose 3*g - 3*g**2 - 3*g**3 + g - 2*g + u*g = 0. Calculate g.
-2, 0, 1
Determine u so that 0 - 6/5*u**2 + 3*u**4 + 9/5*u**3 + 0*u = 0.
-1, 0, 2/5
Let f(t) be the third derivative of -t**8/42 - t**7/21 - t**6/60 - 10*t**2. Determine u so that f(u) = 0.
-1, -1/4, 0
Let u = 229681/180 + -1276. Let g(a) be the third derivative of -u*a**5 + 1/18*a**3 + 0*a + 0*a**4 - a**2 + 0. Let g(w) = 0. Calculate w.
-1, 1
Let l be (-7)/(-12) + (-3)/9. Let i be 19/28 - 6/14. Factor -l - i*s**2 - 1/2*s.
-(s + 1)**2/4
Let i(g) be the first derivative of 2*g**3/9 + g**2 - 5. Factor i(r).
2*r*(r + 3)/3
Factor 5*k**4 - 7*k**3 - 3*k**2 + 6*k + k**3 + 0*k - 2*k**4.
3*k*(k - 2)*(k - 1)*(k + 1)
Let -56 - 8 - 40*r - 5*r**2 + 29 - 45 = 0. What is r?
-4
Let k = -51 - -31. Let l be 1 + 1 - (k + 22). Suppose -10/9*d**5 - 14/3*d**3 - 4/9*d + 34/9*d**4 + 22/9*d**2 + l = 0. What is d?
0, 2/5, 1
Suppose -m = m - 24. Suppose h - m = 5*w + 16, -22 = -4*h + 2*w. Factor 2/3*t**2 - 10/3*t**4 + 0*t + 2/3*t**h + 2*t**5 + 0.
2*t**2*(t - 1)**2*(3*t + 1)/3
Let f be 12/3 - 0/2. Suppose 3*m - 3*v = -6, -3*m - 18 = -f*m - 3*v. Factor 2/3*u**2 + 0 + 0*u + 2/3*u**m.
2*u**2*(u + 1)/3
Suppose 6 = -0*g + 3*g. Let q be ((-16)/(-90))/(g/10). Factor 0*a**2 - q*a**3 + 2/3*a + 2/9.
-2*(a - 1)*(2*a + 1)**2/9
Solve 0*c**2 + 2*c**2 + 32 + 16*c + 6*c**2 - 6*c**2 = 0 for c.
-4
Suppose -2*f = -f. Let b(z) be the second derivative of 3*z + f*z**2 - 3/80*z**5 + 0*z**3 + 1/56*z**7 + 0*z**6 + 0*z**4 + 0. Factor b(y).
3*y**3*(y - 1)*(y + 1)/4
Let s(c) be the second derivative of -c**6/10 - 3*c**5/20 + c**4/4 + c**3/2 - 13*c. Suppose s(y) = 0. What is y?
-1, 0, 1
Let z(y) be the first derivative of 7*y**4/2 - 74*y**3/3 + 38*y**2 - 16*y - 3. Factor z(d).
2*(d - 4)*(d - 1)*(7*d - 2)
Let h(o) be the second derivative of -5*o**7/42 - o**6/3 + 5*o**4/6 + 5*o**3/6 - 3*o. Find z such that h(z) = 0.
-1, 0, 1
Let n = -5 + 8. Factor 48*j**5 + 6*j**3 + n*j**2 + j**2 + j + 4*j**4 - 47*j**5.
j*(j + 1)**4
Let t(r) = 2*r**4 + 8*r**3 + 4*r**2 - 4*r. Let 