*2 - 11*x + 6. Suppose 0 = 2*f - 3*f. Suppose f = -2*m + 12 + 4. Let v(d) = 2*d**2 + 32*d - 18. Let s(r) = m*g(r) + 3*v(r). Factor s(j).
-2*(j - 3)*(j - 1)
Let u = -75 + 65. Let i be ((-4)/u*-1)/(-3). Factor -i*c**2 + 2/15 + 0*c.
-2*(c - 1)*(c + 1)/15
Suppose -2*y - 32*y**3 + 113*y**4 - 83*y**4 + 6 + 6*y - 36*y**2 + 28*y**5 = 0. Calculate y.
-1, -1/2, 3/7, 1
Let c(z) be the third derivative of z**5/330 - 5*z**4/33 + 19*z**3/33 + 100*z**2. Factor c(j).
2*(j - 19)*(j - 1)/11
Let y(l) = -32*l**3 + l**2 + 11*l. Let q(s) = 6*s**3 - 2*s. Let u(d) = -22*q(d) - 4*y(d). What is i in u(i) = 0?
-1, 0
Suppose -5*p - 20 = 5*z, -2*p = -3*z - 3*p - 4. Suppose 3 + z = -3*j, 22 = 5*u - 2*j. Factor -f**3 - f**3 + 0*f**5 - 2*f**5 - u*f**4.
-2*f**3*(f + 1)**2
Let n = -18/61 - -97/122. What is g in g**2 - 1/2*g**4 - n - 1/2*g - 1/2*g**5 + g**3 = 0?
-1, 1
Let z(v) be the second derivative of -1/6*v**4 - 2/3*v**3 - v**2 + 0 - v. Factor z(j).
-2*(j + 1)**2
Let k(z) = -z**2 - 17*z + 25. Let m be k(-17). Factor -m - 34*c + 69*c - 6*c**2 + c**3 - 5*c**2.
(c - 5)**2*(c - 1)
Let x(d) = 4*d + 2. Let h be x(-2). Let y be 2 - ((0 - -4) + h). Let 0*p**2 - 2 - 15*p**y + 4*p**2 - p**3 - p**2 + p + 14*p**4 = 0. What is p?
-2, -1, 1
Factor y**2 - 2*y**3 - 1/4*y**5 + 5/4*y**4 + 0*y + 0.
-y**2*(y - 2)**2*(y - 1)/4
Let t(j) be the first derivative of 5*j**4/4 + 85*j**3/3 - 39. Factor t(n).
5*n**2*(n + 17)
Suppose 6*v + 54 = 7*v. Let g be 27/v*4*2/10. Find d such that -2/5 + 2/5*d**3 + g*d**2 - 2/5*d = 0.
-1, 1
Let c(x) = 4*x**3 - x + 1. Let j = 3 + -2. Let i be c(j). Factor 2*f**2 + f**2 + f**5 - 2*f**i - f**2 - f.
f*(f - 1)**3*(f + 1)
Let u(f) be the second derivative of 0*f**2 + 1/6*f**4 + 2/3*f**3 - 15*f - 1/10*f**5 + 0. Factor u(i).
-2*i*(i - 2)*(i + 1)
Let t(u) be the second derivative of -8*u**7/105 + 22*u**6/75 - 9*u**5/25 + u**4/15 + 2*u**3/15 + 505*u. Solve t(r) = 0.
-1/4, 0, 1
Let g(s) be the first derivative of -s**4/2 - 218*s**3 - 35643*s**2 - 2590058*s + 239. Suppose g(b) = 0. What is b?
-109
Factor 14/3 + 2*o**3 - 19/3*o**2 - 11/3*o.
(o + 1)*(2*o - 7)*(3*o - 2)/3
Let m be -8 - (41624/7986)/((-4)/54). Factor -250/11*h**3 + m - 1470/11*h + 1050/11*h**2.
-2*(5*h - 7)**3/11
Let k be (-8)/26*(-39)/6. Factor 4/13*x + 2/13*x**k + 2/13.
2*(x + 1)**2/13
Let o(r) = -2*r + 6. Let w be o(2). Factor s**3 - 237*s**w - 5*s + 5*s + 238*s**2.
s**2*(s + 1)
Let v be (-2)/(-5) - (-312)/120. Suppose -x + 5 = v. Let -4*w**2 + w**3 - 5*w + 3*w**x + 0*w**2 - 3 = 0. What is w?
-1, 3
Determine l so that -24*l**4 + 31 + 19*l**4 - 64*l + 9 + 14*l - 5*l**5 + 55*l**3 - 35*l**2 = 0.
-4, -1, 1, 2
Let j(h) = h**3 - 2*h**2 - 2*h - 1. Let t be j(3). Factor -3*d + 3*d**2 - 9*d + 3*d - t*d**2.
d*(d - 9)
Suppose -5*l = 86 - 96. Solve 3*i**l - 4*i + 4*i - 2*i - i**4 = 0.
-2, 0, 1
Let h(n) be the first derivative of -1/3*n**3 + 21 + 2/5*n + 9/10*n**2. Let h(y) = 0. Calculate y.
-1/5, 2
Let l(q) be the second derivative of -q**4/90 - 22*q**3/45 - 32*q**2/5 + 6*q + 59. Factor l(g).
-2*(g + 6)*(g + 16)/15
Let s(z) be the third derivative of -z**7/420 - z**6/18 - 3*z**5/20 + 5*z**3 - 28*z**2. Let h(k) be the first derivative of s(k). Let h(m) = 0. What is m?
-9, -1, 0
Let w = 131 - 30. Let v = w + -499/5. Factor -v*o + 8/5*o**2 - 2/5.
2*(o - 1)*(4*o + 1)/5
Let m(q) = -q**2 - 5*q. Let s be m(-4). Let 0*o + s*o + 0*o + 0*o**3 - 8*o**3 + 4*o**5 = 0. Calculate o.
-1, 0, 1
Let i be (-27)/12*(-4)/6. Let d = 6373/2 - 3185. Let -3/2*a**2 + i - 3/2*a + d*a**3 = 0. What is a?
-1, 1
Factor 2/9 - 2/9*k**4 + 0*k**2 - 4/9*k + 4/9*k**3.
-2*(k - 1)**3*(k + 1)/9
Let t(v) be the first derivative of -3*v**4/4 - 41*v**3 - 660*v**2 - 1200*v + 178. Suppose t(i) = 0. What is i?
-20, -1
Let z be ((-128)/(-12))/((-4)/(-12)). Let b be ((-36)/z)/(15/(-20)). Determine y so that -b*y**2 + 0 - 6*y**3 + 0*y = 0.
-1/4, 0
Let f(w) be the third derivative of -w**6/40 + 27*w**5/10 - 195*w**4/2 + 676*w**3 - 2*w**2 - 13*w. Suppose f(b) = 0. Calculate b.
2, 26
Suppose -4*t = 34*r - 39*r + 9, 5*t + 2*r - 30 = 0. Suppose 0*q**2 - 2/5*q**3 + 1/5 + 2/5*q - 1/5*q**t = 0. What is q?
-1, 1
Factor -12*n + 96*n - 5 - 3*n**3 - 9*n**2 + 132*n - 523.
-3*(n - 4)**2*(n + 11)
Let n = -68 - -284. Suppose -h**2 + h**4 - 3*h**3 - 216*h + 3*h**2 + n*h = 0. What is h?
0, 1, 2
Suppose 2*i + 5*y = 19, 10 = i - 6*i - y. Let x(j) = 5*j**2 + 1. Let q(v) = -6*v**2 - 2. Let f(h) = i*q(h) - 4*x(h). Factor f(c).
-2*(c - 1)*(c + 1)
Let t(k) = 2*k**3 + 24*k**2 - 2*k. Let v(d) = -d**2 - 1. Suppose z + 3*m = 0, m + 1 = 5. Let n(a) = z*v(a) - t(a). Factor n(c).
-2*(c - 1)*(c + 1)*(c + 6)
Let n(m) = m**2 - m. Let r be 9 + -2*(1 + 1). Let a(u) = -3*u**3 - 8*u**2 + 8*u + 3. Let g(k) = r*n(k) + a(k). Factor g(b).
-3*(b - 1)*(b + 1)**2
Factor 0*r - 9/2*r**2 + 0 + 3/2*r**3 + 1/2*r**5 + 5/2*r**4.
r**2*(r - 1)*(r + 3)**2/2
Let v = -1713 - -1717. Factor 0 - 2/3*l**2 + 0*l**3 + 0*l + 2/3*l**v.
2*l**2*(l - 1)*(l + 1)/3
Let n(z) be the third derivative of -z**6/600 - 47*z**5/300 + 2*z**4/5 - 183*z**2 + z. What is d in n(d) = 0?
-48, 0, 1
Let s = 24158/10563 + -2/1509. Let i = 3877/1085 + -111/155. Factor i*f**2 - s + 32/7*f.
4*(f + 2)*(5*f - 2)/7
Let z(m) = -m**2 - 5*m. Let a be z(-4). Suppose 4 = -a*p - 5*r, 2*r - 8 = 4*r. Let -4*v**3 + 3*v**3 + 2*v**3 - p + 10*v + v**3 - 8*v**2 = 0. Calculate v.
1, 2
Let g be -1*((-44)/20 + (-12)/(-60)). Let d be (-329)/(-98) + (-10)/4. Factor d*k + 0 - 2/7*k**g.
-2*k*(k - 3)/7
Let o be (8/20)/(4/200). Solve -3*j**2 - 33*j - 432 - o*j - 19*j = 0.
-12
Solve 17/6*n**2 + 5/3 + 13/6*n**3 - 1/2*n**4 - 37/6*n = 0 for n.
-2, 1/3, 1, 5
Let i(o) be the first derivative of -o**3/6 - 73*o**2/2 - 5329*o/2 + 178. Factor i(l).
-(l + 73)**2/2
Let k(v) be the third derivative of -v**7/1470 - 31*v**6/420 - 757*v**5/420 + 527*v**4/14 - 1734*v**3/7 + 546*v**2. Solve k(o) = 0 for o.
-34, 3
Let r(m) be the first derivative of -2*m**6/3 - 64*m**5/5 - 88*m**4 - 256*m**3 - 288*m**2 + 304. Suppose r(g) = 0. Calculate g.
-6, -2, 0
Let j(r) be the second derivative of -r**6/210 - r**5/35 - r**4/14 - 2*r**3/21 - r**2/14 + 79*r. Suppose j(q) = 0. Calculate q.
-1
Suppose 3*c - 21 + 51 = -3*z, 16 = -2*c - 4*z. Let k(m) = 2*m**2 + 8*m + 2. Let p(w) = -1. Let v(b) = c*p(b) + 2*k(b). Determine n so that v(n) = 0.
-2
Let r(i) = 8*i**2 + 8*i - 22. Suppose -4*c + v = -27, 4*c + 3*v = 5 + 10. Let a(q) = q**2 + q - 3. Let g(u) = c*r(u) - 44*a(u). Find j such that g(j) = 0.
-1, 0
Let l be -1*((-4 - -6 - 2) + (-2)/1). Factor 4/5*h**3 - 3/5*h - 2/5 + 0*h**4 + 2/5*h**l - 1/5*h**5.
-(h - 2)*(h - 1)*(h + 1)**3/5
Factor -4/9*v**4 + 0*v**3 + 0 + 8/9*v + 4/3*v**2.
-4*v*(v - 2)*(v + 1)**2/9
Let o(s) be the first derivative of -1/12*s**4 + 15 + 2/3*s**3 - 11/6*s**2 + 2*s. Factor o(t).
-(t - 3)*(t - 2)*(t - 1)/3
Let m(r) be the first derivative of 9 + 8/3*r**3 + 0*r - 2*r**2 - r**4. Factor m(p).
-4*p*(p - 1)**2
Factor 27*m + 12 + 21/2*m**2.
3*(m + 2)*(7*m + 4)/2
Let d(p) be the second derivative of -p**7/21 + 14*p**6/45 - 11*p**5/15 + 2*p**4/3 + p**3/9 - 2*p**2/3 + 7*p - 21. What is c in d(c) = 0?
-1/3, 1, 2
Let b(n) = -n**3 - 7*n**2 + 8*n + 16. Let h(m) = -4*m**3 - 20*m**2 + 25*m + 48. Let q(a) = -7*b(a) + 2*h(a). Factor q(o).
-(o - 8)*(o - 2)*(o + 1)
Find q such that -14 - 42*q**3 + 24*q**2 + 6*q**4 + 21*q**5 - 1 + 18*q**5 - 36*q**5 - 15 + 39*q = 0.
-5, -1, 1, 2
Let w(u) = 31*u**4 + 340*u**3 + 223*u**2 - 94*u. Let k(s) = -s**4 + 2*s**2 - s. Let c(x) = -4*k(x) + w(x). Factor c(f).
5*f*(f + 1)*(f + 9)*(7*f - 2)
Let z = 311 - 307. Let f be z/(-10) - 221/(-65). Factor -2/7*g**f - 2/7*g + 4/7*g**2 + 0.
-2*g*(g - 1)**2/7
Let y be 2 + 2 - (-5 + 1880/15). Let h = -113 - y. Suppose 12*u**5 + 4/3*u**2 - 22/3*u**3 + 0*u + 0 + h*u**4 = 0. Calculate u.
-1, 0, 2/9, 1/2
Let s(r) be the third derivative of -r**6/180 + 29*r**5/45 + 59*r**4/36 - 24*r**2. Find x, given that s(x) = 0.
-1, 0, 59
Let w(y) be the second derivative of -y**8/672 + y**7/140 - y**6/80 + y**5/120 + 3*y**2 + 4*y. Let c(u) be the first derivative of w(u). Factor c(j).
-j**2*(j - 1)**3/2
Let s(f) be the first derivative of 4*f**5/15 - 10*f**4/3 + 32*f**3/3 + 64*f**2/3 - 512*f/3 + 241. Factor s(v).
4*(v - 4)**3*(v + 2)/3
Let k(b) be the third derivative of -b**7/2520 + b**6/810 - b**5/1080 + 11*b**3/6 + 8*b**2. Let q(z) be the first derivative of k(z