)**2/4
Let v(l) = -6*l**2 - 20*l - 4. Let z(w) = 13*w**2 + 42*w + 9. Let y(t) = -9*v(t) - 4*z(t). Factor y(b).
2*b*(b + 6)
Let n = -12 + 18. Suppose 10 = 5*w, -4*w - 1 = -5*v + n. Factor 10*c**2 + c**v + 11*c**2 - 8*c + 7*c**2 + 15*c**3.
4*c*(c + 2)*(4*c - 1)
Let n(r) be the first derivative of -3*r**5/5 + 21*r**4/2 + 48*r**3 + 75*r**2 + 51*r - 205. Find q, given that n(q) = 0.
-1, 17
Suppose -i + 10 = i. Suppose g - 7 = -i. Factor 3*c + c**5 - c**2 - c**2 + 0*c**3 + g - 4*c**3.
(c - 2)*(c - 1)*(c + 1)**3
Let i(s) be the third derivative of -2/45*s**5 + 1/18*s**4 - 31*s**2 - 1/36*s**3 + 0 + 0*s. Find v, given that i(v) = 0.
1/4
Let k = 28 - 24. Factor 3*c - k*c**3 - 4 + c + 3*c**2 + 0*c**3 - c**4 + 2*c**3.
-(c - 1)**2*(c + 2)**2
Let i(b) be the second derivative of -b**6/120 + 41*b**2/2 - 45*b. Let g(t) be the first derivative of i(t). Suppose g(n) = 0. What is n?
0
Let a(g) = g**2 - g - 9. Let t be a(4). Let n be t/5*14/21. Factor -2/5 - n*q + 2/5*q**2 + 2/5*q**3.
2*(q - 1)*(q + 1)**2/5
Let v be 2/(-16)*-3 + 3344/9856. Let a(d) be the first derivative of 1 - 4/7*d - 8/21*d**3 + v*d**2 + 1/14*d**4. Factor a(y).
2*(y - 2)*(y - 1)**2/7
Let j(y) be the first derivative of -3/4*y**3 + 1/8*y**4 - 1/4*y**2 + 0*y + 30 + 9/20*y**5. Factor j(w).
w*(w - 1)*(w + 1)*(9*w + 2)/4
Suppose 79 = 4*z + 63. Let o(r) be the second derivative of -1/12*r**3 + 2*r + 0 - 1/72*r**z - 1/6*r**2. Determine h so that o(h) = 0.
-2, -1
Let u(m) = m**2 + 25*m + 84. Let a be u(-21). Let s(r) be the second derivative of 1/6*r**4 + a + 4/3*r**3 - 5*r + 4*r**2. Factor s(k).
2*(k + 2)**2
Let y = -31 - -33. Let 33*n**4 + 45*n**4 - 81*n**3 + 12*n**y + 12*n - 43*n**5 + 22*n**5 = 0. What is n?
-2/7, 0, 1, 2
Factor -2*a**2 - 1/2*a**3 + 0 - 2*a.
-a*(a + 2)**2/2
Let c(l) be the first derivative of -24/25*l**5 + 3/10*l**2 - 3/10*l**6 + 0*l - 9/10*l**4 + 12 + 0*l**3. Factor c(a).
-3*a*(a + 1)**3*(3*a - 1)/5
Let z(y) = -3*y**2 - 5*y. Let j be z(-1). Let n be (j/8)/((-31)/8 - -4). Suppose 2*o + 3/2*o**3 + 0 - 3*o**n - 1/4*o**4 = 0. Calculate o.
0, 2
Let r(y) = y**2 + 3*y. Let a be r(-5). Suppose a = 4*b + b. Find t, given that 2*t**3 + 0*t**5 + 16*t**b - t - 8*t + 6*t**4 - t**5 + 2 - 16*t**3 = 0.
1, 2
Factor 296*x + 0*x**2 + 50 - 665*x - 6 + 323*x + 2*x**2.
2*(x - 22)*(x - 1)
Let b(l) be the third derivative of -7*l**6/24 - 5*l**5/2 - 15*l**4/2 - 20*l**3/3 - 4*l**2 - 2. Factor b(h).
-5*(h + 2)**2*(7*h + 2)
Let a(y) be the first derivative of 36 - 19*y**2 + 1/2*y**4 - 20*y - 16/3*y**3. Suppose a(i) = 0. Calculate i.
-1, 10
Suppose -15*t - 18*t + 3*t**2 - 16 - 10 - 10 = 0. Calculate t.
-1, 12
Let d(f) be the first derivative of 2*f**3/9 - f**2/3 + 108. Factor d(c).
2*c*(c - 1)/3
Let z(p) be the third derivative of -p**6/150 + 2*p**5/75 + 11*p**4/120 + p**3/10 - 18*p**2 - 2. Factor z(j).
-(j - 3)*(2*j + 1)**2/5
Let l(z) = 2*z**4 - 2*z**3 - 29*z**2 - 18*z + 27. Let i(x) = -2*x**4 + 2*x**3 + 30*x**2 + 20*x - 26. Let j(r) = 5*i(r) + 6*l(r). Factor j(v).
2*(v - 4)*(v - 1)*(v + 2)**2
Let d(o) be the third derivative of 23/32*o**4 + 0*o - 3/4*o**3 + 0 - 1/20*o**6 - 19/80*o**5 + 1/70*o**7 + 30*o**2. Determine s, given that d(s) = 0.
-2, 1/2, 3
Let r(p) be the second derivative of 0*p**4 + 1/30*p**5 + 0 + 0*p**3 - 11*p - 7*p**2 + 1/120*p**6. Let s(u) be the first derivative of r(u). Factor s(o).
o**2*(o + 2)
Let m(a) = 3*a + 7. Let f be m(-5). Let t(u) = 6*u**2 - 28*u - 98. Let r(v) = v**2. Let l(g) = f*r(g) + t(g). Suppose l(d) = 0. What is d?
-7
Let c(x) be the first derivative of 0*x**5 + 5 + 0*x**4 + 5/3*x**3 - 1/210*x**7 + 0*x**6 + 0*x**2 + 0*x. Let m(t) be the third derivative of c(t). Factor m(h).
-4*h**3
Let t(q) = -14*q**2 - 4*q + 42. Let k(r) = -10*r**2 - 3*r + 28. Let i(l) = 8*k(l) - 5*t(l). Factor i(m).
-2*(m - 1)*(5*m + 7)
Factor 32*k + 56*k**2 - 484 - 4*k**5 + 508 + 43*k - 16*k**4 - 8*k + k.
-4*(k - 2)*(k + 1)**3*(k + 3)
Let z(l) = -l**2 + 38*l + 3. Let a be z(38). Let w(o) be the third derivative of 0*o**a + 1/8*o**4 + 0 + 1/40*o**6 + 0*o + 5*o**2 + 1/10*o**5. Factor w(b).
3*b*(b + 1)**2
Suppose -4*r + 3 = 5*h, 5*h + 2 = 5*r + 32. Factor -4/3*y**4 + 4/3*y**2 + 0*y**h - 2/3*y**5 + 2/3*y + 0.
-2*y*(y - 1)*(y + 1)**3/3
Let g(i) be the second derivative of i**5/20 - 11*i**4/12 - 25*i**3/6 - 13*i**2/2 - 9*i - 5. Solve g(u) = 0.
-1, 13
Suppose 0 = 5*n - 10*z + 6*z - 11, -4*n = -2*z - 4. Let w be (8 + 0)/((-11)/n). Factor -8/11*l - 2/11*l**4 - 12/11*l**2 - w*l**3 - 2/11.
-2*(l + 1)**4/11
Let r(y) be the second derivative of -y**4/3 + 40*y**3/3 + 88*y**2 - 806*y. Factor r(w).
-4*(w - 22)*(w + 2)
Let c(h) be the second derivative of -h**6/10 - 3*h**5/4 - 7*h**4/4 - 3*h**3/2 - 36*h + 1. Solve c(n) = 0 for n.
-3, -1, 0
Let 0 + 10/3*t + 5/3*t**3 + 5*t**2 = 0. Calculate t.
-2, -1, 0
Let j(a) be the second derivative of -a**5/20 + a**4 + 13*a**3/2 + 17*a**2/2 - 19*a. Let k(h) = -h**3 - h + 1. Let v(y) = j(y) + 3*k(y). Solve v(w) = 0 for w.
-1, 5
Let j(u) = -4*u - 30. Let b be j(-9). Let q be (-5)/(-105)*b + 0. Factor 2/7 - q*g**4 + 0*g**2 - 4/7*g + 4/7*g**3.
-2*(g - 1)**3*(g + 1)/7
Let g = -2013 + 2015. Let d(v) be the first derivative of 1/14*v**6 + 5 + 0*v + 2/35*v**5 - 3/28*v**4 + 0*v**g - 2/21*v**3. Find q, given that d(q) = 0.
-1, -2/3, 0, 1
Suppose -2*r + 11 - 1 = 0. Suppose 3*y - 42 = r*v, 0*v = y + 3*v. Factor 2*x**4 + 7*x**4 + y*x**3 - 6*x**4 + 9*x**2 + 3*x.
3*x*(x + 1)**3
Factor 4/3*q**3 + 64/3 - 28/3*q**2 - 40/3*q.
4*(q - 8)*(q - 1)*(q + 2)/3
Let t(w) = w**2 - w. Let f(c) = 20*c**2 + 15*c + 25. Let l(p) = -f(p) + 15*t(p). Suppose l(n) = 0. What is n?
-5, -1
Let y(t) be the second derivative of 8*t - 7/5*t**3 - 1/50*t**6 - 3/50*t**5 + 0 + 3/5*t**4 + 3/2*t**2. Factor y(z).
-3*(z - 1)**3*(z + 5)/5
Let z be 33/6 - 9/6. Suppose z*w - 25 = -1. Suppose -4*l**5 + 6*l**3 + 11*l**5 - 5*l**5 + w*l**4 + 2*l**2 = 0. What is l?
-1, 0
Let q(z) = z**3 + 11*z + 11. Let h(l) = -2*l - 2. Let s(c) = 8*c - 9. Let x be s(6). Suppose -5*u - x - 16 = 0. Let n(m) = u*h(m) - 2*q(m). Factor n(k).
-2*k**3
Let o(q) be the second derivative of 0 + 0*q**4 - 3/40*q**5 + 1/60*q**6 - 3*q + 1/3*q**3 + 0*q**2. Factor o(f).
f*(f - 2)**2*(f + 1)/2
Let y be 1 - 4/5 - (-19)/5. Suppose -3*g - g + 20 = 0. What is i in i**3 + 3*i**g + 6*i**3 + 9*i**y - i**3 = 0?
-2, -1, 0
Suppose 40 - 4 = 6*k. Find j such that k*j**2 + 0*j**4 - 20*j**4 + 4*j**2 - 5*j**2 = 0.
-1/2, 0, 1/2
Let s(r) be the first derivative of -3*r**2 + 24*r - 6. Let z be s(4). Let 0*g - 2/11*g**5 + 0 - 4/11*g**4 + z*g**2 - 2/11*g**3 = 0. What is g?
-1, 0
Let f = -87 - -169. Factor -392 - 7*k**2 + 6*k**2 - 26*k - k**2 + f*k.
-2*(k - 14)**2
Let i(j) = j**3 + 25*j**2 - 27*j - 2. Let h be i(-26). Determine u, given that 12*u**3 + h*u - 20*u**4 + 88*u**2 + 6*u**4 + 4*u**3 - 6*u**3 = 0.
-2, -2/7, 0, 3
Let p = -1283 - -1285. What is r in 1/2*r**p - r + 1/2 = 0?
1
Let y(l) be the first derivative of l**4 - 32*l**3/3 + 26*l**2 - 24*l + 124. Find s such that y(s) = 0.
1, 6
Let s(z) be the second derivative of 8*z - 10*z**5 - 15*z**4 + 6*z**5 - 8*z**2 - z**5 - 16*z**3 + 30*z. Factor s(n).
-4*(n + 1)*(5*n + 2)**2
Let t(w) be the first derivative of -w**7/280 - 7*w**6/240 - w**5/40 + 3*w**4/16 - 4*w**3 + 13. Let b(j) be the third derivative of t(j). Factor b(m).
-3*(m + 1)*(m + 3)*(2*m - 1)/2
Let r(j) be the first derivative of 10*j**5/7 + 435*j**4/28 + 251*j**3/7 - 412*j**2/7 + 180*j/7 + 614. Suppose r(n) = 0. Calculate n.
-5, -9/2, 2/5
Let s(z) be the third derivative of -z**8/35280 - z**7/4410 - z**6/1260 + z**5/6 + 36*z**2. Let q(b) be the third derivative of s(b). Factor q(i).
-4*(i + 1)**2/7
Let o(d) be the first derivative of 0*d - 2/75*d**5 - 1/10*d**4 - 4/45*d**3 - 5 + 0*d**2. Suppose o(t) = 0. What is t?
-2, -1, 0
Let a = 19 - 17. Suppose -a*l = -l + l. Factor -2/5*o**4 + 0 + 6/5*o**3 - 4/5*o**2 + l*o.
-2*o**2*(o - 2)*(o - 1)/5
Factor 44/9*n + 2/9*n**2 - 32/3.
2*(n - 2)*(n + 24)/9
Solve -60*x**3 + 375 - 41*x + 65*x**3 - 35*x**2 + 16*x = 0.
-3, 5
Suppose 0 = 4*r - 4*a - 164, -2*r + 159 = 2*r - 3*a. Let s = 39 - r. Solve 0 - 2/3*u**2 + 7/3*u**s + 0*u = 0 for u.
0, 2/7
Let x(s) be the first derivative of s**4/60 - s**3/30 - s**2/5 - 3*s - 7. Let d(b) be the first derivative of x(b). Factor d(v).
(v - 2)*(v + 1)/5
Let t(z) = -2*z**4 - 2*z**3 + 2*z**2 + 2. Let n(v) = 6*v