 4*p**2 + 6*p + 4. Let x(i) = 5*l(i) - 2*q(i). Factor x(n).
2*(n + 1)**3
Let t(g) be the first derivative of -6*g + 3/2*g**4 - 1 + 21/2*g**2 - 7*g**3. Factor t(c).
3*(c - 2)*(c - 1)*(2*c - 1)
Suppose 0 = 3*r - 13 + 1. Suppose 0 = -2*k + 7*f - 4*f + 5, -r*k + f = -15. Find t, given that -t**2 + 1/3*t + 0 - 1/3*t**k + t**3 = 0.
0, 1
Let l(k) = -3*k**3 + 3*k**2 + k. Let u be l(-3). Let i be (-28)/u*6/(-4). Find t, given that i*t**2 + 2/5*t**3 - 2/5 - 2/5*t = 0.
-1, 1
Suppose 3*y - 10 + 1 = 0, 29 = 5*c + 3*y. Let r be (-4)/14 + (-46)/(-14). Factor 2*q**r - q**2 - 1 - 4*q**2 + c*q + 0*q**3.
(q - 1)**2*(2*q - 1)
Let d be (1 - (-4)/(-3))/((-8)/6). Let c(n) be the first derivative of 1/4*n**3 - 3/8*n**2 + d*n - 2 - 1/16*n**4. Solve c(o) = 0.
1
Let o(u) = u**2 - u - 1. Let p = -4 + 6. Suppose p*q + 0 + 8 = 0. Let k(t) = 6*t**2 - 4*t - 4. Let g(i) = q*o(i) + k(i). Factor g(w).
2*w**2
Let 8/7*d + 2/7*d**2 + 0 = 0. What is d?
-4, 0
Suppose 5/4*r**2 + 0*r - 5 = 0. Calculate r.
-2, 2
Let y(v) = v - 6. Let a be y(8). Suppose 0 = -0*n + a*n - 4. Factor 66*i**2 - 24*i**3 - 20*i**n + 6 - 26*i - 2.
-2*(i - 1)*(3*i - 2)*(4*i - 1)
Let z(j) be the third derivative of j**5/20 - 5*j**4/8 + 2*j**3 - 9*j**2. Factor z(o).
3*(o - 4)*(o - 1)
Let f be (-30)/(-4)*(-4)/(-5). Suppose 3*a - f = -0*a. Suppose -3*c - 12*c**2 + 10*c**a + 3*c = 0. What is c?
0
Let l(w) be the second derivative of -1/15*w**3 + 0 + 1/15*w**4 - 1/50*w**5 - 3*w + 0*w**2. What is j in l(j) = 0?
0, 1
Let s be (-1)/3 - 641/(-1905). Let q = s + 5066/4445. Find v such that q*v**3 + 0 + 2/7*v**2 + 0*v - 2/7*v**4 - 8/7*v**5 = 0.
-1, -1/4, 0, 1
Let b(g) be the second derivative of 2*g**6/15 + 2*g**5/5 - g**4/3 - 4*g**3/3 + 4*g. Factor b(i).
4*i*(i - 1)*(i + 1)*(i + 2)
Let r = 500 + -1499/3. Factor -1/6*j**2 - 1/6 + r*j.
-(j - 1)**2/6
Let b = -6 - -9. Let 2*w + 2/3*w**b - 2/3 - 2*w**2 = 0. Calculate w.
1
Let n be (3 + -1)/(1 + 0). Factor 4*c**n - 5*c**2 - 2 + 4 + 3*c - 4.
-(c - 2)*(c - 1)
Let w(y) = y**2 - 1. Let s(d) = -d**2 - 7*d + 3. Let r = -4 + 3. Let l(c) = r*s(c) - 5*w(c). Find q such that l(q) = 0.
-1/4, 2
Let u(n) = -2*n + 5 + 7*n**2 - 2*n**2 - 4*n - 4*n. Let a(z) = 9*z**2 - 19*z + 11. Let m(d) = 4*a(d) - 7*u(d). Factor m(k).
(k - 3)**2
Let b(p) be the third derivative of 1/54*p**4 + 2*p**2 + 0*p + 0 + 1/270*p**5 - 1/540*p**6 + 0*p**3. Factor b(k).
-2*k*(k - 2)*(k + 1)/9
Let w = 140 - 140. Factor -1/4*g**2 + 0*g + 1/4*g**4 + 1/4*g**3 - 1/4*g**5 + w.
-g**2*(g - 1)**2*(g + 1)/4
Let u(b) be the third derivative of 0*b + 0*b**4 + 2*b**2 - 1/240*b**5 + 1/480*b**6 + 0*b**3 + 0. Factor u(d).
d**2*(d - 1)/4
Suppose -t = -4*t. Suppose 0 = -t*n - 4*n + 12. Factor -3/2*k**2 - 1/2*k**n - k + 0.
-k*(k + 1)*(k + 2)/2
Let x(b) = b**3 + 14*b**2 + 13*b + 3. Let u be x(-13). Factor 6*o**2 - 4*o + 75*o**3 - 78*o**u + o.
-3*o*(o - 1)**2
Let s(j) be the second derivative of -j**4/12 - j**3 - 3*j**2/2 - 2*j. Let a be s(-5). Determine d so that 0*d**a + 0 - 1/4*d**3 + 0*d = 0.
0
Suppose 9*w + 16 = 6*w + 5*s, -5*w = -s - 10. Solve 0*a**2 - 1/3 + 2/3*a**w - 2/3*a + 1/3*a**4 = 0.
-1, 1
Let k(t) be the second derivative of -5*t**4/3 - 14*t**3/3 - 4*t**2 - 7*t. Factor k(z).
-4*(z + 1)*(5*z + 2)
Let v(r) be the first derivative of -6/5*r**5 - 2/3*r**3 - 4 + 1/3*r**6 + 3/2*r**4 + 0*r**2 + 0*r. Factor v(g).
2*g**2*(g - 1)**3
Let f = -64 + 194/3. Determine p, given that -f*p**3 + 0 + 0*p + 2/3*p**2 = 0.
0, 1
Suppose -f = f + 5*j + 17, 3*f - 4*j = 9. Let s be (f - (-5)/2) + -1. Determine k so that s*k**4 - 1/2*k**2 + 1/2*k - 1/2*k**3 + 0 = 0.
-1, 0, 1
Let u = 12 + -3. Let 3*b**5 + 12*b**2 + 4*b**3 - 4*b**3 - u*b**4 = 0. What is b?
-1, 0, 2
Factor 4 + 472*l**2 + 88*l + 32*l + 428*l**2.
4*(15*l + 1)**2
Let u(f) be the third derivative of 0 + 1/12*f**4 + f**2 - 1/6*f**3 + 0*f - 1/30*f**5 + 1/180*f**6. Let h(k) be the first derivative of u(k). Factor h(w).
2*(w - 1)**2
Suppose 8 = -2*z, 4*o + 3*z = 3*o - 13. Let f be (3/o)/((-21)/28). Factor -2/11*j**f + 0 + 2/11*j**2 - 2/11*j**3 + 2/11*j.
-2*j*(j - 1)*(j + 1)**2/11
Let k be ((-1 - -1)/2)/(-29 + 26). Suppose -1/5*q + 2/5*q**4 + k + 0*q**3 - 2/5*q**2 + 1/5*q**5 = 0. What is q?
-1, 0, 1
Suppose -t - 3*n - 20 = 2, 4*n + 16 = 0. Let x be -4*(-2)/t - -1. Let -x*a**3 + 0 + 1/5*a**2 + 1/5*a - 1/5*a**4 = 0. What is a?
-1, 0, 1
Let q = -2479/3 + 829. Suppose -q*u - 2 - 2/3*u**2 = 0. What is u?
-3, -1
Suppose -15 = 3*o, -2*c = -2*o - 11 + 1. Factor 8/11*m**2 + 2/11*m**5 + 10/11*m**4 + 0*m + c + 16/11*m**3.
2*m**2*(m + 1)*(m + 2)**2/11
Let c(a) be the first derivative of a**4/12 + a**3/3 + a**2/2 - a - 2. Let d(q) be the first derivative of c(q). Factor d(p).
(p + 1)**2
Let q(h) be the first derivative of -14*h**5/5 - 8*h**4 - 22*h**3/3 - 2*h**2 - 13. Let q(c) = 0. Calculate c.
-1, -2/7, 0
Suppose -3*a + 7 = 4*a. Let m = 6 - 4. Suppose -p - 1/4*p**m - a = 0. What is p?
-2
Suppose -4 = 3*a - 7*a. Suppose -3*r + a = 5*i + 3, -4*i - 5*r - 12 = 0. Factor i*y**2 + 2*y**4 - 3*y**4 + y**3 + 0*y**3.
-y**2*(y - 2)*(y + 1)
Factor 3/2*r**3 + 3*r + 0 + 9/2*r**2.
3*r*(r + 1)*(r + 2)/2
Let g = 87 - 85. Factor 1/2*i + 1/4 + 1/4*i**g.
(i + 1)**2/4
Suppose -a = -4*a + 3. Let n = 1 + a. Factor 2*h + n*h - h**3 - 2*h**3 + 3*h**2 - 5*h + h**4.
h*(h - 1)**3
Let t(m) be the first derivative of -4*m**3/3 + 4*m**2 - 4*m - 6. Determine p, given that t(p) = 0.
1
Let l(r) be the second derivative of -r**6/72 - r**5/15 + r**4/6 + r**3/2 - 4*r. Let q(z) be the second derivative of l(z). Factor q(c).
-(c + 2)*(5*c - 2)
Let t be (2/3)/(14/147). Let c = -4 + t. Factor -4*b**3 + 0 - 2 + 0*b**c - 2*b**4 + 4 + 4*b.
-2*(b - 1)*(b + 1)**3
Let k be 10/(-25) - (-134)/35. Find f, given that k*f + 18/7*f**4 - 8/7 - 10/7*f**2 - 24/7*f**3 = 0.
-1, 2/3, 1
Let d(s) = 3*s + 12. Let x(y) = y + 1. Let m(u) = d(u) - 4*x(u). Let g be m(6). Solve -1/3*n - 1/3*n**g + 0 = 0 for n.
-1, 0
Let k = 288 + -285. Factor 1/2*x**2 + 0 + 1/4*x**k + 1/4*x.
x*(x + 1)**2/4
Let t = 1 - -7. Let d be (t/(-14))/(4/(-14)). Suppose h**2 + 16 + 8*h**2 + d*h**3 + 24*h + 3*h**2 = 0. Calculate h.
-2
Let r be (6/5)/((-4)/(-10)). Determine k so that -k**2 + r*k**2 - 4*k**2 = 0.
0
Let a(z) be the first derivative of 4*z**5/5 + z**4 - 4*z**3/3 - 2*z**2 + 2. Factor a(g).
4*g*(g - 1)*(g + 1)**2
Factor -6*o**2 - o - 3*o**3 + 4*o**3 + 6*o**2.
o*(o - 1)*(o + 1)
Let v(d) be the first derivative of -d**6/27 - 2*d**5/15 - d**4/6 - 2*d**3/27 + 16. Determine i, given that v(i) = 0.
-1, 0
Let x = -13164475/33 - -398954. Let c = x + -91/3. Find d, given that -4/11*d**2 + 0 - 2/11*d - c*d**3 = 0.
-1, 0
Let p(h) = -8*h**4 - 36*h**3 - 40*h**2 - 12*h - 4. Let m(a) = -a**5 - 9*a**4 - 36*a**3 - 39*a**2 - 11*a - 5. Let y(k) = 4*m(k) - 5*p(k). Factor y(r).
-4*r*(r - 4)*(r + 1)**3
Let n = -2 - -8. Let k = -1 + n. Determine i, given that 2*i + 0*i + 12*i**k - 30*i**5 - 16*i**3 + 4*i**2 - 36*i**4 = 0.
-1, -1/3, 0, 1/3
Let n = -55 - -119/2. Find i such that 0 + 11/2*i**2 + i + n*i**3 = 0.
-1, -2/9, 0
Factor 4*l - 3/2*l**2 + 1/6*l**3 - 8/3.
(l - 4)**2*(l - 1)/6
Let d be (128/56)/(30/14). Let q(o) be the second derivative of 27/25*o**6 + 0*o**2 + 9/10*o**5 + 3*o - d*o**4 + 4/15*o**3 + 0. Factor q(a).
2*a*(a + 1)*(9*a - 2)**2/5
Let g(t) be the third derivative of t**7/105 - t**6/20 + 2*t**2. Factor g(k).
2*k**3*(k - 3)
Let f(u) = 3 - 5 + 4*u - 7 - 3*u. Let d be f(9). Let 3*r + 0*r + d*r**3 - 2*r**3 - 5*r + 4*r**2 = 0. Calculate r.
0, 1
Let y(u) = -u**3 - u**2 - u + 2. Let r be y(0). Factor r*q - 4*q + 2*q**3 + 2*q.
2*q**3
Let s be (-29)/(-174) + 65/42. Determine g, given that 16/7*g**3 - s*g - 4/7*g**5 - 8/7*g**2 + 0*g**4 + 8/7 = 0.
-2, -1, 1
Let o = 6 + -4. Suppose 2*c + 2*t - 16 = -o*t, 0 = 3*c + 5*t - 20. What is w in 0*w + c - 1/3*w**2 = 0?
0
Let g(n) be the third derivative of -n**6/60 - n**5/10 - n**4/6 + 3*n**2. Determine h so that g(h) = 0.
-2, -1, 0
Let m(y) be the third derivative of -1/200*y**6 - 2/5*y**3 + 3/100*y**5 + 0*y + 0 + 0*y**4 - 7*y**2. Let m(p) = 0. What is p?
-1, 2
Let l be 1/((-28)/(-26) + -1). Let j be (15 - l)*(-4)/(-14). Factor -j*k**2 + 2/7*k**4 + 2/7 - 4/7*k**3 + 2/7*k**5 + 2/7*k.
2*(k - 1)**2*(k + 1)**3/7
Determine m so that -2/3*m**4 - 16/15*m**3 + 8/15*m**2 + 0 + 0*m = 0.
-2, 0, 2/5
Let 2/3*h + 2/3*h**4 - 2/3*h**2 - 2/3*h**3 + 0 = 0. Calculate h.
-1, 0, 1
Suppose 10 