et d(s) = -s**2 + 6*s - 3. Let k be d(5). Factor -4*n**3 - 2*n**2 - 3*n**4 - n**k + 10*n**3.
-3*n**2*(n - 1)**2
Suppose 0 = -3*y + 5 + 10. Let w be y/2 - (-3)/(-6). Solve 0 - 9*g**w - 3*g - 2 - 4*g - 5*g**3 - g**4 = 0.
-2, -1
Factor -4/7*t - 2/7*t**2 - 2/7.
-2*(t + 1)**2/7
Let a(l) be the first derivative of -3/2*l**2 - 6*l + 3/4*l**4 - 5 + 2*l**3. Factor a(y).
3*(y - 1)*(y + 1)*(y + 2)
Let h be 5 - (-1 + 56/10). Solve 0 - h*l**3 + 4/5*l - 2/5*l**2 = 0.
-2, 0, 1
Let x(t) be the first derivative of 2 - 1/15*t**6 + 4/25*t**5 + 0*t**3 - 1/10*t**4 + 0*t**2 + 0*t. Determine p so that x(p) = 0.
0, 1
Let w = 88 + -86. Let v(m) be the second derivative of 1/66*m**4 - 1/33*m**3 + 0 - 2/11*m**w - 2*m. Determine f, given that v(f) = 0.
-1, 2
Factor -2*q**4 - 48*q - 65*q**2 - 119*q**2 + 140*q**2 - 18 - 16*q**3.
-2*(q + 1)**2*(q + 3)**2
Let l be -3 - (1 + -3 + -1). Determine w, given that l*w**2 + 0*w + 1/3*w**4 + 1/3*w**5 + 0 + 0*w**3 = 0.
-1, 0
Let f be 0*(8 - 5)/(-3)*-1. Determine q, given that q**2 + 2/3*q + 1/3*q**3 + f = 0.
-2, -1, 0
Let x(h) = -5*h - 27. Let c be x(-6). Factor -2/7*w + 0 + 6/7*w**2 - 6/7*w**c + 2/7*w**4.
2*w*(w - 1)**3/7
Let k(c) = 2*c**2 - 13*c + 8. Let p be k(6). Factor -3/4 + 3/4*a - 3/2*a**3 + 3/4*a**5 + 3/2*a**p - 3/4*a**4.
3*(a - 1)**3*(a + 1)**2/4
Let j be 3*(-1)/(-3)*-2. Let i = j - -16. Factor 30*a**2 - 26*a**3 + 5*a**4 + 5*a**4 - i*a - 2*a**4 + 2.
2*(a - 1)**3*(4*a - 1)
Let n(w) = 6*w**2 + 5*w. Let l(o) = -o**2 + 2*o + 0*o - 3*o. Let a = -6 + 8. Let d(j) = a*n(j) + 11*l(j). Suppose d(u) = 0. What is u?
0, 1
Let i(r) = 6*r + 18. Let w be i(-3). Find g, given that w + 2/3*g**3 + 2/9*g**2 + 0*g + 2/9*g**5 + 2/3*g**4 = 0.
-1, 0
Factor -2/3 + 2/3*l - 2/3*l**3 + 2/3*l**2.
-2*(l - 1)**2*(l + 1)/3
Let t = 26 + -23. Let m(h) be the third derivative of 3/40*h**6 + 0*h + 0 - 3/8*h**4 + 1/30*h**5 - 1/3*h**t + 2*h**2. Determine d, given that m(d) = 0.
-1, -2/9, 1
Let v(b) be the first derivative of b**6/180 + b**5/60 - b**4/6 - 4*b**3/3 + 4. Let y(i) be the third derivative of v(i). What is m in y(m) = 0?
-2, 1
Let p be (3273/994 - 3) + 0. Let k = -1/142 + p. Determine l so that 2/7 - k*l**2 + 0*l = 0.
-1, 1
Factor -2*n**2 - 2*n**4 + 0*n**2 + 0*n**2 + 4*n**4.
2*n**2*(n - 1)*(n + 1)
Solve 0*t - 4/7*t**3 + 8/7*t**2 + 0 = 0.
0, 2
Let z = 7 - -1. Let r = z - 6. Factor -10*u**4 + 12*u**2 + r*u**5 + 9*u**3 - 2*u**4 + u**5 - 12*u.
3*u*(u - 2)**2*(u - 1)*(u + 1)
Let f(n) = 7*n**5 - n**3 + 6. Let a(j) = 6*j**5 - j**3 + 5. Let y(z) = -6*a(z) + 5*f(z). Factor y(i).
-i**3*(i - 1)*(i + 1)
Let t(l) = 6*l**2 + 5*l + 6*l + 13 - 5*l**2. Let p be t(-10). Factor 0*y - 1/2*y**p - 1/2*y**2 + 0.
-y**2*(y + 1)/2
Let t(x) be the third derivative of -x**6/30 + x**5/15 + 2*x**2. What is q in t(q) = 0?
0, 1
Let a(n) be the third derivative of 0*n + 0*n**3 + 1/210*n**7 + 0*n**4 + 0 - 1/120*n**6 - 3*n**2 + 0*n**5. Solve a(d) = 0.
0, 1
Solve 0 + 1/6*h + 0*h**2 - 1/3*h**3 + 0*h**4 + 1/6*h**5 = 0.
-1, 0, 1
Let h(l) = -2*l**2 + 8 - 7 - 2*l**2 - l. Let g(i) = -17*i**2 - 3*i + 5. Let p(d) = -2*g(d) + 9*h(d). Factor p(f).
-(f + 1)*(2*f + 1)
Let v(n) be the first derivative of n**4 - 4*n**3 + 6*n**2 - 4*n + 32. Solve v(x) = 0.
1
Let q(h) be the second derivative of 0 + 1/45*h**6 + 0*h**3 - 1/18*h**4 + 0*h**5 + 0*h**2 - 2*h. What is j in q(j) = 0?
-1, 0, 1
Let q be 26/39 - 2/12. Let a(b) be the first derivative of 4/5*b**5 - 3 + 1/6*b**6 + 4/3*b**3 + 0*b + q*b**2 + 3/2*b**4. Determine p, given that a(p) = 0.
-1, 0
Let d(q) be the second derivative of 2*q + 9/20*q**5 + 0 + 0*q**2 - 1/2*q**4 - 1/2*q**3. Let d(k) = 0. Calculate k.
-1/3, 0, 1
Let y(s) = -s**3 + 7*s**2 + 10*s - 13. Let k be y(8). Suppose -3*o**3 + 0 - 21/2*o**4 + 21/2*o**2 + k*o = 0. Calculate o.
-1, -2/7, 0, 1
Let k be 3 + (-2 - -2)/4. Let -k*t + 0*t**3 - 3*t**3 + 4*t**3 + 2*t = 0. Calculate t.
-1, 0, 1
Factor -5*m**2 - 9*m + 21*m - 22*m.
-5*m*(m + 2)
Suppose -z + 5*z - 16 = 0. Factor 12*o**4 - 6*o + 27*o**2 + 3*o**z + 10*o**2 - 10*o**2 - 36*o**3.
3*o*(o - 1)**2*(5*o - 2)
Let s(j) = j - 5. Let w be s(8). What is g in -9*g + w + 3*g**3 + 2 + 1 = 0?
-2, 1
Factor 3 + 9/2*u**2 + 27/4*u + 3/4*u**3.
3*(u + 1)**2*(u + 4)/4
Let s(n) be the third derivative of -1/90*n**5 + 0*n + 0*n**3 + 0*n**4 + 1/180*n**6 - 2*n**2 + 0. Factor s(z).
2*z**2*(z - 1)/3
Let d(j) = 5*j**2 + 10*j + 2. Let t(a) = 1. Let z(k) = d(k) - 2*t(k). Find u such that z(u) = 0.
-2, 0
Suppose -u - 1 = -5. Let o be (u/5*1)/2. Factor 4/5*i - o*i**2 - 2/5.
-2*(i - 1)**2/5
Suppose 5*d + 7 - 27 = 0. Let j(r) be the third derivative of 0*r - 1/48*r**d + 1/24*r**3 + 1/240*r**5 + 0 + r**2. Factor j(f).
(f - 1)**2/4
Let p = 10 - -4. Factor -4*d - d + p*d**2 + d + 8*d**3.
2*d*(d + 2)*(4*d - 1)
Let w(l) = l**2 - l - 1. Let a(u) = 3*u**2 - 8. Let p(g) = a(g) - 4*w(g). Factor p(i).
-(i - 2)**2
Let w(n) = -2*n + 1. Let b be w(-2). Factor 4*x - 2*x**2 + b*x**2 - 2*x.
x*(3*x + 2)
Suppose -2*q + 8 - 28 = 0. Let h = q + 10. Factor 0 + 2/3*k**4 - 4/3*k**3 + h*k + 2/3*k**2.
2*k**2*(k - 1)**2/3
Let n(d) = -d**2 - 7*d + 3. Let s be n(-7). Suppose -5*r + 25 = -0*k - s*k, 0 = 4*k - 2*r + 10. Determine t so that -1/3*t**4 + 0*t + k + 0*t**3 + 1/3*t**2 = 0.
-1, 0, 1
Let o(b) be the second derivative of 0 + 4*b - 2*b**2 + 1/10*b**5 - 1/3*b**3 + 1/3*b**4. Suppose o(m) = 0. What is m?
-2, -1, 1
Let q = 404/615 - -2/205. Let -2*x**2 + 4/3*x + q = 0. What is x?
-1/3, 1
Let a = 1849/5 + -369. Factor 0 - 6/5*s**2 - a*s.
-2*s*(3*s + 2)/5
Let o(t) be the first derivative of t**6/6 - 2*t**5/3 - 2*t**4 - 2*t**3/3 + 5*t**2/6 - 38. Determine p so that o(p) = 0.
-1, 0, 1/3, 5
Let z(y) = 9*y**2 - 9*y + 4. Let v(r) = r**2 - r. Let p(o) = 22*v(o) - 2*z(o). Determine a, given that p(a) = 0.
-1, 2
Factor 2*j**3 + 2*j**3 - 3*j**3 + 2*j - 3*j**2.
j*(j - 2)*(j - 1)
Let a(g) be the third derivative of -g**5/5 + 5*g**4/6 - 4*g**3/3 - 14*g**2. What is w in a(w) = 0?
2/3, 1
Let h = -326/15 + 112/5. Let -2/3 - h*r + 2/3*r**2 + 2/3*r**3 = 0. What is r?
-1, 1
Let c(y) = -y**3 + 6*y**2 - 4*y - 1. Let p(q) be the third derivative of q**5/60 - q**4/24 + 3*q**2. Let j(n) = c(n) - 5*p(n). Determine i so that j(i) = 0.
-1, 1
Let r(l) be the second derivative of -l**6/195 + 4*l**4/39 - 16*l**2/13 - 7*l. Determine t so that r(t) = 0.
-2, 2
Let v be (-5)/(-5) - 2/(-2). Factor -3*s + 2*s + 2*s**3 + v*s**2 + 2*s - s**3.
s*(s + 1)**2
Factor 0*j + 0 - 2/3*j**5 - 10/3*j**3 + 8/3*j**4 + 4/3*j**2.
-2*j**2*(j - 2)*(j - 1)**2/3
Determine d so that 12*d + 6*d - 13*d - 10 + 5*d**2 = 0.
-2, 1
Let y(x) be the second derivative of -x**7/112 - x**6/20 - 3*x**5/40 + 41*x. What is w in y(w) = 0?
-2, 0
Let g(d) be the second derivative of 0 + 1/15*d**6 + 3/10*d**5 - 2*d + 1/3*d**3 + 0*d**2 + 1/2*d**4. Factor g(h).
2*h*(h + 1)**3
Factor -1/9*j**3 - 1/9*j**2 + 1/9*j + 1/9.
-(j - 1)*(j + 1)**2/9
Let f(s) be the first derivative of s**2 - 3 - 4/3*s**3 + 1/2*s**4 + 0*s. Factor f(w).
2*w*(w - 1)**2
Suppose -2*g = -7*g + 25. Determine l so that l**5 + 13*l - 2*l**g + l**3 - 13*l = 0.
-1, 0, 1
Let x(w) be the third derivative of w**6/240 + w**5/60 + 2*w**2. Factor x(n).
n**2*(n + 2)/2
Factor -11 + 11*s**2 + 14*s**2 + 23 + 88 - 260*s.
5*(s - 10)*(5*s - 2)
Let 10 + 16*g + 5 + 3 - 2 + 4*g**2 = 0. What is g?
-2
Let h(d) = -d**2 + 7*d - 1. Let b be h(7). Let u be (2/(-2) + 1)/b. Factor -6*j**3 - 2 + 3*j**4 + u + 2.
3*j**3*(j - 2)
Determine v, given that -42*v**3 - 81 - 27*v**2 - 81*v + 16*v**3 + 23*v**3 = 0.
-3
Let l(j) be the third derivative of 5*j**8/112 + 13*j**7/42 + 17*j**6/24 + j**5/4 - 5*j**4/3 - 10*j**3/3 - 11*j**2. Let l(f) = 0. What is f?
-2, -1, 2/3
Let z(p) = -3*p**2 - 3*p - 2. Let c be z(-2). Let n be (c/84*-6)/2. Factor -2*r**2 - 4/7*r - 18/7*r**3 + 0 - 10/7*r**4 - n*r**5.
-2*r*(r + 1)**3*(r + 2)/7
Let t(p) be the second derivative of -p**7/98 + 3*p**5/140 - 4*p. Factor t(g).
-3*g**3*(g - 1)*(g + 1)/7
Let r(o) = o + 1. Let a(k) = k**2 - k + 14. Let t(x) = 2*a(x) - 10*r(x). Suppose t(n) = 0. What is n?
3
Let k(a) = -3*a. Let t(s) = s**2 - 18*s + 2. Let b(n) = 15*k(n) - 3*t(n). Factor b(o).
-3*(o - 2)*(o - 1)
Let d(n) = -2*n**3. Let g be d(1). Let a = 0 - g. Factor 3*q + 0*q**a - 2*q**2 - q.
-2*q*(q - 1)
Let m(v) = -v**4 - v**2 - 1. Let f(t) = 25*t**4 - 30*t**3 + 20*t**2 + 20. Let g(r) = f(r) + 20*m(r). Determine s, given that 