 = n**2 - n. Let t(q) = -2*a(q) + 6*i(q). Find m such that t(m) = 0.
1, 3
Let y(n) be the second derivative of 1/6*n**3 - 1/24*n**4 + 3*n + 0 - 1/4*n**2. Factor y(x).
-(x - 1)**2/2
Let d be (-28)/8 + (2 - -2). Determine f so that 3/4*f**4 - 1/2*f**3 - 1/4 + 3/4*f - d*f**2 - 1/4*f**5 = 0.
-1, 1
Let o(p) = -10*p**3 + 9*p**2 + 12*p. Let w = 9 + -7. Let m(l) = -l**3 + l**2 + l. Let f(s) = w*o(s) - 22*m(s). Factor f(j).
2*j*(j - 1)**2
Let h(d) = 22*d**2 - 16*d**2 - d - 2 - 3*d. Let f(t) = -5*t**2 + 4*t + 1. Let m(j) = -4*f(j) - 3*h(j). Factor m(l).
2*(l - 1)**2
Let d(z) be the third derivative of 1/60*z**6 - 4/21*z**3 + 0 - z**2 - 1/7*z**4 + 0*z + 3/70*z**5. Factor d(b).
2*(b - 1)*(b + 2)*(7*b + 2)/7
Let g(m) be the third derivative of -m**5/150 - 7*m**4/60 + 8*m**3/15 - 26*m**2. Let g(f) = 0. Calculate f.
-8, 1
Let r(k) be the first derivative of -k**3 - 3*k**2 - 3*k - 16. Suppose r(w) = 0. Calculate w.
-1
Factor -w**3 - 4*w**4 + w**4 - w + 0*w**4 + 3*w**2 + 2*w**5.
w*(w - 1)**2*(w + 1)*(2*w - 1)
Factor -2*b + 3*b - 3*b**2 - 2 + 2*b**2 + 2*b.
-(b - 2)*(b - 1)
Suppose -1/2*f + 0 + 1/4*f**3 - 1/4*f**2 = 0. What is f?
-1, 0, 2
Let f(r) be the second derivative of -2*r - 1/7*r**3 - 2/7*r**2 + 1/21*r**4 + 0. Factor f(a).
2*(a - 2)*(2*a + 1)/7
Let w(j) be the third derivative of -j**5/30 - j**4/6 - j**3/3 + 24*j**2. Determine x, given that w(x) = 0.
-1
Factor 2/17*a**2 + 0 - 2/17*a.
2*a*(a - 1)/17
Let c(a) = 11*a**2 + 15*a + 4. Let l(g) = 6*g**2 + 8*g + 2. Let y = -13 - -6. Suppose -16 = -5*t + t. Let x(i) = t*c(i) + y*l(i). Suppose x(h) = 0. Calculate h.
-1
Let u(p) = -2*p**2 - 7*p + 4. Let t be u(-4). Let i(w) be the first derivative of 1/5*w**3 + 3/20*w**4 + 1 + t*w - 3/10*w**2 - 3/25*w**5. Factor i(x).
-3*x*(x - 1)**2*(x + 1)/5
Let y(j) be the first derivative of j**5/20 - 3*j**4/16 + j**3/4 - j**2/8 - 7. Determine k so that y(k) = 0.
0, 1
Let m(c) be the second derivative of -3*c**5/40 - c**4/8 + 2*c**3 + 9*c**2 - 12*c. Factor m(x).
-3*(x - 3)*(x + 2)**2/2
Let j(i) = -14*i + 184. Let f be j(13). Factor -8/7*z**3 - 8/7*z - 12/7*z**f - 2/7*z**4 - 2/7.
-2*(z + 1)**4/7
Let d(i) = -i**3 - 2*i**2 - 1 + 3*i**2 + 4*i**3 - 4*i**3. Let a(q) = -3*q**3 - q**2 + 6*q - 7. Let m(o) = -a(o) + 5*d(o). Determine r so that m(r) = 0.
1
Let i(s) be the first derivative of 2*s**5/85 - 2*s**4/17 + 4*s**3/17 - 4*s**2/17 + 2*s/17 + 25. What is p in i(p) = 0?
1
Let k(y) be the third derivative of y**10/45360 + y**9/11340 + y**8/10080 + y**4/8 + 3*y**2. Let w(l) be the second derivative of k(l). Factor w(q).
2*q**3*(q + 1)**2/3
Let g(r) = -r + 8. Let l be g(8). Let s(i) be the second derivative of 1/45*i**6 + l*i**5 - 2*i + 0*i**3 + 0 - 1/18*i**4 + 0*i**2. Solve s(j) = 0.
-1, 0, 1
Let a = 8 - 7. Let z be ((-3)/6)/(a/(-5)). Determine g, given that 3/2*g**3 + g - z*g**2 + 0 = 0.
0, 2/3, 1
Let l(u) be the first derivative of u**6/33 - 4*u**5/55 - 3*u**4/22 + 8*u**3/33 + 4*u**2/11 + 8. Determine o so that l(o) = 0.
-1, 0, 2
Let v(j) be the second derivative of -5*j**6/21 - 3*j**5/7 + 6*j**4/7 - 8*j**3/21 - 13*j. Let v(o) = 0. Calculate o.
-2, 0, 2/5
Let b(x) = 2*x**2 - 4*x + 2. Let h(c) be the first derivative of -4*c**3/3 + 9*c**2/2 - 5*c - 3. Let w(g) = 5*b(g) + 2*h(g). Factor w(l).
2*l*(l - 1)
Factor -148*k + 4*k**4 - 15*k**2 + k**4 + 138*k.
5*k*(k - 2)*(k + 1)**2
Let m(f) be the second derivative of 0 + 3/20*f**4 - 4*f - 1/5*f**2 - 1/10*f**3. Solve m(s) = 0.
-1/3, 2/3
Let k(a) be the second derivative of a**5/240 + a**4/32 + a**3/12 - 3*a**2/2 - a. Let i(d) be the first derivative of k(d). Let i(y) = 0. Calculate y.
-2, -1
Factor -1/2*g - 1/2*g**2 + 0 + 1/2*g**4 + 1/2*g**3.
g*(g - 1)*(g + 1)**2/2
Let m(y) = 16*y**4 + 41*y**3 + 24*y**2 - y - 5. Let w(c) = 8*c**4 + 20*c**3 + 12*c**2 - 2. Let p = -3 + -2. Let z(a) = p*w(a) + 2*m(a). Factor z(g).
-2*g*(g + 1)**2*(4*g + 1)
Let s(b) = b**2 + 6*b + 5. Let d be s(-5). Let z(l) be the first derivative of -1/3*l**3 - 1 - 1/2*l**2 + d*l. Let z(o) = 0. Calculate o.
-1, 0
Let v be ((-30)/8 + 4)*0. Let d(y) be the first derivative of y**2 + 2 - 2/3*y**3 + v*y. Find x, given that d(x) = 0.
0, 1
Let g = -11/2 - -89/16. Let n(q) be the second derivative of 0 + g*q**5 + 1/12*q**4 - q + 1/24*q**3 + 1/60*q**6 + 0*q**2. Determine a so that n(a) = 0.
-1, -1/2, 0
Let m(x) be the first derivative of -8 + 0*x + 2/5*x**2 + 2/15*x**3. Let m(o) = 0. Calculate o.
-2, 0
Let w(b) be the first derivative of b**4/4 + 10*b**3/9 + 3*b**2/2 + 2*b/3 + 2. Factor w(k).
(k + 1)*(k + 2)*(3*k + 1)/3
Let g be 356/(-240) - 3/(-2). Let f(m) be the third derivative of 0*m**5 + 0*m + 5/672*m**8 + 1/120*m**6 + 0 - g*m**7 + 0*m**3 + m**2 + 0*m**4. Factor f(u).
u**3*(u - 1)*(5*u - 2)/2
Let n(f) be the first derivative of f**3/6 - 5*f**2/4 + 2*f - 17. Determine m, given that n(m) = 0.
1, 4
Let z(q) be the first derivative of q**4/4 - q**2/2 - 3. Factor z(j).
j*(j - 1)*(j + 1)
Let y(h) be the first derivative of -h**6/21 + 6*h**5/35 - h**4/7 - 8. Factor y(s).
-2*s**3*(s - 2)*(s - 1)/7
Let u be 8/(-36) - (-6)/27. Let h(c) be the second derivative of 1/9*c**3 - c + u*c**2 + 7/36*c**4 + 0. Factor h(k).
k*(7*k + 2)/3
Let c(l) be the third derivative of -l**6/30 - 8*l**5/75 - l**4/30 + 4*l**3/15 + 7*l**2. Find u, given that c(u) = 0.
-1, 2/5
Let b(n) = n**2 - 5*n. Let a be b(5). Let u(r) = r**2 + 9*r - 31. Let j be u(-12). Factor g**4 + a*g**2 - 1/3*g**j - 2/3*g**3 + 0 + 0*g.
-g**3*(g - 2)*(g - 1)/3
Suppose 17 = -5*s + 3*r + 2, 4*s + 25 = 5*r. Factor -2*k**2 - 1 + 2*k**3 + s - 2*k - 1 + 4.
2*(k - 1)**2*(k + 1)
Factor -3/2*p**2 - 1/2*p**3 - 3/2*p - 1/2.
-(p + 1)**3/2
Let v(n) = -n**3 - 7*n**2 + 7*n - 4. Let z be v(-8). Solve z - 7*x**2 + 5*x**2 - 5*x + 3*x = 0 for x.
-2, 1
Let i(n) be the first derivative of n**5/6 - 5*n**4/6 + 5*n**3/9 + 5*n**2/3 - 5*n/2 + 9. Suppose i(p) = 0. Calculate p.
-1, 1, 3
Let j(f) be the second derivative of -f**7/14 + 2*f**6/5 - 9*f**5/20 - f**4 + 2*f**3 + 16*f. Suppose j(t) = 0. Calculate t.
-1, 0, 1, 2
Let z(p) be the first derivative of 2*p**3/3 + p**2/2 - p + 8. Factor z(q).
(q + 1)*(2*q - 1)
Let c(i) be the second derivative of i**5/360 + i**4/144 + i**2/2 + i. Let v(a) be the first derivative of c(a). Solve v(r) = 0 for r.
-1, 0
Let l(x) be the third derivative of -x**8/53760 - 11*x**7/40320 - x**6/960 + x**5/15 - 5*x**2. Let j(u) be the third derivative of l(u). Factor j(w).
-(w + 3)*(3*w + 2)/8
Let p = 4 + -10. Let b be ((-1)/p)/(4/16). Find g such that -b*g**3 - 4/3*g**2 - 2/3*g + 0 = 0.
-1, 0
Let p be (5 - 4/2)/1. Factor 1/4*f**p + 0*f - 1/4*f**2 + 1/4*f**4 + 0 - 1/4*f**5.
-f**2*(f - 1)**2*(f + 1)/4
Let z(j) = 21*j**2 + 147*j + 4. Let f be z(-7). Suppose 0 - 1/3*i**3 - 1/3*i**2 + 1/3*i**f + 1/3*i = 0. What is i?
-1, 0, 1
Determine m, given that -5/3*m + 4/3*m**2 - 2/3 + m**3 = 0.
-2, -1/3, 1
Let r(m) = m**3 + 8*m**2 + 12*m + 4. Let n be r(-6). Find i, given that 0*i**n + 0 - 2/3*i - 2/3*i**5 + 4/3*i**3 + 0*i**2 = 0.
-1, 0, 1
Factor 11/3*q - 121/6 - 1/6*q**2.
-(q - 11)**2/6
Let m = 23 - 21. Factor -2*s + 5*s**m - 5*s**2 - 2*s**2 + 4.
-2*(s - 1)*(s + 2)
Let v(q) be the third derivative of 0*q + 0*q**3 + 0*q**4 + 1/120*q**6 - q**2 + 1/60*q**5 + 0. Find o, given that v(o) = 0.
-1, 0
Let k(x) = x + 8. Let o be k(-8). Let d(t) be the first derivative of -8/15*t**5 - 2 + 2/9*t**3 - 1/2*t**4 + 0*t + o*t**2. Let d(l) = 0. What is l?
-1, 0, 1/4
Suppose 3 = 5*q - 3*o + 12, -4*q + 2*o - 6 = 0. Let b be 3 + -2 + q + 1. Determine k so that 11*k**2 - 32*k + 8 + k**b + 2*k**2 = 0.
2/7, 2
Let m(h) = -h**2 + 14*h + 17. Let x be m(15). Find q such that q**3 - 2/5*q**4 + 2/5*q**x + 0*q + 0 - q**5 = 0.
-1, -2/5, 0, 1
Suppose 4*p = -32 + 44. Factor -3/2*i - 1/2*i**p + 3/2*i**2 + 1/2.
-(i - 1)**3/2
Let i(b) be the third derivative of -b**7/70 - 3*b**6/40 + b**4/2 - 40*b**2. Determine g, given that i(g) = 0.
-2, 0, 1
Let 1/3*i**4 - 1/3*i**3 + 1/3*i**5 - 1/3*i**2 + 0*i + 0 = 0. What is i?
-1, 0, 1
Let a(c) be the first derivative of 0*c**2 + 1/9*c**3 + 0*c - 1/12*c**4 + 2. Factor a(g).
-g**2*(g - 1)/3
Suppose 3*u = 3*x + 2*u, -4*u = 3*x. Let r(m) be the third derivative of 0*m**6 + 1/105*m**7 + m**2 - 1/30*m**5 + 0 + 0*m + x*m**3 + 0*m**4. Solve r(b) = 0.
-1, 0, 1
Let -1/6*d**2 + 1/2*d + 2/3 = 0. What is d?
-1, 4
Let y be 2/(-3)*24*1. Let c(n) = n**3 + n**2. Let 