*n**3 - 8*n**3 + 12*n**2 + 212*n - 4*n**3.
3*n*(n - 2)**2*(n + 1)**2
Let p be (24/(-28))/((-9)/42). Determine a so that a**2 - 12*a**3 - 12*a**p - 3*a**2 - 2*a**2 + 2*a**5 - 6*a**5 = 0.
-1, 0
Let r be (-34 - -1)/3*1. Let m(n) = 8*n**2 + 6*n - 3. Let v(t) = -3*t**2 - 2*t + 1. Let f(o) = r*v(o) - 4*m(o). Let f(a) = 0. Calculate a.
1
Factor -4 - 5*b**3 - 2*b**3 + b**3 + 10*b + 0 + 8*b**2.
-2*(b - 2)*(b + 1)*(3*b - 1)
Let c(n) = -n + 12. Suppose 0*q - 50 = -5*q. Let z be c(q). Factor -2/5 - 4/5*b - 2/5*b**z.
-2*(b + 1)**2/5
Let n be 6/3*((-48)/28)/(-3). Factor -44/7*c - n - 36/7*c**2.
-4*(c + 1)*(9*c + 2)/7
Let y(u) be the second derivative of 8/3*u**3 + 1/21*u**7 + 0 + 0*u**2 - 7/15*u**6 + 5*u + 9/5*u**5 - 10/3*u**4. Solve y(g) = 0 for g.
0, 1, 2
Let w(a) = 9*a**3 + 92*a**2 + 572*a + 484. Let t(f) = 4*f**3 + 46*f**2 + 286*f + 242. Let z(d) = -5*t(d) + 2*w(d). Find j, given that z(j) = 0.
-11, -1
Let h(a) be the first derivative of 0*a + 1/16*a**4 + 0*a**2 + 2 + 1/6*a**3. Suppose h(p) = 0. What is p?
-2, 0
Let w(m) be the third derivative of -5*m**2 + 0 + 0*m**4 + 0*m**3 + 0*m - 1/240*m**6 - 1/60*m**5. What is q in w(q) = 0?
-2, 0
Let c(t) be the second derivative of -t**8/10080 + t**7/3780 - t**4/6 + 2*t. Let b(n) be the third derivative of c(n). Factor b(u).
-2*u**2*(u - 1)/3
Let p(c) = -3*c**2 - 2*c - 5. Let y(s) = -s - 1. Let g(t) = p(t) - 5*y(t). Let g(x) = 0. What is x?
0, 1
Suppose 9 = 5*j - 2*y, -2 = 4*j - 3*y - 5. Let g(u) be the first derivative of -3 + 0*u**4 + 1/2*u**2 + 1/10*u**5 + 0*u - 1/2*u**j. What is o in g(o) = 0?
-2, 0, 1
Let b(k) be the first derivative of 5/8*k**2 + 1/4*k + 1 + 1/3*k**3. Factor b(t).
(t + 1)*(4*t + 1)/4
Solve -33/7*j + 6/7 - 3*j**3 + 48/7*j**2 = 0.
2/7, 1
Let u(n) be the third derivative of n**6/1020 - 7*n**5/510 - 7*n**2. Factor u(w).
2*w**2*(w - 7)/17
Let y(q) be the second derivative of -q + 0 + 1/30*q**5 + 1/9*q**4 + 1/9*q**3 + 0*q**2. Factor y(n).
2*n*(n + 1)**2/3
Let i be -3 + ((-7044)/(-1920) - (-4)/(-6)). Let m(g) be the third derivative of -g**2 + 0*g**3 + 0*g**4 - 1/840*g**7 + 0 + 0*g**5 + 0*g - i*g**6. Factor m(c).
-c**3*(c + 1)/4
Let z = -8 - -12. Determine r so that z*r**4 - 3*r**2 - 7*r**3 + 1 + 1 - 3 + 2*r**3 + 5*r = 0.
-1, 1/4, 1
Let k be 2/4 + 15/10. Suppose -8 + 2 = -k*h. Suppose -u - u**2 - h*u + 2 + 3*u**2 = 0. Calculate u.
1
Suppose 2*p + 2*h - 28 = -3*p, p = -2*h + 12. Let -1/6*t**2 + 0*t + 1/6*t**5 + 1/6*t**p + 0 - 1/6*t**3 = 0. Calculate t.
-1, 0, 1
Let l(w) be the third derivative of 1/135*w**5 - 1/540*w**6 - 1/108*w**4 - 8*w**2 + 0 + 0*w + 0*w**3. Factor l(r).
-2*r*(r - 1)**2/9
Suppose 0 = -5*j + 5*f, 5*f - 3 = 2*f. Let b be j/(-2)*1 - -1. Determine o so that 0*o + 0 + b*o**2 = 0.
0
Let v(r) = 23*r**3 - 125*r**2 + 121*r - 29. Let b = -2 + 5. Let l(q) = -11*q**3 + 63*q**2 - 61*q + 15. Let a(j) = b*v(j) + 5*l(j). Factor a(y).
2*(y - 3)*(y - 1)*(7*y - 2)
Let p(g) be the second derivative of g**7/28 - g**6/40 - g**5/8 + g**4/8 + g**2 + g. Let a(n) be the first derivative of p(n). Suppose a(i) = 0. What is i?
-1, 0, 2/5, 1
Suppose 3*z - 5 = 8*z. Let d be (z - 2)*(-6)/9. Factor -d*y + y + 2*y - y**3.
-y*(y - 1)*(y + 1)
Suppose n + 5*n = 18. Factor 1/4 + 3/4*b**2 - 3/4*b - 1/4*b**n.
-(b - 1)**3/4
Let n(d) be the third derivative of 0*d**4 - 1/210*d**7 + 0*d**3 - 1/60*d**6 - 1/60*d**5 + 0*d + 5*d**2 + 0. Solve n(v) = 0 for v.
-1, 0
Let o be (0 - (-2)/(-2))*6. Let j be (-26)/o + 2 + -5. Factor -j - 1/3*d**2 + 4/3*d.
-(d - 2)**2/3
Let j(h) be the second derivative of h**4/27 - 4*h**3/27 + 11*h. Suppose j(p) = 0. Calculate p.
0, 2
Let g(s) be the third derivative of -s**5/15 + 5*s**4/6 + 4*s**3 - 4*s**2. Solve g(u) = 0.
-1, 6
Let z(r) be the third derivative of -9*r**8/112 - 3*r**7/70 + 13*r**6/20 + 7*r**5/5 + r**4 - 7*r**2. Let z(n) = 0. Calculate n.
-1, -2/3, 0, 2
Factor 19*t**4 - 60*t**5 - 62*t**5 + 123*t**5 + 99*t**3 + 81*t**2.
t**2*(t + 1)*(t + 9)**2
Suppose -n = 3*b - 14, 5*b + 10 = -3*n + 32. Let g(v) be the third derivative of 1/80*v**b - 3/160*v**6 + 0 + 1/16*v**4 - 2*v**2 + 0*v**3 + 0*v. Factor g(a).
-3*a*(a - 1)*(3*a + 2)/4
Suppose -10*n = -9*n - 3*n. Factor -3/2*k**4 + n*k**2 + 0*k - 3/4*k**3 + 0 - 3/4*k**5.
-3*k**3*(k + 1)**2/4
Let i(h) be the third derivative of -h**5/570 - h**4/57 - h**3/19 - 8*h**2. Factor i(v).
-2*(v + 1)*(v + 3)/19
Factor 3 - 3/4*l**2 + 0*l.
-3*(l - 2)*(l + 2)/4
Suppose 5 = 2*s + z, 3*z + 2*z = -5*s + 5. Let g = s - 2. Factor g*y**2 + 7 + 48*y**4 + 32*y**5 + 15*y**3 - 7 + 3*y**3.
2*y**2*(y + 1)*(4*y + 1)**2
Let v(t) be the second derivative of 5*t**4/12 - 5*t**3/2 - 28*t. Factor v(m).
5*m*(m - 3)
Solve -2/3*w**3 + 32/9*w - 10/9*w**2 + 8/3 = 0.
-3, -2/3, 2
Factor 1/12*c**4 + 1/2*c**2 - 2/3 + 5/12*c**3 - 1/3*c.
(c - 1)*(c + 2)**3/12
Let f = -37 - -52. Suppose 0 = 3*m - 21 + f. Find h such that m*h**2 + 20/7*h + 6/7 = 0.
-1, -3/7
Let c be (-2 - (-138)/33) + 2. Suppose 0 = -q + 3, -2*b + 2*q + 3*q = -9. Find f such that -24/11*f + b*f**3 - c*f**2 + 8/11 - 70/11*f**4 = 0.
-2/5, 2/7, 1
Let -3*t**2 + 2*t**2 - 20 - 4*t**2 + 20*t = 0. What is t?
2
Let l(h) = -2*h + 20. Let d be l(10). Suppose 12*g - 9*g - 12 = d. Factor -24/5*m - 2/5*m**g - 26/5*m**2 - 8/5 - 12/5*m**3.
-2*(m + 1)**2*(m + 2)**2/5
Let b = 0 + 1. Factor 6*p**3 + 1 - 3*p + b + 6*p**2 - 5 + 0 - 3*p**5 - 3*p**4.
-3*(p - 1)**2*(p + 1)**3
Let w(l) = 10*l + 90. Let i be w(-9). Suppose 1/3*v**3 + 0 + 2/3*v**2 + i*v = 0. Calculate v.
-2, 0
Factor -2 + a**3 + 3*a + 3*a**2 - 1 + 4.
(a + 1)**3
Let a be 2/(-1 + (-2)/(-3)). Let v be a/(-4) - (-4)/8. Suppose -y**3 + 2*y**2 - 3*y + v*y + 0*y**2 = 0. Calculate y.
0, 1
Let f(v) be the first derivative of 27*v**6/2 + 198*v**5/5 + 157*v**4/4 + 44*v**3/3 + 2*v**2 + 15. Solve f(m) = 0.
-1, -2/9, 0
Suppose 2 + 6 = 4*z. Let h = z - 2. What is j in h - 2/3*j**5 + 4/3*j**4 - 4/3*j**2 + 0*j**3 + 2/3*j = 0?
-1, 0, 1
Let i = 206 - 2059/10. Let g(k) be the second derivative of -i*k**6 - 3/4*k**4 - 9/20*k**5 - 1/2*k**3 + 0*k**2 + 0 - 3*k. Find y such that g(y) = 0.
-1, 0
Let o(n) = 3*n**3 - 3*n**2 + 4*n - 4. Let r = 38 + -34. Let h(x) = 2*x**3 - 2*x**2 + 3*x - 3. Suppose -2*f - 7 = -1. Let k(a) = f*o(a) + r*h(a). Factor k(w).
-w**2*(w - 1)
Let w(r) be the third derivative of -r**6/240 + r**5/120 - 7*r**2. Solve w(f) = 0 for f.
0, 1
Let d(b) = -b**3 + 6*b**2 - 3*b - 2. Let h(s) = -s**2 + s. Let f(q) = -d(q) - 4*h(q). Determine y so that f(y) = 0.
-1, 1, 2
Suppose 0 = a + 5*y - 17, -a = 2*a - 2*y. Let l be (1 - 0)*(a + 3). What is g in g**3 + g**4 - g**2 - g**l + g - g = 0?
-1, 0, 1
Let a(o) be the second derivative of o**5/40 + o**4/32 - o**3/48 - 38*o. Determine q, given that a(q) = 0.
-1, 0, 1/4
Factor 1/2*t**3 + 5/2 - 9/2*t + 3/2*t**2.
(t - 1)**2*(t + 5)/2
Let z(s) = -s**3 - 38*s**2 - s - 35. Let u be z(-38). Factor 2/3 - 2/3*t**4 - 4/3*t**u + 4/3*t + 0*t**2.
-2*(t - 1)*(t + 1)**3/3
Let h(z) be the second derivative of 5*z**4/12 + 65*z**3/3 + 845*z**2/2 - 41*z. What is o in h(o) = 0?
-13
Let z(b) be the first derivative of 2/9*b - 1/18*b**4 + 2 - 2/27*b**3 + 1/9*b**2. Factor z(l).
-2*(l - 1)*(l + 1)**2/9
Let o(y) be the first derivative of 3*y**5/20 - 3*y**4/4 + 3*y**3/2 - 3*y**2/2 + 5*y + 1. Let p(g) be the first derivative of o(g). Find u such that p(u) = 0.
1
Let o(b) be the first derivative of -b**3/5 + b**2/5 - 1. Solve o(g) = 0.
0, 2/3
Let i(v) be the third derivative of 0*v**3 + 0*v**4 + 0*v**5 + 0 + 0*v + 1/448*v**8 - 1/280*v**7 + 0*v**6 + 2*v**2. Determine g so that i(g) = 0.
0, 1
Suppose 2*u + 3 = 3*u. Factor 2/7*z - 2/7*z**u - 4/7*z**2 + 4/7.
-2*(z - 1)*(z + 1)*(z + 2)/7
Let g(l) = -l**2 + 3*l. Let p be g(2). Solve -n**2 - n - n**p - 3*n + 0*n = 0.
-2, 0
Let 4/5*p**4 - 8/5*p**2 + 4/5 - 4/5*p**3 + 2/5*p**5 + 2/5*p = 0. Calculate p.
-2, -1, 1
Let s(p) = -10*p - 1. Let t be s(-1). Factor t*b - 2*b**2 - 3*b + 4 - 4*b**2 + 8*b**2.
2*(b + 1)*(b + 2)
Let r(s) be the third derivative of s**8/1512 + s**7/315 - 2*s**5/135 - 13*s**2. Solve r(x) = 0 for x.
-2, 0, 1
Let s = 9 + -8. Let k be s + ((-6)/(-9))/(-1). Find b such that 0 + b**2 - k*b = 0.
0, 1/3
Let a(t) be the second derivative of 0 + 5*t - 3*t**2 - 2*t**4 + 7/2*t**3 + 9/20*t**5. Factor a(c).
3*(c - 1)**2*(3*c - 2)
Suppose 2*k - b = -k - 20, 30 = -5*k + b. Let g be (-1 - (-46)/50)*k. What is f in 2/5*f**2 - 2/5*f**3 - 