
Let y(b) be the first derivative of -b**6/40 + b**5/10 - b**4/8 + b**2/2 - 3. Let g(q) be the second derivative of y(q). Factor g(a).
-3*a*(a - 1)**2
Let q(j) be the third derivative of 3*j**7/28 - 3*j**6/8 - j**5 - 65*j**4/72 - 5*j**3/12 + 7*j**2. Factor q(f).
5*(f - 3)*(3*f + 1)**3/6
Let i(y) be the first derivative of y**5/10 - 3*y**4/8 + y**3/3 - 9. Factor i(x).
x**2*(x - 2)*(x - 1)/2
Let g(q) be the first derivative of -q**4/2 - 18*q**3 - 243*q**2 - 1458*q - 13. Find d, given that g(d) = 0.
-9
Let v(p) = -12*p**2 - 87*p - 183. Let o(i) be the first derivative of -i**3 - 11*i**2 - 46*i - 7. Let k(z) = 9*o(z) - 2*v(z). Factor k(c).
-3*(c + 4)**2
Find t such that 1/4*t**2 - 1/2 + 1/4*t = 0.
-2, 1
Let m(z) be the third derivative of z**8/10080 - z**6/360 - z**5/90 - z**4/12 - 4*z**2. Let f(l) be the second derivative of m(l). Factor f(x).
2*(x - 2)*(x + 1)**2/3
What is c in -6*c**3 + 5100*c**2 - 5100*c**2 - c**5 + 4*c**5 - 3*c**4 = 0?
-1, 0, 2
Let l = 497/5 + -99. Let s(i) be the first derivative of 4*i**4 - l*i**5 + 2 - 32*i + 32*i**2 - 16*i**3. Factor s(c).
-2*(c - 2)**4
Solve 3*q**2 - 18*q**4 - 3*q**5 - 39*q**3 + 0*q**2 - 12*q - 39*q**2 = 0.
-2, -1, 0
Let c(r) = -2*r. Let b(z) = -5*z - 1. Let d(q) = -3*b(q) + 8*c(q). Let k be d(3). Determine w so that 0*w**4 + 0 + 1/5*w**3 + 0*w + k*w**2 - 1/5*w**5 = 0.
-1, 0, 1
Suppose 0 = -3*f + 2*f - 4, 0 = -5*v + 3*f + 32. Factor q - q**2 - 1 + 0 - v*q + q.
-(q + 1)**2
Suppose 0 = -n + 5 - 3. Let t be (0 + (-9)/(-6))*n. Solve -4*q**t - q**4 + 3*q + q**3 - 2*q**4 + q**2 + 2*q**2 = 0.
-1, 0, 1
Let x be (6/(-4))/((-3)/4). Let u(h) = -7 - 4*h + 2 - 4*h**x + 3. Let o(y) = -y**3 + y**2 + y + 1. Let k(a) = 2*o(a) + 2*u(a). Solve k(r) = 0 for r.
-1
Let b(o) be the second derivative of -1/3*o**4 + 0 + o + 1/2*o**3 + 0*o**2 + 1/20*o**5. Find r, given that b(r) = 0.
0, 1, 3
Let t(u) be the third derivative of -u**8/2016 + u**7/1260 + u**6/720 - u**5/360 + 10*u**2. Factor t(i).
-i**2*(i - 1)**2*(i + 1)/6
Let w be 0 - (-4 - 22*(-4)/32). Let n(v) be the first derivative of w*v**4 + 3*v**3 + 7/2*v**2 + 1/5*v**5 + 2*v + 4. Suppose n(f) = 0. Calculate f.
-2, -1
Let u(l) = -l**4 - 2*l**3 - 2*l**2 + 2*l - 3. Suppose -7 = -3*y + 2. Let b(v) = 2*v**4 + 3*v**3 + 3*v**2 - 3*v + 5. Let s(n) = y*b(n) + 5*u(n). Factor s(k).
k*(k - 1)**2*(k + 1)
Let b(v) be the second derivative of v**6/60 - v**5/10 + 4*v**3/3 + v**2/2 + 7*v. Let k(r) be the first derivative of b(r). Factor k(j).
2*(j - 2)**2*(j + 1)
Suppose -2*o - 59 = -4*x - 3, 0 = 3*x + 2*o - 35. Factor -9*p**2 - 6 + 2 - p + x*p.
-(3*p - 2)**2
What is q in 6*q**3 + 8*q**4 - 9*q**4 - 3*q**4 - 2*q**5 = 0?
-3, 0, 1
Let c be (6/(-14) - (-6)/14)/(-2). Factor 3/7*w + 3/7*w**2 + c.
3*w*(w + 1)/7
Factor -24*t + 221*t**4 + 2*t**5 - 115*t**4 - 94*t**4 + 18*t**3 - 8*t**2.
2*t*(t - 1)*(t + 2)**2*(t + 3)
Determine m, given that 0*m**3 - 6*m + 4*m + 2*m**3 = 0.
-1, 0, 1
Let a(i) be the third derivative of i**7/525 - 7*i**6/450 + 2*i**5/225 + i**4/6 + i**3/5 + 2*i**2. Determine m so that a(m) = 0.
-1, -1/3, 3
Let c(y) = y**2 - 3*y + 3. Let t be c(3). Solve 2*a**2 - 4*a + 2*a**3 - a**3 + 4*a**t - 3*a**3 = 0 for a.
-2, 0, 1
Determine n, given that 8*n**2 - 16*n**3 + 7 + 8*n + 8*n**5 - 3 - 6 - 2 - 4*n**4 = 0.
-1, 1/2, 1
Factor 4/7*i**2 - 6/7*i + 0 + 2/7*i**3.
2*i*(i - 1)*(i + 3)/7
Let b(t) be the second derivative of -3/16*t**4 + 1/2*t**3 + 3/2*t**2 - 3/40*t**5 + 1/40*t**6 - t + 0. Factor b(r).
3*(r - 2)**2*(r + 1)**2/4
Determine y so that 3/2*y**4 - 6*y**3 + 9/2*y**2 - 6 + 6*y = 0.
-1, 1, 2
Let y(v) be the second derivative of -v - 1/40*v**5 + 0*v**2 + 0 + 0*v**3 + 0*v**4 + 1/60*v**6. Factor y(s).
s**3*(s - 1)/2
Find g such that 3*g**3 + 3*g + 2/3*g**4 + 2/3 + 14/3*g**2 = 0.
-2, -1, -1/2
What is w in -75/2 - 3/2*w**2 + 15*w = 0?
5
Let g(h) be the second derivative of h**6/10 - h**4/4 + 5*h. Let z(w) = 9*w**4 - 9*w**2. Let t(b) = 17*g(b) - 6*z(b). Factor t(m).
-3*m**2*(m - 1)*(m + 1)
Let f(h) be the first derivative of -h**6/135 - h**5/90 + h**4/54 + h**3/27 + h - 1. Let w(u) be the first derivative of f(u). Determine p, given that w(p) = 0.
-1, 0, 1
Suppose -3*j = j. Let o be (12/(2/(-1)))/(-2). Suppose -4 + j - o*h + 2*h**2 + 5*h = 0. Calculate h.
-2, 1
Let o be 3/18*6/45. Let x(b) be the second derivative of o*b**5 + 1/189*b**7 - 1/9*b**3 + 1/27*b**4 + 1/9*b**2 + 0 - 1/45*b**6 + 2*b. Factor x(n).
2*(n - 1)**4*(n + 1)/9
Let w(j) be the second derivative of j**7/210 + j**6/50 + 3*j**5/100 + j**4/60 - 6*j. Find n such that w(n) = 0.
-1, 0
Let y be (-3)/(0 - 3/4). Solve h**2 + 12*h**5 - 5*h**2 - 12*h**3 + 7*h**4 - 4*h**y + h**2 = 0.
-1, -1/4, 0, 1
Let r(w) be the first derivative of w**3/3 - 2*w**2 + 4*w - 15. Factor r(f).
(f - 2)**2
Let m = 17 + -14. Let z be (-2)/(-8) - 7/(-4). Suppose -4*o**2 - 26*o**m + 18*o**5 + 4*o**z + 8*o = 0. Calculate o.
-1, -2/3, 0, 2/3, 1
Let x(s) be the third derivative of s**6/80 - 3*s**5/40 + s**3 + 9*s**2. Factor x(l).
3*(l - 2)**2*(l + 1)/2
Let u(k) be the third derivative of -k**7/840 + k**6/240 + k**5/240 - k**4/48 - 46*k**2. Factor u(c).
-c*(c - 2)*(c - 1)*(c + 1)/4
Suppose -4*o + 5 = -3*o + 3*k, 0 = 2*k. Let l(a) be the third derivative of 1/20*a**6 + a**2 + 0*a + 0 + 1/8*a**4 - 1/140*a**7 - 1/8*a**o + 0*a**3. Factor l(x).
-3*x*(x - 2)*(x - 1)**2/2
Let g be (6/(-32))/(((-1173)/(-34))/(-23)). Factor 0*h**2 + g*h**3 - 1/4 - 3/8*h.
(h - 2)*(h + 1)**2/8
Suppose -3*f = -7*f + 12. Factor -1/4*d + 0*d**2 + 1/4*d**f + 0.
d*(d - 1)*(d + 1)/4
Let i = -533/2 - -267. Factor -1/2*h**3 + 1/4 + 1/4*h**4 + 1/4*h - i*h**2 + 1/4*h**5.
(h - 1)**2*(h + 1)**3/4
Let h(k) be the second derivative of k**7/210 + 7*k**6/150 + 19*k**5/100 + 5*k**4/12 + 8*k**3/15 + 2*k**2/5 + 4*k. Let h(z) = 0. What is z?
-2, -1
Let x + 1/2*x**2 + 1/2 = 0. Calculate x.
-1
Let l(f) be the second derivative of 19/54*f**4 + 0 + 6*f - 11/9*f**3 - 1/30*f**5 + f**2. Factor l(v).
-2*(v - 3)**2*(3*v - 1)/9
Suppose -3*t + 3 = -4*t. Let u be t/(-5) - (-441)/15. Determine k so that 0*k**3 + u*k + 3*k**3 + 14*k**2 - k**3 + 18 = 0.
-3, -1
Let z be (-5 - -1)/(6/9). Let p be ((-14)/1)/(z - -4). Factor -p + 0*n**2 - 2*n**2 + 9.
-2*(n - 1)*(n + 1)
Let b(s) = 15*s**4 - 21*s**3 + 9*s**2 - 3. Let x(c) = 29*c**4 - 42*c**3 + 17*c**2 + c - 5. Suppose -3*r - 11 = 4. Let j(z) = r*b(z) + 3*x(z). Solve j(o) = 0.
-1/4, 0, 1
Let x(r) = -25*r**2 + 86*r - 50. Let g(h) = -5*h**2 + 17*h - 10. Let j(f) = 11*g(f) - 2*x(f). Factor j(u).
-5*(u - 2)*(u - 1)
Let v(b) be the third derivative of -b**8/840 - b**7/150 - 3*b**6/200 - b**5/60 - b**4/120 + 6*b**2. Factor v(r).
-r*(r + 1)**3*(2*r + 1)/5
Suppose 5*c + 8 = 2*g + 12, -c + 2*g = 4. Factor -3/4 - 1/4*y**c - y.
-(y + 1)*(y + 3)/4
Let v be -3 - (-6)/((-432)/(-582)). Let k(u) be the second derivative of 2*u**2 + 3/10*u**6 + 0 + v*u**4 - 4*u - 21/10*u**5 - 14/3*u**3. Factor k(o).
(o - 2)**2*(3*o - 1)**2
Solve 159/4*g**2 + 15/4*g**5 + 18*g + 165/4*g**3 + 3 + 81/4*g**4 = 0 for g.
-2, -1, -2/5
Let y(u) = u**3 - 10*u**2 + 10*u - 5. Let c be y(9). Let h(x) be the second derivative of 1/48*x**c + 1/8*x**2 + 0 - 2*x - 1/12*x**3. Factor h(k).
(k - 1)**2/4
Let v(m) be the second derivative of m**5/100 + 2*m**4/15 + 8*m**3/15 + 14*m. Determine b so that v(b) = 0.
-4, 0
Let l = 52 + -155/3. Factor 3*h - l*h**4 - 5/3*h**3 - h**2 + 0.
-h*(h - 1)*(h + 3)**2/3
Factor 14/3*r - 4 - 2/3*r**2.
-2*(r - 6)*(r - 1)/3
Let a = 2211/4 + -552. Find w, given that 0 - 1/4*w + 3/4*w**3 - a*w**2 + 11/4*w**4 + 3/2*w**5 = 0.
-1, -1/3, 0, 1/2
Solve -d**4 - 3*d**2 - 7*d + 7*d + d**2 - 3*d**3 = 0 for d.
-2, -1, 0
Let o(d) be the second derivative of d**6/300 - d**5/75 + d**2/2 - 2*d. Let m(p) be the first derivative of o(p). Let m(t) = 0. Calculate t.
0, 2
Let g(o) = -o**3 + o**2 + o + 6. Let j be g(0). Let z = j - 4. Suppose -q + 3*q**2 + 3*q - 5*q**z = 0. What is q?
0, 1
Factor -13*b**5 + 12*b**2 + 8*b + 100*b**4 - 46*b**3 - 28*b**3 - 10*b**3 - 23*b**5.
-4*b*(b - 1)**3*(9*b + 2)
Let t be (3 - 3/2)/(2/4). Let p(o) be the third derivative of 0*o - 1/3*o**t - 1/24*o**4 + 1/60*o**5 + 0 + o**2. Determine r, given that p(r) = 0.
-1, 2
Let u = 6/17 + -1/51. Let x(n) be the first derivative of -4*n - 2*n**2 - u*n**3 + 4. Factor x(t).
-(t + 2)**2
Find y such that 0*y - 1/6*y**3 - 1/6*y**4 + 1/6*y**5 + 0 + 1/6*y**2 = 0.
-1, 0