*2 + 64*d - 6. Suppose f(j) = 0. Calculate j.
-4
Let q(v) = 12*v**5 - 56*v**4 + 52*v**3 - 16*v**2. Let p(d) = 8*d**5 - 37*d**4 + 35*d**3 - 11*d**2. Let u(t) = 8*p(t) - 5*q(t). Suppose u(n) = 0. Calculate n.
0, 1, 2
Let m(k) be the first derivative of -k**8/6720 + k**7/1120 - k**6/1440 - k**5/160 + k**4/48 - k**3 - 2. Let t(w) be the third derivative of m(w). Factor t(a).
-(a - 2)*(a - 1)**2*(a + 1)/4
Let i(c) be the third derivative of c**6/24 + c**5/4 + 5*c**4/8 + 5*c**3/6 + 32*c**2. Determine h, given that i(h) = 0.
-1
Let r(v) be the first derivative of 0*v + 1/12*v**3 + 1/8*v**2 + 1. Factor r(h).
h*(h + 1)/4
Let s(x) be the second derivative of 5*x**4/6 - 8*x**3/9 + x**2/3 + x. Factor s(o).
2*(3*o - 1)*(5*o - 1)/3
Determine s, given that s**2 - 4*s**3 - 5*s**2 + 2*s**2 + 2*s**3 + 4*s = 0.
-2, 0, 1
Let z(y) be the second derivative of y**9/45360 + y**8/6720 + y**7/2520 + y**6/2160 - y**4/12 + y. Let h(n) be the third derivative of z(n). Factor h(w).
w*(w + 1)**3/3
Let r(a) be the second derivative of 3*a**5/20 + a**4/10 + 8*a. Let r(u) = 0. What is u?
-2/5, 0
Let h be ((-1)/1)/(4/(-60)). Let c be 1/2 + h/10. Factor -p**c + 4*p + 1 - 4*p + 1 - p.
-(p - 1)*(p + 2)
Factor -z**3 + 0*z + 0 + z**4 - 1/3*z**5 + 1/3*z**2.
-z**2*(z - 1)**3/3
Factor 11*h + 4*h - 4 + 14 + 5*h**2.
5*(h + 1)*(h + 2)
Suppose -2*j + 6*j = 20. Factor -2/3*t + 2/3 + 4/3*t**3 - 4/3*t**2 - 2/3*t**j + 2/3*t**4.
-2*(t - 1)**3*(t + 1)**2/3
Let a(h) be the first derivative of -1/12*h**4 + 0*h**3 + 1/6*h**2 + 1 + 0*h. Factor a(v).
-v*(v - 1)*(v + 1)/3
Let p be (1/2)/((-3)/(-96)). Suppose 3*u + 14 = 5*d - u, -2*d + p = u. Factor -3*m + 2*m**3 - 3*m**2 + d*m**2 + m + 3*m**3.
m*(m + 1)*(5*m - 2)
Factor 6*p**2 - 7*p**2 + 2*p**2 + 2*p + 1.
(p + 1)**2
Let c = -13 + 13. Suppose 2*w - 2*p - 2 = c, -p + 2 = -w + 3*p. Find a such that 2/3*a + 2/3*a**w + 0 = 0.
-1, 0
Let k = 125 - 123. Let m(a) be the third derivative of -2*a**k + 1/12*a**4 + 0*a**5 + 1/210*a**7 + 0*a - 1/6*a**3 + 0 - 1/60*a**6. Factor m(i).
(i - 1)**3*(i + 1)
Factor -f**2 + 3*f**5 + f**2 + 3*f**4 + 3*f**3 - 9*f**4.
3*f**3*(f - 1)**2
Let s(c) be the first derivative of -5 + 1/2*c**3 + 3/2*c - 3/2*c**2. Factor s(q).
3*(q - 1)**2/2
Suppose 8/7 - 20/7*a**3 + 10/7*a**2 + 24/7*a - 18/7*a**4 - 4/7*a**5 = 0. What is a?
-2, -1, -1/2, 1
Let c(s) = -2*s**2 + 2*s**2 + 0*s**2 + 2*s - 9*s**2. Let r(n) = 4*n**2 - n. Let p(i) = 6*c(i) + 14*r(i). Factor p(j).
2*j*(j - 1)
Let g(v) be the second derivative of 2/35*v**5 + 0*v**4 + 0*v**2 + 1/147*v**7 + 0 + 4*v + 0*v**3 + 4/105*v**6. Factor g(y).
2*y**3*(y + 2)**2/7
Let r(u) = 3*u + 3*u**2 - 2*u**3 - 4*u**2 - 2*u + u**3. Let g be r(0). Determine c so that -1/4*c**2 + g + 1/4*c - 1/4*c**3 + 1/4*c**4 = 0.
-1, 0, 1
Let g(j) be the first derivative of 28*j**6/27 - 2*j**5/45 - j**4/9 + 28. Let g(b) = 0. Calculate b.
-1/4, 0, 2/7
Factor -322*c**4 + 644*c**4 + 2*c**3 - 8*c + 3*c**2 + 4 - 323*c**4.
-(c - 2)*(c - 1)**2*(c + 2)
Factor -1/9*h**2 - 1/9*h**3 + 0*h + 0 + 1/9*h**4 + 1/9*h**5.
h**2*(h - 1)*(h + 1)**2/9
Suppose -14*t = -28 - 28. Let l(v) be the second derivative of 8*v**2 - t*v + 0 - 1/10*v**5 + 4/3*v**3 - 1/3*v**4. Find f such that l(f) = 0.
-2, 2
Factor -4/13 + 4/13*i**3 + 4/13*i**4 + 14/13*i - 16/13*i**2 - 2/13*i**5.
-2*(i - 1)**4*(i + 2)/13
Suppose 3*d - 5 = 16. Suppose -4 = p - d. Let 7*c**2 + 0*c**2 - p*c**2 - 2*c**2 = 0. Calculate c.
0
Suppose 0 = -5*v - 17 + 32. Solve -8/7*k**v + 6/7*k**2 - 8/7 + 2/7*k**4 + 8/7*k = 0 for k.
-1, 1, 2
Let g be (-7)/14*8/1. Let k = -1 - g. What is c in -c - 6*c**3 - c**5 + k*c**2 + c**2 + 0*c + 4*c**4 = 0?
0, 1
Let r(w) be the third derivative of -w**5/45 - 4*w**4/9 - 32*w**3/9 + 16*w**2. Determine b, given that r(b) = 0.
-4
Let n(d) = -9*d**2 + 6*d - 2. Let o(k) = -4*k**2 + 3*k - 1. Let g(j) = j + 1. Let i be g(2). Let r = i - 1. Let x(t) = r*n(t) - 5*o(t). Factor x(w).
(w - 1)*(2*w - 1)
Let r = 11 - 9. Let u be r/(-8) + (-18)/(-8). Find k, given that -1/2*k**3 + 0*k**u + 1/2*k**4 + 0*k + 0 = 0.
0, 1
Let n = 1 - -2. Suppose -n*x + 4*o + 32 = 0, 5*o + 42 - 17 = 0. Determine l so that -2 + x*l**2 + 0 - 2*l**2 = 0.
-1, 1
Let h be 2*(2/12 - 0). Let x be (2/18)/((-5)/(-15)) + 0. Factor x*b**2 + 2/3*b + h.
(b + 1)**2/3
Let v(z) be the third derivative of z**8/588 - z**7/147 + z**6/140 + z**5/210 - z**4/84 + z**2 - 2. Factor v(b).
2*b*(b - 1)**3*(2*b + 1)/7
Let l(z) be the first derivative of 5/18*z**4 + 4/27*z**3 + 0*z + 2 + 0*z**2. Factor l(p).
2*p**2*(5*p + 2)/9
Let w(j) = 3*j - 30. Let l be w(12). Let h be (0 - 0)*l/(-6). Factor h*a + 4/3*a**2 - 14/3*a**3 + 16/3*a**4 - 2*a**5 + 0.
-2*a**2*(a - 1)**2*(3*a - 2)/3
Let a(z) = 4*z**2 + 2*z - 3. Suppose -3*g - 30 = 2*g. Let q(b) = 7*b**2 + 3*b - 5. Let u(t) = g*q(t) + 10*a(t). Solve u(d) = 0.
0, 1
Suppose 2*h - 19 = -3*o - 7, -5*o + 22 = 4*h. Factor -2*b**2 + h + 0 - 1.
-2*(b - 1)*(b + 1)
Let r be -4 - -1 - (-18)/(-6). Let j(l) = -5*l**2 + 10*l + 4. Let b(m) = 14*m**2 - 29*m - 12. Let g(k) = r*b(k) - 17*j(k). Factor g(v).
(v + 2)**2
Determine d so that -d**2 + 16 + d**2 - 4*d**2 = 0.
-2, 2
Let l(r) be the second derivative of -5/6*r**3 - 3*r - r**2 - 1/4*r**4 + 0. Suppose l(v) = 0. What is v?
-1, -2/3
Solve -4/5*g - 24/5 + 4/5*g**2 = 0.
-2, 3
Let t(i) be the second derivative of i**5/60 - i**4/18 - 4*i. Solve t(p) = 0 for p.
0, 2
Determine z, given that 7*z**2 - 74*z**5 + 5*z**2 + 70*z**5 - 7*z**3 + 20*z - 18*z**4 + 6 - 9*z**3 = 0.
-3, -1, -1/2, 1
Let v(d) = -d**4 + d**3 - 4*d**2 + 4*d. Let i(c) = c**4 - c**3 + 6*c**2 - 6*c. Let x(b) = -5*i(b) - 7*v(b). What is f in x(f) = 0?
-1, 0, 1
Find v, given that 0*v**4 + 0*v**4 - 4*v**3 + 3*v**4 - v**4 = 0.
0, 2
Suppose -3*s**4 - 41/7*s**3 - 4/7*s + 0 - 24/7*s**2 = 0. What is s?
-1, -2/3, -2/7, 0
Let u(s) be the third derivative of s**7/1260 - s**6/120 + s**5/30 + s**4/4 + 4*s**2. Let v(d) be the second derivative of u(d). Suppose v(q) = 0. What is q?
1, 2
Let q(y) be the second derivative of -y**4/4 - y**3/2 - 4*y. Factor q(d).
-3*d*(d + 1)
Suppose -5*h + 10 = -5*x, -4*h = 27 - 11. Let b be 2/(-6) - 2/x. Determine r so that -2/5*r**3 - 2/5*r - 4/5*r**2 + b = 0.
-1, 0
Let d = 84/13 + -827/130. Let k(m) be the second derivative of 0*m**3 + 1/6*m**4 - d*m**5 - 1/4*m**6 + 2*m + 0*m**2 + 0. Suppose k(f) = 0. What is f?
-2/3, 0, 2/5
Factor 2/5*z - 2/5*z**3 - 4/5 + 4/5*z**2.
-2*(z - 2)*(z - 1)*(z + 1)/5
Let w(i) be the first derivative of i**6/9 + 4*i**5/5 + 13*i**4/6 + 8*i**3/3 + 4*i**2/3 + 72. Factor w(z).
2*z*(z + 1)**2*(z + 2)**2/3
Let b be ((-24)/(-70))/((-12)/(-40)). Factor -8/7*k - b + 4/7*k**3 + 6/7*k**2 - 2/7*k**4.
-2*(k - 2)**2*(k + 1)**2/7
Let f(g) be the first derivative of g**6/8 - 3*g**5/10 + 13. Let f(w) = 0. What is w?
0, 2
Factor -8/5*d**3 - 12/5*d**4 + 0 - 4/5*d**5 + 0*d**2 + 0*d.
-4*d**3*(d + 1)*(d + 2)/5
Let z = -1 - -2. Let g be z - 3 - 2*-2. Factor -5 - 16*x - 32*x**g + 3 + 0.
-2*(4*x + 1)**2
Factor 28*f**3 + 35*f**4 + 11*f**2 + 4*f**2 - 45*f**2 + 67*f**3.
5*f**2*(f + 3)*(7*f - 2)
Let b = -869/3 - -299. Let -4/3*z**5 - 6*z**2 - 4/3*z - 6*z**4 + 0 - b*z**3 = 0. Calculate z.
-2, -1, -1/2, 0
Let z(k) be the first derivative of -46/35*k**5 - 27/14*k**4 - 2 + 0*k - 2/7*k**2 - 26/21*k**3 - 1/3*k**6. Find s such that z(s) = 0.
-1, -2/7, 0
Suppose 90 = 3*m + 4*s, 0 = 2*m + 2*s - 4*s - 60. Let m*q**2 + 7*q**3 - 33*q**2 + 2*q**3 + 3*q**5 - 9*q**4 = 0. What is q?
0, 1
Let r(p) be the third derivative of p**6/900 - p**4/60 - p**3/2 + p**2. Let l(y) be the first derivative of r(y). Factor l(s).
2*(s - 1)*(s + 1)/5
Let s(h) be the second derivative of -h**4/12 - 3*h**2/2 - h. Let q(p) = 3*p**2 + p + 10. Let g(t) = 4*q(t) + 14*s(t). Factor g(r).
-2*(r - 1)**2
Let h(t) be the first derivative of t**6/60 + t**5/10 + 7*t**4/40 + t**3/10 - 16. Factor h(v).
v**2*(v + 1)**2*(v + 3)/10
Let f be 4*-3*(-2 - 10/(-6)). Let m(i) be the second derivative of 1/18*i**3 + 0*i**2 + 0*i**f + i + 0 - 1/30*i**5 + 0*i**6 + 1/126*i**7. Factor m(p).
p*(p - 1)**2*(p + 1)**2/3
Let p = -421 + 425. Factor 2/11*t**p + 0 - 2/11*t**2 + 0*t + 0*t**3.
2*t**2*(t - 1)*(t + 1)/11
Let o(j) be the first derivative of 3*j**4/4 - j**3/2 - 6*j**2 + 6*j - 17. Factor o(x).
3*(x - 2)*(x + 2)*(2*x - 1)/2
Let v(o) = -3*o**2 + 6*o - 7. Let j(a) be the second derivative of -3*a**4/4 + 3*a**3 - 10*a**2 - 4*a. Let 