ive of c**6/30 - 4*c**5/15 - c**4/6 + 8*c**3/3 + 35*c**2. Factor z(x).
4*(x - 4)*(x - 1)*(x + 1)
Let x be 5/(-35) + 72/14. Suppose 0*k = x*k. Factor -1/3 + 0*d + k*d**3 + 2/3*d**2 - 1/3*d**4.
-(d - 1)**2*(d + 1)**2/3
Let b(d) = 1 + 0*d + 3*d**2 - d - d. Let k be b(1). Determine v, given that -3*v + v**k + 5 + 3*v - 4 + 2*v = 0.
-1
Let a be ((-18)/(-60))/(12/5). Let o(f) be the first derivative of -2 + a*f**4 + 0*f**3 - 1/4*f**2 + 0*f. Factor o(p).
p*(p - 1)*(p + 1)/2
Let w = -5 - -8. Suppose -o = 10 - 31. What is h in 22*h**3 - 9*h - 15*h + 0*h + o*h**5 - 84*h**2 - 4*h**w + 69*h**4 = 0?
-2, -2/7, 0, 1
Let y(g) be the third derivative of 0 + 1/30*g**5 + 0*g**4 + 0*g**3 + 1/60*g**6 + 0*g + g**2. Suppose y(h) = 0. Calculate h.
-1, 0
Let j = -219/4 + 55. Suppose 1/4 + j*f**3 - 1/4*f - 1/4*f**2 = 0. What is f?
-1, 1
Let q(k) be the second derivative of k**6/60 - k**4/4 + 2*k**3/3 - 3*k**2/4 + 13*k - 2. Determine z so that q(z) = 0.
-3, 1
Let b(g) be the second derivative of -g**4/6 - 3*g**3 - 8*g**2 + 3*g - 4. Factor b(q).
-2*(q + 1)*(q + 8)
Let s(c) be the second derivative of c**8/36960 - c**6/3960 - 7*c**4/12 - c. Let q(z) be the third derivative of s(z). What is h in q(h) = 0?
-1, 0, 1
Let f(n) be the second derivative of n**5/15 - n**4/6 - 3*n**2 + 4*n. Let w(k) be the first derivative of f(k). Factor w(x).
4*x*(x - 1)
Suppose 2*q + 2*q + 2 = c, -5*c + 32 = 2*q. Let -o**4 + 8*o - 4*o + c*o**2 + 4*o**3 + 2*o**4 + 1 = 0. What is o?
-1
Let a(p) be the first derivative of 0*p + 0*p**2 - 1/4*p**4 + 4 - 1/3*p**3. What is l in a(l) = 0?
-1, 0
Let n(s) be the first derivative of s**6/3 - 6*s**5/25 - s**4/5 - 7. Factor n(b).
2*b**3*(b - 1)*(5*b + 2)/5
Let z = -404/9 - -2047/45. Factor -z + 0*g + 3/5*g**2.
3*(g - 1)*(g + 1)/5
Let w(s) be the second derivative of 5*s**4/12 - 10*s**3 + 90*s**2 - 25*s. Solve w(h) = 0.
6
Suppose -6*l + l = -2*x - 21, 3*x = -3*l. Factor 5*u**l - 2*u - 4*u**3 + 0*u - u**2.
u*(u - 2)*(u + 1)
Suppose 0 = 2*v + 4*c - 28, -c = -5*v + 2*c + 5. Solve -5*a**v - a - a + 6*a**4 - 3*a**2 = 0.
-1, 0, 2
Let h(d) = -2*d**2 + 24*d - 75. Let u(w) = -10*w**2 + 120*w - 374. Let l(x) = -14*h(x) + 3*u(x). Factor l(g).
-2*(g - 6)**2
Let a = 33 + -28. Find p such that -3/4*p**3 - 7/4*p**4 - 1/2*p + 0 + 7/4*p**2 + 5/4*p**a = 0.
-1, 0, 2/5, 1
Let o(k) = 3*k**2 - k - 4. Let a be o(-2). Solve 6*n**2 - 12*n - 4*n**2 - 3*n**3 + a*n**2 = 0.
0, 2
Let k(y) be the second derivative of -1/20*y**5 - 5*y + 0 + 0*y**2 + 1/60*y**6 + 1/6*y**3 - 1/24*y**4. Suppose k(p) = 0. What is p?
-1, 0, 1, 2
Suppose -4 = -3*m + 2. Let p = -3 - -5. Factor 0 + 3 - 2*g**m + 1 - p*g.
-2*(g - 1)*(g + 2)
Factor 1/2*d**3 - 1/2*d**2 + 0 + 1/2*d**4 - 1/2*d.
d*(d - 1)*(d + 1)**2/2
Let f be 1/(-4) + 19/12. Let j = -1453 + 1453. Factor -f*q**3 + j*q**2 - 2/3*q**4 + 2/3 + 4/3*q.
-2*(q - 1)*(q + 1)**3/3
Let g be 36/(-27) - (-38)/6. Suppose 2*q + 3*q - 40 = 0. Factor 0*n**2 + q*n**3 - 3 + 3*n**5 - 6*n - 4*n**2 - 5*n**g + 7.
-2*(n - 1)**3*(n + 1)*(n + 2)
Suppose 3*o + 2*o = 0. Let d(h) be the third derivative of -1/48*h**4 + o + 1/240*h**6 - h**2 + 0*h + 0*h**3 + 0*h**5. Find y such that d(y) = 0.
-1, 0, 1
Find a such that 5*a**2 + 7*a - a - 5 + 5*a**3 - 11*a = 0.
-1, 1
Let g(x) be the first derivative of -x**7/105 - x**6/30 + x**5/30 + x**4/6 - x**2/2 + 5. Let z(p) be the second derivative of g(p). Factor z(i).
-2*i*(i - 1)*(i + 1)*(i + 2)
Let n(d) = 2*d**3 + d + 1. Let m(a) = 9*a**3 - 6*a**2 - 7*a - 3. Let p(u) = 3*m(u) - 15*n(u). Factor p(y).
-3*(y + 2)**3
Let c be 1/2*24/6. Let o(x) be the second derivative of x**3 - 1/6*x**4 - x - c*x**2 + 0. Factor o(t).
-2*(t - 2)*(t - 1)
Let r(m) be the first derivative of 1/6*m**3 - 1/8*m**4 + 2 + 0*m + 0*m**2. Factor r(b).
-b**2*(b - 1)/2
Let a(x) = 3*x + 16. Let q be a(-4). Let g(n) be the second derivative of -1/80*n**5 - 1/8*n**2 + 0 - 3*n - 1/16*n**q - 1/8*n**3. Factor g(v).
-(v + 1)**3/4
Let a = 22 + -18. Let 10 - z**a + 4*z**3 - 10 = 0. What is z?
0, 4
Let m(h) be the first derivative of 0*h**5 + 0*h - 1/21*h**6 + 1/14*h**4 + 0*h**3 + 1 + 0*h**2. Suppose m(b) = 0. What is b?
-1, 0, 1
Let t = 2 + 1. Factor 2*p**2 + 84*p - 84*p - t*p**2.
-p**2
Let w(h) be the first derivative of -h**6/18 - h**5/15 - 2. Factor w(x).
-x**4*(x + 1)/3
Let m(v) be the second derivative of v**4/42 + 13*v**3/21 - 2*v**2 - 2*v + 11. Factor m(g).
2*(g - 1)*(g + 14)/7
Suppose -8*b = -b. Let c(z) be the first derivative of 0*z**2 - 32/15*z**5 + 3 - 4/9*z**3 + b*z - 7/9*z**6 - 11/6*z**4. Factor c(f).
-2*f**2*(f + 1)**2*(7*f + 2)/3
Let m(v) be the second derivative of 2/3*v**3 - v**2 - 1/6*v**4 + 0 - 9*v. Solve m(x) = 0 for x.
1
Suppose -6*y + 46 + 2 = 0. Suppose -y*w - 6 = -22. Factor -1/4*p + 0 + 0*p**w + 1/4*p**3.
p*(p - 1)*(p + 1)/4
Let u(l) be the first derivative of 2*l**5/25 - l**4/5 - 2*l**3/5 + 4*l**2/5 + 8*l/5 + 54. Factor u(s).
2*(s - 2)**2*(s + 1)**2/5
Let -2*z**2 - 72 - 5*z - 3*z + 16*z + 16*z = 0. Calculate z.
6
Let d(y) be the third derivative of -y**8/672 + y**6/80 - y**5/60 + 5*y**2. Factor d(r).
-r**2*(r - 1)**2*(r + 2)/2
Let d(v) be the second derivative of v**5/100 - v**4/30 - v**3/10 - 26*v. What is g in d(g) = 0?
-1, 0, 3
Let v(i) be the second derivative of -i**6/6 + 3*i**5/4 - 5*i**4/6 + 12*i. Solve v(y) = 0 for y.
0, 1, 2
Let s be ((-3)/(-54)*1)/((-10)/(-40)). Factor -8/9 - 10/9*m**2 - s*m**3 - 16/9*m.
-2*(m + 1)*(m + 2)**2/9
Let o(s) be the second derivative of -s**4/36 + s**3/9 + s. Suppose o(j) = 0. Calculate j.
0, 2
Let n be 2/3 - (-32)/(-12). Let x = n - -4. Determine f so that 4*f**2 - x - f**2 - f - 2*f**2 = 0.
-1, 2
Let v(s) = -4 + s**2 + 4 - 3*s**3 - s - 1 + 4. Let f(k) = -15*k**3 + 6*k**2 - 6*k + 15. Let u(j) = -4*f(j) + 21*v(j). Factor u(h).
-3*(h - 1)*(h + 1)**2
Let a(t) be the first derivative of 3*t**5/7 - 9*t**4/28 - t**3 + 9*t**2/14 + 6*t/7 + 2. Solve a(q) = 0 for q.
-1, -2/5, 1
Let d be (((-4)/(-6))/2)/(-20 + 21). Let a be 2/3 - 2/6. Determine j, given that -1/3*j**3 + a*j**2 + 1/3*j + 0 - d*j**4 = 0.
-1, 0, 1
Let -39*m - 4*m**3 + 20*m**2 - 50 + 10*m**3 + 4*m - m**3 = 0. Calculate m.
-5, -1, 2
Let v(h) be the second derivative of 0 + 0*h**2 + 0*h**4 + 0*h**5 - 1/84*h**7 + 0*h**6 + 3*h + 0*h**3. Factor v(c).
-c**5/2
Let k(u) be the first derivative of -2/35*u**5 - 2/7*u**2 + 0*u**4 - 2 + 0*u + 2/7*u**3. Factor k(v).
-2*v*(v - 1)**2*(v + 2)/7
Let w = 2 - -2. Suppose -29 = -5*l + 3*h + 13, -4*l + w = 5*h. Let -l*t**2 - 2*t + 0*t**2 + 2 + 4*t**2 + 2*t**3 + 0*t**3 = 0. What is t?
-1, 1
What is v in -4/9*v**3 - 1/9*v**5 + 0*v**2 + 0*v - 5/9*v**4 + 0 = 0?
-4, -1, 0
Let l(y) be the first derivative of y**6/21 + 8*y**5/35 + 5*y**4/14 + 4*y**3/21 - 9. Let l(z) = 0. What is z?
-2, -1, 0
Find y such that -12*y**3 + 13 - 3 + 12*y - 1 - 6*y**2 - 5*y**4 + 2*y**4 = 0.
-3, -1, 1
Let i(x) be the first derivative of -2*x**3/45 + x**2/3 - 28. Factor i(m).
-2*m*(m - 5)/15
Let z(c) be the third derivative of c**6/120 + c**5/12 + c**4/8 - 2*c**3/3 - 2*c**2. Let h be z(-3). Factor 5*q**2 - 3*q**2 + q**2 - h*q**2.
-2*q**2
Solve 0 - 36/5*o**3 - 3/5*o**5 - 9/5*o + 6*o**2 + 18/5*o**4 = 0 for o.
0, 1, 3
Let l(z) = -z**5 - z**4 - 8*z**2 - 8*z + 8. Let u(y) = -y**5 - y**4 - 5*y**2 - 5*y + 5. Suppose 0 = -5*m - 12 + 52. Let g(b) = m*u(b) - 5*l(b). Factor g(k).
-3*k**4*(k + 1)
Determine k, given that 33*k**4 + 45*k**3 + k + 123*k**2 + 93*k**3 + 17*k = 0.
-3, -1, -2/11, 0
Let l be (-90)/(-25) + (-3 - 0). Let j(a) be the first derivative of -3*a**3 + 6*a + 4 - 3/4*a**4 + 3/2*a**2 + l*a**5. Factor j(r).
3*(r - 2)*(r - 1)*(r + 1)**2
Let t(x) be the second derivative of 0 + 0*x**3 - 1/24*x**4 - 3/80*x**5 + 1/24*x**6 + 0*x**2 - 3*x. Factor t(q).
q**2*(q - 1)*(5*q + 2)/4
Let s(q) = q + 1. Let f be s(3). Suppose f*p**3 + p**3 - 4*p**3 = 0. Calculate p.
0
Let u(s) be the first derivative of s**7/1680 - s**6/360 + s**5/240 - 2*s**3/3 + 1. Let i(b) be the third derivative of u(b). Factor i(p).
p*(p - 1)**2/2
Let z(t) be the third derivative of -t**7/280 + t**6/60 + t**5/40 - t**4/4 - 4*t**3/3 - 4*t**2. Let m(r) be the first derivative of z(r). Factor m(w).
-3*(w - 2)*(w - 1)*(w + 1)
Suppose -342*o**3 - 2*o**2 + o + o**5 - o + 341*o**3 + 2*o**4 = 0. Calculate o.
-2, -1, 0, 1
Let a(h) = -5*h**3 + 8*h**2 - 7*h - 2. Let n(f) = -9*f**3 + 15*f**2 - 13*f - 4. Let o(q) = -11*a(