k - 1)**3
Factor 1/3*f**2 + 0 + 1/3*f**3 - 2/3*f.
f*(f - 1)*(f + 2)/3
Let r(m) be the second derivative of -2*m**7/105 + 2*m**6/75 + 2*m**5/25 - 4*m - 9. What is q in r(q) = 0?
-1, 0, 2
Let x(o) be the first derivative of -5*o**4/4 - 32*o**3/3 + 4*o**2 + 8*o - 26. Let w(h) = 3*h**3 + 21*h**2 - 5*h - 5. Let f(i) = 8*w(i) + 5*x(i). Factor f(z).
-z**2*(z - 8)
Let y(x) be the second derivative of 13*x**5/20 + 15*x**4/8 + x**3 - 2*x**2 + 6*x. Let c(m) be the first derivative of y(m). Factor c(w).
3*(w + 1)*(13*w + 2)
Suppose 0*m + 3*m = 6. Let j be (6/(-15))/(m/(-10)). Factor -3 - 6*w - w**2 + 0*w**j - 6.
-(w + 3)**2
Solve -8/3*b**2 + 0*b + 0*b**3 + 2/3*b**4 + 0 = 0.
-2, 0, 2
Let t be 1*-5*3/(-5). Factor s**3 + 0*s**3 - 4*s**t + 15*s**2 + 12*s**2.
-3*s**2*(s - 9)
Let n(t) be the third derivative of -14*t**2 + 0*t**4 + 1/105*t**7 + 1/15*t**5 - 1/20*t**6 + 0*t**3 + 0*t + 0. Factor n(h).
2*h**2*(h - 2)*(h - 1)
Let c = 1 + 2. Suppose 22*b = 20*b + 4. Factor c*l**4 + l**5 + 267 - 4*l**b - 267.
l**2*(l - 1)*(l + 2)**2
Let g(x) be the second derivative of x**6/45 + x**5/30 - 7*x**4/18 - 13*x**3/9 - 2*x**2 - 14*x - 4. Find h such that g(h) = 0.
-2, -1, 3
Let v(o) be the first derivative of 4/5*o - 21 + 2/5*o**2 - 1/5*o**3. Suppose v(z) = 0. Calculate z.
-2/3, 2
Factor 1/3*h**2 + 0*h + 0 + 1/6*h**5 - 1/3*h**4 - 1/6*h**3.
h**2*(h - 2)*(h - 1)*(h + 1)/6
Let k(w) = -28*w - 616. Let h be k(-22). What is i in 9/7*i**2 + 0*i - 2/7*i**5 - 11/7*i**4 + h - 12/7*i**3 = 0?
-3, 0, 1/2
Let i(v) be the second derivative of 21*v + 0 + 1/8*v**2 + 1/96*v**4 + 1/16*v**3. Factor i(a).
(a + 1)*(a + 2)/8
Suppose 2*h + 308 = 2*u, 5*u - 2*h - 761 = -0*h. Find w such that -u*w**2 + 155*w**2 + 4*w + 0*w = 0.
-1, 0
Suppose 0 = -2*i + 3*m + 14, -2*m + m - 5 = -i. Let l be 0 - i - 8/(-2). Factor 0*b**5 + 14*b**2 + 18*b**l + 10*b**4 + 4*b - b**5 - b**5 + 4*b**5.
2*b*(b + 1)**3*(b + 2)
Let k(r) be the second derivative of r**6/300 - r**4/20 + 2*r**3/15 - 3*r**2/2 - 11*r. Let s(x) be the first derivative of k(x). Let s(v) = 0. Calculate v.
-2, 1
Let d = -1006 - -1009. Factor -3/5*s**4 - 6/5*s**d + 0 + 3/5*s**2 + 6/5*s.
-3*s*(s - 1)*(s + 1)*(s + 2)/5
Let m(i) be the third derivative of -i**4/24 + i**3/3 + 8*i**2. Let t be m(-8). Factor 5*h + h - 4*h**2 + t*h - 12.
-4*(h - 3)*(h - 1)
Let l(t) be the first derivative of 2*t**5 - 25*t**4/4 + 5*t**3 + 5*t**2/2 - 5*t + 6. Factor l(c).
5*(c - 1)**3*(2*c + 1)
Factor 2/11*a**4 + 32/11 + 38/11*a**3 + 102/11*a**2 + 98/11*a.
2*(a + 1)**3*(a + 16)/11
Let k = 23136/38585 - -3/7717. Factor 0*u + k*u**2 - 3/5.
3*(u - 1)*(u + 1)/5
Let z(f) be the second derivative of -3*f**8/2240 - f**7/224 - f**6/480 + f**5/160 - 13*f**3/3 - 30*f. Let s(u) be the second derivative of z(u). Factor s(x).
-3*x*(x + 1)**2*(3*x - 1)/4
Let r = -259/416 + 19247/18720. Let o = 7/36 + r. Suppose -o*b**4 + 0 + 0*b + 0*b**2 + 6/5*b**3 = 0. What is b?
0, 2
Let s be (6 - (-4)/4) + -4. Suppose -30 = -6*c + s*c. Solve 26 + 4*p - 14 - c + 2*p**2 = 0 for p.
-1
Let d be (-30)/(-48)*(-6)/(-15). Let q(s) be the first derivative of 1 + 0*s**3 + 0*s + 1/8*s**4 + 0*s**2 - d*s**5. Factor q(u).
-u**3*(5*u - 2)/4
Let u = 49/2 + -24. Let v(l) = -4*l**2 - 11*l - 3. Let s be v(-2). Suppose -1/4*c + 1/4*c**s + 3/4*c**2 - u - 1/4*c**4 = 0. Calculate c.
-1, 1, 2
Let r(b) be the second derivative of 0*b**3 + 16*b - 1/30*b**6 + 0*b**2 - 3/20*b**5 - 1/6*b**4 + 0. Suppose r(l) = 0. What is l?
-2, -1, 0
Let d(s) be the first derivative of -s**6/60 + s**5/15 + s**4/12 - 2*s**3/3 - 2*s**2 + 12. Let t(q) be the second derivative of d(q). Solve t(z) = 0 for z.
-1, 1, 2
Suppose -25 + 26 = u. Let j be u/(0 - 5/(-130)). Suppose 10*a**3 - 15*a - 15*a + j*a - 6*a**2 = 0. Calculate a.
-2/5, 0, 1
Let a(k) be the third derivative of -k**6/75 - 19*k**5/75 + 79*k**4/240 - k**3/6 - k**2 + 135. Find w, given that a(w) = 0.
-10, 1/4
Let l(j) = -1. Let r(x) = -2*x**2 - 38*x - 4. Let n(q) = l(q) - r(q). Let h be n(-19). Find s such that -s**4 - 7/5*s**5 - 2/5*s + 9/5*s**h + s**2 + 0 = 0.
-1, 0, 2/7, 1
Suppose -2*o + 5*a = 3*a + 6, 18 = 4*o + 2*a. Solve 0*k**o + k**2 + 0*k**2 = 0 for k.
0
Let w be (-2)/(14/(-3)) - 165/385. Let o(h) be the third derivative of 0 - 1/300*h**6 - 1/25*h**5 + h**2 - 3/20*h**4 + w*h**3 + 0*h. Factor o(t).
-2*t*(t + 3)**2/5
Let l(q) = 18*q**4 - 26*q**3 - 64*q**2 + 26*q + 72. Let s(j) = -2*j**4 + 3*j**3 + 7*j**2 - 3*j - 8. Let t(r) = 6*l(r) + 52*s(r). Solve t(m) = 0.
-2, -1, 1, 2
Suppose -125 = -54*h - 17. Let r(a) be the third derivative of 0 - 1/24*a**4 + 3*a**h + 1/80*a**5 - 1/840*a**7 - 1/6*a**3 + 1/240*a**6 + 0*a. Factor r(p).
-(p - 2)**2*(p + 1)**2/4
Let m(q) be the first derivative of q**4/16 + 17*q**3/6 - q**2/8 - 17*q/2 + 329. Factor m(c).
(c - 1)*(c + 1)*(c + 34)/4
Let l(k) be the first derivative of 1/2*k + 1/6*k**3 + 3 - 5/8*k**2. Solve l(j) = 0 for j.
1/2, 2
Let g = 42 + -30. Let m = 16 - g. Determine d, given that -2/3 - 4/3*d + 0*d**2 + 2/3*d**m + 4/3*d**3 = 0.
-1, 1
Let a(l) be the first derivative of l**2/2 + l - 6. Let r(b) = b**2 + 9*b + 9. Let q(p) = -18*a(p) + 2*r(p). Factor q(d).
2*d**2
Let u = 321397/201 + -1599. Let y = 611/804 + u. Let -y*n**2 + 3/4*n - 1/4 + 1/4*n**3 = 0. What is n?
1
Suppose -10 = -2*u, 3 = 2*o - 4*o + 3*u. Let h(j) = 5*j**4 + 11*j**3 + 6. Let s(b) = -5*b**4 - 10*b**3 - 5. Let n(a) = o*s(a) + 5*h(a). Factor n(c).
-5*c**3*(c + 1)
What is a in 8*a**2 + 10*a**3 + 140*a - 160 - 20*a**2 - 15*a**3 - 8*a**2 = 0?
-8, 2
Suppose 70*a - 33 = 107. Factor 6/5*z - 9/5 - 1/5*z**a.
-(z - 3)**2/5
Let j(v) be the third derivative of 10/3*v**3 + 0*v + 1/12*v**5 - 5/6*v**4 + 0 - 10*v**2. Solve j(q) = 0 for q.
2
Let r(f) be the third derivative of f**6/150 + f**5/90 - f**4/15 + 4*f**3/45 + 2*f**2 - 1. Determine q, given that r(q) = 0.
-2, 1/2, 2/3
Let j(v) be the first derivative of -v**5/4 - 5*v**4/8 - 5*v**3/12 + 32. Let j(q) = 0. What is q?
-1, 0
Let q = -408 - -412. Let t(u) be the second derivative of -1/12*u**q - u**2 + 5*u + 1/2*u**3 + 0. Factor t(w).
-(w - 2)*(w - 1)
Determine k so that 2/5*k**5 - 4/5*k**3 + 2/5*k + 0*k**2 + 0 + 0*k**4 = 0.
-1, 0, 1
Let f(y) be the third derivative of -y**6/80 + 43*y**5/360 + 4*y**4/9 + y**3/3 - 177*y**2. Find z such that f(z) = 0.
-1, -2/9, 6
Let p = 563/784 - 3/784. Factor 2/7 - p*v + 4/7*v**2 - 1/7*v**3.
-(v - 2)*(v - 1)**2/7
Let y(j) be the second derivative of -j**5/70 - j**4/21 + j**3/21 + 2*j**2/7 + j + 90. Suppose y(r) = 0. Calculate r.
-2, -1, 1
Find v, given that 182/15*v**2 - 2/15*v**3 + 0 + 0*v = 0.
0, 91
Let u(p) be the second derivative of 0 - 16*p + 6/5*p**2 - 3/100*p**5 + 7/10*p**3 + 1/10*p**4. Factor u(n).
-3*(n - 4)*(n + 1)**2/5
Suppose m = 2*v + 32, 5*m - 21*v = -18*v + 146. Let -80/3*i**3 - 2/3 - 23/3*i - m*i**2 + 64/3*i**4 = 0. Calculate i.
-1/4, 2
Suppose 3*a - 7 = j + 3, -j - 4*a + 18 = 0. Factor 4 - 2*b**2 - j*b**2 - 8 + 8*b.
-4*(b - 1)**2
Let t(b) be the third derivative of -b**5/20 + b**4 - 6*b**3 + b**2 - 5. Factor t(f).
-3*(f - 6)*(f - 2)
Let m(f) be the third derivative of -f**5/80 - 3*f**4/8 + 7*f**3/2 + 3*f**2 + 1. Factor m(n).
-3*(n - 2)*(n + 14)/4
Let c = -250314/7 + 35760. What is i in 2/7*i - 6/7*i**2 - 4/7*i**5 + c*i**4 + 0 + 2/7*i**3 = 0?
-1, 0, 1/2, 1
Suppose -3*q + 58 = 43. Suppose 2*m + 3*j + 6 = 8*j, 2*m = -q*j + 14. Solve 0 + 0*h**m + 2/3*h**5 + 2/3*h - 4/3*h**3 + 0*h**4 = 0.
-1, 0, 1
Let v(w) be the first derivative of -2*w**3/3 + 3*w**2 + 63. Factor v(l).
-2*l*(l - 3)
Let x = 27455/9449 + 3/859. Determine c so that -16/11*c - x - 2/11*c**2 = 0.
-4
Let a(m) = -m**2 + 19*m - 45. Let o be a(16). Let l(v) be the first derivative of -4 - v**2 - v - 1/3*v**o. Solve l(n) = 0.
-1
Factor 0 + 65*i**3 - 125*i**3 - 24*i + 63*i**3 - 31 + 15*i**2 - 5.
3*(i - 2)*(i + 1)*(i + 6)
Factor -52/5*l**2 + 0*l + 2/5*l**3 + 0.
2*l**2*(l - 26)/5
Let b be (0 - (-60)/18)*123/1025. Let -b*y**4 - 6/5*y**3 + 8/5*y + 0*y**2 + 0 = 0. What is y?
-2, 0, 1
Let b(x) be the first derivative of -x**5/10 - 3*x**4 - 32*x**3 - 128*x**2 - 53. Factor b(m).
-m*(m + 8)**3/2
Factor 25*u**4 + 10*u**4 + 10*u + 20*u**3 - 40*u**4 - 25*u**2.
-5*u*(u - 2)*(u - 1)**2
Let y be (-264)/(-77) - (-8)/14. Let h(r) be the first derivative of -1/3*r**2 + 8 - 4/3*r - 5/6*r**y + 16/9*r**3. Factor h(u).
-2*(u - 1)**2*(5*u + 2)/3
Let q(k) be the third de