k**2 - 12*k - 5. Let s(a) = -21*a**2 + 42*a + 18. Let t(c) = 18*h(c) + 5*s(c). Factor t(m).
3*m*(m - 2)
Let p(d) be the third derivative of -d**5/90 - d**4/9 + 4*d**3/3 - 11*d**2. Factor p(y).
-2*(y - 2)*(y + 6)/3
Let i(q) = 5*q + 52. Let h be i(-10). Find x such that 5/3*x + x**3 - 1/3 - 7/3*x**h = 0.
1/3, 1
Let o(w) be the first derivative of -w**6/3 - 2*w**5/5 + w**4 + 4*w**3/3 - w**2 - 2*w - 12. Factor o(r).
-2*(r - 1)**2*(r + 1)**3
Suppose -5*u + 2*g + 19 = 0, -3*u + 2*g + 3 = 5*g. Factor 0 + 1/2*i**u - 1/2*i**2 - i.
i*(i - 2)*(i + 1)/2
Let h(c) = -3*c**3 - 25*c**2 + 34*c + 28. Let n(l) = -2*l**3 - 17*l**2 + 23*l + 18. Let m(i) = 5*h(i) - 7*n(i). Let m(p) = 0. What is p?
-7, -1, 2
Suppose 134*a - 136*a = 0. Factor 1/2*f**3 - 1/2*f + a*f**2 + 0.
f*(f - 1)*(f + 1)/2
Suppose 0*i + 2*i = 6. Suppose -6*f**4 - 56/9*f**2 + 0 - 34/3*f**i - 8/9*f = 0. Calculate f.
-1, -2/3, -2/9, 0
Let q(c) be the third derivative of -c**6/80 - c**5/120 + 5*c**4/12 - c**3 + c**2. Factor q(p).
-(p - 2)*(p + 3)*(3*p - 2)/2
Factor -4/7*h**4 + 2/7*h**5 + 2/7*h**3 + 0*h + 0 + 0*h**2.
2*h**3*(h - 1)**2/7
Let g(r) be the third derivative of -r**8/80640 - r**7/5040 - r**6/720 + r**5/60 + r**2. Let x(h) be the third derivative of g(h). Solve x(l) = 0 for l.
-2
Let l be 2/(-6)*(-6)/10. Solve 0*v - l*v**3 + 0 + 1/5*v**2 = 0 for v.
0, 1
Let j(f) = -8*f**2 - 32*f - 24. Let g(t) be the second derivative of -t**4/6 - 4*t**3/3 - 3*t**2 - 7*t. Let p(y) = -22*g(y) + 6*j(y). What is k in p(k) = 0?
-3, -1
Let m(r) = 21*r**4 + 18*r**3 - 81*r**2 - 24*r - 18. Let d(q) = -6*q**4 - 5*q**3 + 23*q**2 + 7*q + 5. Let l(j) = 18*d(j) + 5*m(j). Solve l(h) = 0 for h.
-1, 0, 2
Let f(c) be the first derivative of c**6/21 + 8*c**5/35 + 2*c**4/7 - 26. Find t such that f(t) = 0.
-2, 0
Let x(l) = 18*l**4 - 7*l**3 - 54*l**2 + 77*l - 29. Let y(h) = -9*h**4 + 3*h**3 + 27*h**2 - 39*h + 15. Let p(m) = 3*x(m) + 5*y(m). Factor p(o).
3*(o - 1)**2*(o + 2)*(3*o - 2)
Let x(b) be the first derivative of 1/11*b**2 - 4/33*b**3 + 0*b + 4 + 1/22*b**4. Let x(q) = 0. What is q?
0, 1
Let m(x) be the first derivative of 4*x**5/5 - 4*x**3/3 - 8. Factor m(i).
4*i**2*(i - 1)*(i + 1)
Let h(f) be the first derivative of 0*f - 1 + 1/60*f**5 + 0*f**2 - 2/3*f**3 - 1/360*f**6 - 1/24*f**4. Let x(c) be the third derivative of h(c). Factor x(v).
-(v - 1)**2
Let r(u) be the third derivative of 5*u**6/96 + 7*u**5/48 + 5*u**4/48 - 10*u**2. Factor r(z).
5*z*(z + 1)*(5*z + 2)/4
Let k(o) be the third derivative of 2/21*o**3 + 1/210*o**5 + 2*o**2 - 1/28*o**4 + 0*o + 0. Factor k(u).
2*(u - 2)*(u - 1)/7
Factor 2/9*f**3 + 2/3*f - 2/9 - 2/3*f**2.
2*(f - 1)**3/9
Let s = -3 - -2. Let b = 1 - s. Let 2*i**b + 3*i**2 + i - 2*i**2 = 0. What is i?
-1/3, 0
Let b(o) be the third derivative of -o**7/210 + o**5/30 - o**3/6 + 6*o**2. Suppose b(s) = 0. What is s?
-1, 1
Let m(q) be the first derivative of 4*q**3/3 + 4*q**2 - 9. What is f in m(f) = 0?
-2, 0
Find h, given that 0 + 2/15*h**3 - 2/5*h**2 - 4/15*h + 2/15*h**5 + 2/5*h**4 = 0.
-2, -1, 0, 1
Suppose 8*a**4 - 3 + 12*a**3 - 87/2*a**2 - 47/2*a = 0. Calculate a.
-3, -1/4, 2
Let k(h) = -2*h - 13. Let r(s) = s + 6. Let f(t) = -6*k(t) - 13*r(t). Let o be f(-2). Factor 2/7*z**3 + 0 + 0*z - 4/7*z**o + 6/7*z**4.
2*z**2*(z + 1)*(3*z - 2)/7
Let s(j) be the third derivative of j**7/490 - j**6/140 - j**5/140 + j**4/28 + 4*j**2. Factor s(p).
3*p*(p - 2)*(p - 1)*(p + 1)/7
Let l(z) be the third derivative of 0 + 4*z**2 - 2/1365*z**7 - 5/2184*z**8 + 1/52*z**6 + 1/39*z**4 + 0*z**3 + 0*z + 8/195*z**5. Suppose l(r) = 0. What is r?
-1, -2/5, 0, 2
Solve 2/9*n**4 + 4/9 + 10/9*n**3 + 14/9*n + 2*n**2 = 0.
-2, -1
Let k(o) = o**3 - o - 1. Let z(m) = 4*m**4 - 5*m**3 + 4*m**2 - 5*m - 5. Let p(d) = -5*k(d) + z(d). Factor p(x).
2*x**2*(x - 2)*(2*x - 1)
Factor -150/7 - 6/7*z**2 - 60/7*z.
-6*(z + 5)**2/7
Let z(q) be the second derivative of 0*q**5 + 1/60*q**6 + 0*q**2 + 0 + 0*q**3 - q - 1/24*q**4. Factor z(n).
n**2*(n - 1)*(n + 1)/2
Let s be (-123)/(-105) - 57/95. Factor 2/7*n**2 + 6/7*n + s.
2*(n + 1)*(n + 2)/7
Let c be ((-41)/(-2))/((-3)/(-4)). Let t = c + -27. Factor 1/3*b - 2/3*b**3 - 1/3*b**4 + 2/3*b**2 + 1/3*b**5 - t.
(b - 1)**3*(b + 1)**2/3
Let y(c) = c**3 + 15. Let n be y(0). Suppose 5*d - n = 0, -2*d + 22 = 4*i + 8. Find u such that -u**3 + u**3 - i*u**3 + 2*u**2 = 0.
0, 1
Let j(q) be the first derivative of -3*q + 0*q**2 + 0*q**4 + 0*q**3 + 1/105*q**6 - 1 - 1/70*q**5. Let u(i) be the first derivative of j(i). Solve u(l) = 0.
0, 1
Let f(x) be the second derivative of 8*x**5/15 + 2*x**4/3 + x**3/3 + x**2/12 - 26*x. Find k, given that f(k) = 0.
-1/4
Let k(s) be the second derivative of s**4/3 - 2*s**3/3 + 8*s. Factor k(b).
4*b*(b - 1)
Let o = -17 + 19. Let p(f) be the first derivative of -5/16*f**4 + 0*f - 2 + 1/8*f**6 - 1/12*f**3 + 1/4*f**o + 1/20*f**5. What is x in p(x) = 0?
-1, 0, 2/3, 1
Let p(z) be the third derivative of 1/40*z**5 - 5*z**2 + 0*z + 0*z**3 - 1/60*z**6 + 1/48*z**4 + 0. Factor p(y).
-y*(y - 1)*(4*y + 1)/2
Let j(a) = a + 9. Let z be j(-7). Determine g so that -g**4 - 3*g**z - g**4 + 3*g**2 - 2*g**3 = 0.
-1, 0
Let z(s) be the third derivative of s**6/300 - s**5/50 + s**4/20 - s**3/15 - 11*s**2. Factor z(p).
2*(p - 1)**3/5
Let r(x) be the second derivative of 1/18*x**3 + 0*x**2 + 1/20*x**5 + 0 - 5/36*x**4 + 1/18*x**6 - 2*x - 2/63*x**7. Suppose r(a) = 0. What is a?
-1, 0, 1/4, 1
Let i(n) be the third derivative of 0 + 0*n + 7/8*n**4 - n**3 + 3/40*n**6 - 2/5*n**5 + 4*n**2. Let i(t) = 0. Calculate t.
2/3, 1
Find g, given that 0 + 0*g - 1/10*g**4 + 0*g**3 + 1/10*g**2 = 0.
-1, 0, 1
Let k(i) = i**2 - 2*i + 1. Let y be k(1). Find b such that 1/4*b**5 + 1/4*b**4 + y + 0*b**3 + 0*b + 0*b**2 = 0.
-1, 0
Let o = 4 + -2. Suppose o*n = 2*w + 4, -5*n = -0*n + 5*w - 10. Find s, given that 2/5*s**n + 4/5*s + 2/5 = 0.
-1
Suppose u + 6 = -u. Let v = u - -5. Factor -2*r**2 + r**2 - 2 + 3*r**v.
2*(r - 1)*(r + 1)
Let c(z) be the second derivative of -z**4/12 - z**3/6 + z**2 + 14*z. Factor c(k).
-(k - 1)*(k + 2)
Let t(i) be the third derivative of -1/945*i**7 + 0*i**4 + 1/270*i**5 + 0*i**3 + i**2 + 0 + 0*i**6 + 0*i. Factor t(n).
-2*n**2*(n - 1)*(n + 1)/9
Let h(y) = y**5 + y**4 + y**3 + y + 1. Let s(o) = 3*o + 6*o - 11*o**3 - 5*o**2 + 0*o - 7*o**4 + 4 - 4*o. Let q(f) = -2*h(f) + s(f). Factor q(j).
-(j + 1)**3*(j + 2)*(2*j - 1)
Let 5/7*b**2 - 5/7*b**4 + 3/7*b**5 - 1/7*b**3 - 2/7*b + 0 = 0. What is b?
-1, 0, 2/3, 1
Let l(x) be the third derivative of x**8/84 - 2*x**7/21 + 4*x**6/15 - 4*x**5/15 - 12*x**2. Factor l(k).
4*k**2*(k - 2)**2*(k - 1)
Let h(k) be the first derivative of k**5/10 - 3*k**4/2 + 23*k**3/3 - 15*k**2 + 25*k/2 - 48. Factor h(x).
(x - 5)**2*(x - 1)**2/2
Let s(r) be the second derivative of r**4/4 + 5*r**3 + 27*r**2/2 + 39*r. What is v in s(v) = 0?
-9, -1
Let r be (-10)/15*(-6)/10. Factor 4/5*b**2 - r*b**3 + 0 - 6/5*b**4 + 0*b.
-2*b**2*(b + 1)*(3*b - 2)/5
Let n be (56/70)/((-3)/(-5)). What is y in -n*y - 2 + 2/3*y**2 = 0?
-1, 3
Let x(z) be the third derivative of z**7/3780 - z**6/540 + z**5/180 + z**4/8 + 3*z**2. Let r(j) be the second derivative of x(j). Solve r(n) = 0 for n.
1
Let r = -381/7 + 5716/105. Let m(g) be the second derivative of 0*g**2 + 0 - 3*g + 1/15*g**4 - 2/75*g**6 + 0*g**5 + 1/15*g**3 - r*g**7. Factor m(w).
-2*w*(w - 1)*(w + 1)**3/5
Let i(t) be the second derivative of -t**6/6 + t**5/2 - 5*t**3/3 + 5*t**2/2 + 10*t. Let i(r) = 0. Calculate r.
-1, 1
Let -6*q**2 - 3*q**3 - 6*q + 12*q**2 + 2 + q**3 = 0. What is q?
1
Let z(d) be the second derivative of -d**5/40 - d**4/12 - d**3/12 - 3*d. Factor z(n).
-n*(n + 1)**2/2
Let t be (-13)/(-4) - (-1)/(-4). Let z be (9 - 9)/((-3)/(-1)). Factor -4/3*w**2 + 0*w + 2*w**4 - 2/3*w**t + z.
2*w**2*(w - 1)*(3*w + 2)/3
Let k = 69 + -413/6. Let u(x) be the first derivative of 1/2*x - k*x**3 + 0*x**2 + 1. Factor u(c).
-(c - 1)*(c + 1)/2
Let v(j) be the first derivative of -2*j**5/45 + j**4/9 - 2*j**2/9 + 2*j/9 + 18. Factor v(x).
-2*(x - 1)**3*(x + 1)/9
Let x(j) be the second derivative of j**7/84 - j**6/15 + j**5/8 - j**4/12 + 25*j. Solve x(c) = 0.
0, 1, 2
Let w(m) be the second derivative of -m**9/12096 + m**7/3360 - m**3/3 + m. Let x(j) be the second derivative of w(j). Solve x(p) = 0.
-1, 0, 1
Suppose -1 = -5*u + y - 5, -u = 4*y - 16. Let q(z) be the second derivative of 