7/6. Factor 0 - j*k**4 + 1/2*k**5 + 1/2*k**3 + 1/2*k**2 - 1/3*k.
k*(k - 1)**3*(3*k + 2)/6
Let f(s) be the first derivative of -s**8/7560 - s**7/630 - s**6/180 - s**5/135 + 34*s**3/3 - 24. Let b(q) be the third derivative of f(q). Factor b(t).
-2*t*(t + 1)**2*(t + 4)/9
Let k = -38 - -43. Solve -k*x - 35*x**3 - 25*x**2 - 17*x**4 + x**4 + x**4 = 0 for x.
-1, -1/3, 0
Factor 6/19*d**4 - 4/19*d**2 - 2/19*d**3 + 0*d + 0.
2*d**2*(d - 1)*(3*d + 2)/19
Let u be (-11)/(66/48) - (-8 + (-5)/10). Factor -u*q**4 + 5/2*q**2 - 2 + 3/2*q - 3/2*q**3.
-(q - 1)**2*(q + 1)*(q + 4)/2
Suppose 522*f - 14 = 520*f. Suppose f*x = -2*x. Factor x - 2/9*o**4 + 2/9*o**2 + 0*o**3 + 0*o.
-2*o**2*(o - 1)*(o + 1)/9
Let x be 207/(-132) + (-42)/(-24). Find i such that 0 - 20/11*i**2 + x*i**3 + 50/11*i = 0.
0, 5
Let g(n) = -252*n + 1011. Let a be g(4). Factor 16/7*m + 16/7*m**a - 24/7*m**2 - 4/7*m**4 - 4/7.
-4*(m - 1)**4/7
Let d(j) be the second derivative of 3*j**6/220 + 2*j**5/55 + j**4/33 - 15*j**2/2 - 11*j. Let a(w) be the first derivative of d(w). Let a(x) = 0. Calculate x.
-2/3, 0
Let o(s) = -2*s**3 - 27*s**2 - 12*s + 15. Let h be o(-13). Factor -j + 4*j**2 - 61 - 5*j + 52 - j**h.
3*(j - 3)*(j + 1)
Solve 2/5*c + 0 - 9/5*c**3 - c**5 - 13/5*c**4 + 1/5*c**2 = 0 for c.
-1, 0, 2/5
Factor 160*u**2 + 2/5*u**4 + 16*u**3 + 0*u + 0.
2*u**2*(u + 20)**2/5
Let m be ((-2)/(-38))/(1/6). Let l = 148/133 + m. Determine w, given that -2*w**2 + 4/7 - l*w = 0.
-1, 2/7
What is z in 2/3*z + 1/3*z**4 - 25/3*z**2 + 8 - 2/3*z**3 = 0?
-4, -1, 1, 6
Let h(t) = t**3 - 9*t**2 + 2*t - 14. Suppose -36 - 11 = -3*b - 5*n, -2*b + 2*n + 10 = 0. Let u be h(b). Factor c**5 - c**2 - c**3 + u*c**4 - 3*c**4 + 0*c**5.
c**2*(c - 1)*(c + 1)**2
Let y(m) be the second derivative of 0*m**3 - 1/28*m**7 + 3/40*m**5 - 1/20*m**6 + 0*m**2 + 15*m + 1/8*m**4 + 0. Determine p so that y(p) = 0.
-1, 0, 1
Let n be ((-2)/(-6))/((-1)/(-4)). Let b be ((-1)/5)/((171/855)/((-1)/3)). Factor b*k**3 + 1/3*k**2 - 4/3*k - n.
(k - 2)*(k + 1)*(k + 2)/3
Let t = 366 - 148. Let y = t + -1960/9. Factor -2/3*m + 2/3*m**3 + y*m**4 - 4/9 + 2/9*m**2.
2*(m - 1)*(m + 1)**2*(m + 2)/9
Let r(m) be the second derivative of 3*m**7/14 - 4*m**6/5 - 11*m**5/20 + 7*m**4/2 + 2*m**3 - 4*m**2 - 67*m - 1. What is y in r(y) = 0?
-1, -2/3, 1/3, 2
Factor 32/7*a**2 + 288/7 + 24*a + 2/7*a**3.
2*(a + 4)*(a + 6)**2/7
Suppose -2468*h = -2477*h. Let p(y) be the second derivative of -2/75*y**6 - 16/15*y**3 - 6/25*y**5 - 9*y - 4/5*y**4 + 0 + h*y**2. Factor p(b).
-4*b*(b + 2)**3/5
Let p(c) be the second derivative of c**9/15120 + c**8/2240 + c**7/1260 + 11*c**4/12 + 4*c. Let q(l) be the third derivative of p(l). Factor q(v).
v**2*(v + 1)*(v + 2)
Let z = -7137 - -3425761/480. Let g(b) be the third derivative of 0*b + z*b**6 - b**2 - 1/24*b**3 + 1/32*b**4 + 0 - 1/80*b**5. Factor g(m).
(m - 1)**3/4
Determine u, given that 4/3*u**2 + 0*u**3 - 16/9*u - 2/9*u**4 + 2/3 = 0.
-3, 1
Let g(i) = -i**2 - 64*i - 1164. Let s(c) = -2*c**2 - 129*c - 2326. Let n(y) = -7*g(y) + 4*s(y). Suppose n(f) = 0. What is f?
-34
Let y = -1236/11 - -1238/11. Factor 12/11*h - y*h**2 - 18/11.
-2*(h - 3)**2/11
Factor -1/2*b + 5/2 + 1/2*b**3 - 5/2*b**2.
(b - 5)*(b - 1)*(b + 1)/2
Let c(z) be the first derivative of -z**4/18 + 10*z**3/27 + 2*z**2/3 - 28. Suppose c(r) = 0. Calculate r.
-1, 0, 6
Let u(g) = 2*g**3 + 5*g**2 + 5*g + 2. Let i(s) = 4*s - 2*s + 0*s - s**2 - 3*s. Let n(d) = 14*i(d) + 2*u(d). Factor n(p).
4*(p - 1)**2*(p + 1)
Let c(f) be the third derivative of -2*f**2 - 1/270*f**5 + 4/27*f**3 + 0*f**4 + 0 + 0*f. Factor c(s).
-2*(s - 2)*(s + 2)/9
Let z = 439 + -9218/21. Let m(b) be the second derivative of z*b**3 + b + 0 - 1/70*b**5 - 1/42*b**4 + 1/7*b**2. Find y, given that m(y) = 0.
-1, 1
Let o(w) = -2*w**3 + 14*w**2 + 2*w - 14. Suppose 2*t = 4*t + 2. Let r(c) = c**3 + c**2 - c - 1. Suppose 2*i - 2 = 2. Let y(p) = i*r(p) + t*o(p). Factor y(d).
4*(d - 3)*(d - 1)*(d + 1)
Let l(d) be the first derivative of -5*d**6/12 - 7*d**5/2 - 95*d**4/8 - 125*d**3/6 - 20*d**2 - 10*d - 11. Suppose l(v) = 0. What is v?
-2, -1
Let m = 358 + -355. Let a(k) be the first derivative of 3 - 1/2*k**4 - 2/3*k**2 + 11/9*k**m - 1/3*k. Factor a(h).
-(h - 1)**2*(6*h + 1)/3
Let j(o) be the second derivative of 0 + 0*o**2 - 1/10*o**4 - 3/10*o**3 - 11*o - 1/100*o**5. Determine w so that j(w) = 0.
-3, 0
Let n be (-1)/3 + -1*(-3)/9. Let q be 4/18 + (-4)/18. Factor q*k**2 + 0*k**2 + k**2 + n*k**2.
k**2
Suppose 33*l + 12 = 37*l. Let m = -2 - -4. Factor -l*p**m - 72 + 72.
-3*p**2
Suppose 3*j - 4 = w, j + w - 4 = -0*w. Suppose 3*n - 20 = -j*n - 5*u, 0 = -3*u + 3. Suppose -1 + 1/2*r - 1/2*r**n + 3/2*r**2 - 1/2*r**4 = 0. Calculate r.
-2, -1, 1
Let i(l) be the second derivative of -l**7/210 - l**6/30 + 2*l**4/3 + 5*l**3/3 - 15*l. Let a(p) be the second derivative of i(p). Suppose a(b) = 0. Calculate b.
-2, 1
Suppose -55*f - 30*f + 98*f = 0. Find u, given that 0*u + 4/5*u**4 + 8/5*u**2 - 12/5*u**3 + f = 0.
0, 1, 2
Let d = 79 + -147/2. Let a(q) be the first derivative of 0*q**2 - d*q**4 - 4/3*q**3 + 0*q + 5. Suppose a(z) = 0. Calculate z.
-2/11, 0
Let c(q) = q**2 - q - 1. Let t(z) = -9*z**2 - 18*z - 4. Suppose 0 = 2*j + 5*d - 7, -j - 24 = -4*d + d. Let i = 8 + j. Let p(v) = i*t(v) - 4*c(v). Factor p(a).
(a + 4)*(5*a + 2)
Suppose -5/2*n**2 - 56*n - 22 = 0. Calculate n.
-22, -2/5
Suppose 4*y - z - 14 = -0*z, 3*z = -4*y + 22. Suppose -26*r**2 + 4*r**y + r - 12*r**2 + 36 + 34*r**3 - 43*r - 10*r**4 = 0. Calculate r.
-1, 2/3, 3
Factor 17/2*c - c**2 + 6 - 7/2*c**3.
-(c + 1)**2*(7*c - 12)/2
Let a(y) = 5*y**4 + 25*y**3 + 111*y**2 + 107*y + 40. Let f(b) = 6*b**4 + 24*b**3 + 113*b**2 + 108*b + 41. Let u(n) = -7*a(n) + 6*f(n). Factor u(d).
(d - 34)*(d + 1)**3
Let l = 257 - 256. Let i(a) = 0*a - 9*a**2 - 7*a - 5*a - 3. Let c(s) = -s**2 - s. Let t(j) = l*i(j) - 6*c(j). Determine m so that t(m) = 0.
-1
Let d be 4/18 - (-1280)/(-90). Let q = d - -13. Let j(i) = -i. Let n(b) = -5*b**2. Let s(x) = q*n(x) - 5*j(x). Factor s(u).
5*u*(u + 1)
Let o(h) = 3*h - 10. Let l be o(4). Let g(u) = u + 2. Let j be g(l). Factor 0*i**3 + 10*i - 14*i + j*i**3.
4*i*(i - 1)*(i + 1)
Let d(k) = -22*k**3 + 4328*k**2 - 315353*k + 311005. Let l(a) = -7*a**3 + 1443*a**2 - 105118*a + 103670. Let b(u) = -2*d(u) + 7*l(u). Factor b(z).
-5*(z - 144)**2*(z - 1)
Let u(t) be the first derivative of 1/180*t**5 + 10 - 1/2160*t**6 + 0*t**2 - 1/36*t**4 + 10/3*t**3 + 0*t. Let v(b) be the third derivative of u(b). Factor v(p).
-(p - 2)**2/6
Suppose -5*k + 747 = 154*s - 157*s, 8 = -2*s. Factor 9*a**2 + k + 63*a + 3/7*a**3.
3*(a + 7)**3/7
Let m(b) = -21*b**3 + 93*b**2 - 12*b - 30. Let g(l) = 20*l**3 - 93*l**2 + 11*l + 30. Let z(x) = 3*g(x) + 2*m(x). Factor z(j).
3*(j - 5)*(2*j + 1)*(3*j - 2)
Suppose -896*q = -881*q. Let a = 15 + -10. Solve q + 0*m**3 + 3/5*m**a - 6/5*m**2 - 3/5*m + 6/5*m**4 = 0.
-1, 0, 1
Suppose -5 = -n, 4*p + 11 = 5*n - 2. Let t = 7 - p. Factor 6*x**4 + 3*x**5 - 2*x**4 - 3*x**2 + 9*x**3 - 3*x**t - 10*x**4.
3*x**2*(x - 1)**3
Let c be (-1 - (-3)/6)/(-1*(-8)/(-16)). Determine b so that -b**2 - 1/2*b**5 - 2*b**3 - c + 2*b**4 + 5/2*b = 0.
-1, 1, 2
Let j(q) be the first derivative of 0*q**2 - 7*q - 7/24*q**4 - 12 - 1/6*q**3. Let p(n) be the first derivative of j(n). Factor p(b).
-b*(7*b + 2)/2
Let x(u) be the first derivative of 0*u + 2/35*u**5 + 0*u**2 - 5/28*u**4 - 1/7*u**3 + 49. What is v in x(v) = 0?
-1/2, 0, 3
Factor 8/5*p**2 - 14/5*p**4 + 0 + 4/5*p**5 + 0*p + 8/5*p**3.
2*p**2*(p - 2)**2*(2*p + 1)/5
Let m(p) be the third derivative of 25*p**2 + 0*p**3 + 1/15*p**4 + 0*p + 0 - 1/150*p**5. Determine o, given that m(o) = 0.
0, 4
Suppose 12*s - 152 + 80 = 0. Let g(n) be the third derivative of -1/80*n**s + 0*n + 0 - 1/2*n**3 + 1/20*n**5 + 8*n**2 + 1/16*n**4. Let g(i) = 0. Calculate i.
-1, 1, 2
Factor 0*w + 50/7*w**2 + 0 - 1/7*w**4 + 7*w**3.
-w**2*(w - 50)*(w + 1)/7
Suppose 3*t - 6*t = 4*t. Suppose -8 = 12*a - 13*a + 2*x, -3*a - 4*x - 6 = t. Factor 10/7*g**a - 2/7*g**3 - 2*g + 6/7.
-2*(g - 3)*(g - 1)**2/7
Let k = 2/101529 - -101525/203058. Let -1/6*u**2 - k - 2/3*u = 0. Calculate u.
-3, -1
Let o(w) be the third derivative of 1/40*w**6 - 1/70*w**7 + 0 + 0*w**4 - 9*w**2 + 0*w**3 - 1/112*w**8 + 1/20*w**5 + 0*w. Solve o(m) = 0.
-1, 0, 1
Let g(k) be the third derivative of -k**9/12096 + k**8/4032 