**2 - 3*r + r**2. Let s be a(9). What is v in 4/5*v + 2/5 + 2/5*v**s = 0?
-1
Suppose 17*n = 19*n - 4. Factor 2*z**3 + 0 + 0*z - 1/2*z**n.
z**2*(4*z - 1)/2
Let w(l) = -l**3 + 9*l**2 - 5*l + 4. Let x be w(8). Factor 61/3*q**2 + 1/3 + 12*q**4 - 14/3*q - x*q**3.
(q - 1)**2*(6*q - 1)**2/3
Let i(z) be the first derivative of 0*z - 6 + 0*z**2 - 1/20*z**5 + 0*z**3 + 0*z**4. Factor i(y).
-y**4/4
Let x(g) be the second derivative of g**6/105 - 2*g**5/35 + 5*g**4/42 - 2*g**3/21 + 3*g. Factor x(n).
2*n*(n - 2)*(n - 1)**2/7
Let s(y) be the second derivative of y**9/52920 - y**8/11760 + y**7/8820 + y**4/12 - 2*y. Let b(m) be the third derivative of s(m). Factor b(r).
2*r**2*(r - 1)**2/7
Let s = 164/3 - 54. Let p(h) be the first derivative of h**2 - 2/3*h**3 - s*h + 1/6*h**4 - 3. Solve p(d) = 0.
1
Suppose -16 = 4*p, 0*a + 3*a - 5*p = 32. Let x be (-8)/12*(-30)/a. Factor y**3 - y**x - 2*y + 2*y.
-y**3*(y - 1)*(y + 1)
Let o(q) = 18*q**3 - 30*q**2 + 14*q - 4. Let c(l) = -18*l**3 + 30*l**2 - 14*l + 5. Let f(z) = -2*c(z) - 3*o(z). Factor f(s).
-2*(s - 1)*(3*s - 1)**2
Suppose -7*t = -2*t + 20. Let o be (2/(-10))/(t/10). Suppose -o*l**2 - 1/4*l**5 + 0 + 0*l + 3/4*l**3 + 0*l**4 = 0. Calculate l.
-2, 0, 1
Let j(v) be the third derivative of v**6/30 + 2*v**5/15 - 4*v**2. Factor j(n).
4*n**2*(n + 2)
Let d(b) = -b**2 + 12*b - 1. Let v(r) = 6*r. Let j(f) = -3*d(f) + 7*v(f). What is i in j(i) = 0?
-1
Let f(r) be the first derivative of 2*r**5/5 + 4*r**4/3 + 14*r**3/9 + 2*r**2/3 - 4. Factor f(m).
2*m*(m + 1)**2*(3*m + 2)/3
Factor -10*h - 2 + 0*h**3 + 2*h**2 + 9*h - 2*h**3 + 3*h**3.
(h - 1)*(h + 1)*(h + 2)
Let t(z) = z**2 - 2*z - 1. Let r be t(-1). Factor -3*p**2 + 0*p**r + 2*p**2.
-p**2
Let r be ((-153)/(-60))/((-84)/(-10)). Let p = r - -15/56. Factor 0 + 2/7*m**5 + 0*m**2 - p*m**3 + 2/7*m**4 + 0*m.
2*m**3*(m - 1)*(m + 2)/7
Suppose -8*q - 14 = -54. Let y(m) be the third derivative of 0*m - 3*m**2 - 1/9*m**3 + 0 - 1/315*m**7 + 0*m**4 + 1/45*m**q + 0*m**6. Factor y(t).
-2*(t - 1)**2*(t + 1)**2/3
Let s(z) be the first derivative of z**4/18 - 8*z**3/27 + 4*z**2/9 - 33. Let s(y) = 0. What is y?
0, 2
Let n = 2/209 - -404/1463. Factor 0*q**2 + 0*q + 0 + n*q**3 - 6/7*q**4.
-2*q**3*(3*q - 1)/7
Let m(u) be the second derivative of 3*u**5/160 + 14*u. Solve m(y) = 0 for y.
0
Let i(o) be the second derivative of 3*o**5/20 - o**4/4 - o**3/2 + 3*o**2/2 - 6*o. Find m, given that i(m) = 0.
-1, 1
Factor -2/3*i**2 + 8*i - 24.
-2*(i - 6)**2/3
Let h = 414 - 11174/27. Let d = h - -127/54. Let -3/2*b**5 + 0*b + 0*b**2 + d*b**4 - b**3 + 0 = 0. What is b?
0, 2/3, 1
Factor -2*q - 8*q**2 - 4*q - 3*q**2 - 4*q**2.
-3*q*(5*q + 2)
Let f = -1093/5 + 219. Factor -4/5*a**3 - 2/5*a**2 - f*a**4 + 0*a + 0.
-2*a**2*(a + 1)**2/5
Let u be (-1)/(-8)*2 + (-203)/(-84). Factor 30*o**2 - 125/3*o**4 + u - 25/3*o**3 + 52/3*o.
-(o - 1)*(5*o + 2)**3/3
Let o(a) be the third derivative of a**6/30 + a**5/15 - 2*a**4/3 - 8*a**3/3 + 18*a**2. Solve o(j) = 0 for j.
-2, -1, 2
Suppose -5*f = -4*u - 1 - 9, f = 2*u + 2. Suppose 0 + 1/4*c**f + 0*c + 1/4*c**4 - 1/2*c**3 = 0. Calculate c.
0, 1
Let r(j) be the first derivative of -7*j**6/2 - 48*j**5/5 - 33*j**4/4 - 2*j**3 + 5. Factor r(a).
-3*a**2*(a + 1)**2*(7*a + 2)
Factor 8/5*x - 12/5 + 4/5*x**2.
4*(x - 1)*(x + 3)/5
Let l(v) be the second derivative of -v**6/120 + v**5/20 - v**4/16 + 43*v. Find w, given that l(w) = 0.
0, 1, 3
Let c(w) = 5*w**3 + 47*w**2 + 223*w + 377. Let g(i) = 6*i**3 + 48*i**2 + 222*i + 378. Let k(j) = 3*c(j) - 2*g(j). Factor k(t).
3*(t + 5)**3
Let -3/8 - 1/8*c**4 - 3/2*c**2 + 5/4*c + 3/4*c**3 = 0. Calculate c.
1, 3
Let l(g) be the third derivative of g**9/45360 + g**8/10080 - g**6/1080 - g**5/360 + g**4/8 - g**2. Let i(h) be the second derivative of l(h). Factor i(a).
(a - 1)*(a + 1)**3/3
Let i(l) be the second derivative of l**7/2520 - l**6/240 + l**5/60 + l**4/12 + 4*l. Let y(t) be the third derivative of i(t). Find q such that y(q) = 0.
1, 2
Suppose 0*q + 25 = 5*q. Factor -3*f + 3*f**4 + 3*f + 2*f**3 - 2*f**q - 2*f**2 - f**4.
-2*f**2*(f - 1)**2*(f + 1)
Let j = -3 + 7. Let -8*y**4 - 2*y**3 + 2*y**j + 4*y**2 - 2*y**3 + 2 - 2*y**5 + 6*y = 0. What is y?
-1, 1
Factor 2/5*q**2 + 2/5*q - 2/5 - 2/5*q**3.
-2*(q - 1)**2*(q + 1)/5
Let m be (-8)/(-5) - 4/(-10). Factor 14*v**2 + 6*v**3 + 10*v - 5*v**3 + m + 5*v**3.
2*(v + 1)**2*(3*v + 1)
Let j = -6 - -1. Let h(n) = -4*n**4 + 8*n**3 - 3*n**2 + 5*n + 5. Let u(m) = 5*m**4 - 9*m**3 + 4*m**2 - 6*m - 6. Let f(y) = j*u(y) - 6*h(y). Factor f(q).
-q**2*(q + 1)*(q + 2)
Let p(n) be the third derivative of -n**7/2520 + n**5/120 - 7*n**4/24 - 7*n**2. Let a(v) be the second derivative of p(v). Factor a(y).
-(y - 1)*(y + 1)
Suppose 144*i**4 - 817*i**3 + 187*i**4 + 16 - 129*i**3 + 395*i**4 + 68*i**2 + 136*i = 0. Calculate i.
-2/11, 2/3, 1
Suppose -4*n = -18 - 2. Factor -6*w**4 - w**n + w + 8*w**4 - w.
-w**4*(w - 2)
Let q be (-2)/7 + (-111)/(-21). Suppose 0 = -5*x - u + 10, q*u = -x + u + 2. Find k, given that 1/4*k**x - 1/4*k**4 + 0 + 1/4*k**3 - 1/4*k = 0.
-1, 0, 1
Suppose 32 = 2*d - 6*g + 4*g, 2*g - 23 = -3*d. Factor -v**3 + 8*v + d*v**2 - v**2 + 8 + 8*v + 3*v**3.
2*(v + 1)*(v + 2)**2
Let v(j) = j**3 - 5*j**2 + j - 5. Let f be v(5). Let l(t) be the second derivative of -1/60*t**5 + 1/18*t**3 + f*t**2 + 0 + 0*t**4 - t. Factor l(p).
-p*(p - 1)*(p + 1)/3
Let 5/6 - 5/3*q + 5/6*q**2 = 0. What is q?
1
What is m in -2/11*m + 2/11*m**2 + 2/11*m**3 - 2/11 = 0?
-1, 1
Let v(x) = -3*x**2 + 6*x - 2. Let m(f) = 48*f**2 - 96*f + 33. Let i(j) = 2*m(j) + 33*v(j). Factor i(r).
-3*r*(r - 2)
Let i(t) be the third derivative of -t**5/90 + t**3/9 + 6*t**2. Factor i(x).
-2*(x - 1)*(x + 1)/3
Let o = 24 + -22. Let k(t) be the second derivative of t + 0 + 0*t**o + 0*t**4 + 0*t**3 - 3/20*t**5. Factor k(c).
-3*c**3
Let n = 1 + -6. Let y be (-15)/n + (-33)/12. Determine w so that 1/4 - 1/2*w + y*w**2 = 0.
1
Let c(d) = -4*d - 34. Let w be c(-9). Suppose 0 = -5*x - 0*x. Factor -1/4 + 1/4*k**w + x*k.
(k - 1)*(k + 1)/4
Let d be (3 + -4)/(35/20 + -2). Let j(y) be the first derivative of 5*y**2 - 5/2*y**d + 2 - 4/3*y**3 + 4*y. Let j(s) = 0. What is s?
-1, -2/5, 1
Let w = 28 + -25. Let l be (-3)/(-2 - 1)*w. Find b such that -1/2 - 1/2*b + 1/2*b**2 + 1/2*b**l = 0.
-1, 1
Let t(a) be the third derivative of -1/80*a**6 + 0 + 8*a**2 - 3/40*a**5 + 0*a - 3/16*a**4 - 1/4*a**3. Factor t(b).
-3*(b + 1)**3/2
Determine o so that -65/2*o**4 + 0 - 5*o - 45/2*o**2 + 60*o**3 = 0.
-2/13, 0, 1
Let s(a) be the first derivative of -1 - 2/7*a + 6/35*a**5 + 4/7*a**3 + 0*a**2 + 4/7*a**4. Factor s(o).
2*(o + 1)**3*(3*o - 1)/7
Let v be ((-14)/560*-16)/((-8)/(-5)). What is t in -v*t - 1/2 + 1/2*t**2 + 1/4*t**3 = 0?
-2, -1, 1
Let b(p) be the third derivative of p**5/80 + p**4/16 - 2*p**2. Suppose b(n) = 0. Calculate n.
-2, 0
Suppose 0 = -5*k + 4*q + 1, 5*q = -4*k + 5 + 4. Suppose -3*t - 2*o = 2, -3*o - 21 = -5*t + k. Factor 2*f**2 + 3*f**3 - 9*f**3 + t*f**2.
-2*f**2*(3*f - 2)
Let v = 495/564928 - 1/7566. Let p(j) be the third derivative of 0*j - 1/280*j**7 - 1/240*j**5 + 0 + 0*j**3 + 0*j**4 + 1/160*j**6 + v*j**8 - j**2. Factor p(g).
g**2*(g - 1)**3/4
Suppose 19*r + r**3 - 16*r - 36 + 11*r**2 + 21*r = 0. Calculate r.
-6, 1
Let w = -1/21 - -65/42. Determine s, given that -w*s + 1/2*s**2 + 0 = 0.
0, 3
Let t(o) be the first derivative of -1 - 1/3*o**3 - 1/4*o**4 + o + 1/2*o**2. Factor t(k).
-(k - 1)*(k + 1)**2
Let n(u) be the second derivative of -8*u**4/15 - 8*u**3/15 - u**2/5 - 5*u. Factor n(g).
-2*(4*g + 1)**2/5
Let z(b) be the third derivative of -b**8/84 + 4*b**7/105 - b**6/30 + 13*b**2. Let z(s) = 0. Calculate s.
0, 1
Find w such that -5/4 - 5/4*w**2 + 5/2*w = 0.
1
Suppose -18*i = -11*i - 9*i. Let p(f) be the second derivative of i - 1/12*f**3 - f - 1/8*f**2 - 1/48*f**4. Factor p(q).
-(q + 1)**2/4
Let z(m) = 135*m**3 + 679*m**2 + 407*m - 137. Let b(k) = 34*k**3 + 170*k**2 + 102*k - 34. Let o(t) = -9*b(t) + 2*z(t). Find c such that o(c) = 0.
-4, -1, 2/9
Suppose 4*d = -d. Let k(r) be the second derivative of 2*r**2 + 1/12*r**4 - 2/3*r**3 - r + d. Factor k(j).
(j - 2)**2
Find g, given that 2 - 2 + 2*g**4 + 2*g**5 = 0.
-1, 0
Let g(n) be the first derivative of n**5/20 + n**4/12 - 5*n - 6. Let s(a) be the first derivative of g(a). Factor s(x).
x**2*(x + 1)
Let a = 2 + 2. Suppose 0*o - a*o + 8 = 0.