**2 - r + 3. Let a be w(0). Let i(p) be the first derivative of -2/5*p - 2/15*p**a + 2/5*p**2 + 1. Factor i(u).
-2*(u - 1)**2/5
Let i(t) be the first derivative of -2*t**3/9 + 6*t**2 + 49. Factor i(q).
-2*q*(q - 18)/3
Let s(k) be the second derivative of -163*k**4/48 + 20*k**3/3 + 3*k**2/8 - k - 14. Find o such that s(o) = 0.
-3/163, 1
Let i be (-8)/6*8/(-32). Let o(z) be the second derivative of -1/12*z**4 + 3*z + i*z**2 + 1/18*z**3 + 0. Factor o(s).
-(s - 1)*(3*s + 2)/3
Let u(f) be the first derivative of f**3/3 + 8*f**2 - 57*f - 69. Factor u(y).
(y - 3)*(y + 19)
Solve 14*l**3 - 5*l**4 - 58*l**3 + 33*l**2 + 29*l**3 - 13*l**2 = 0 for l.
-4, 0, 1
Let i(q) be the first derivative of 2/3*q**3 + 14 + 6*q**2 + 10*q. Factor i(r).
2*(r + 1)*(r + 5)
Let x be 2/4*160/72. Determine k so that x*k + 4/9 + 8/9*k**2 + 2/9*k**3 = 0.
-2, -1
Let p(z) be the first derivative of -2*z**5/5 - 3*z**4 + 2*z**3/3 + 6*z**2 - 10. Factor p(w).
-2*w*(w - 1)*(w + 1)*(w + 6)
Factor 25*x + 5*x**2 + 0 + 1/4*x**3.
x*(x + 10)**2/4
Suppose -13*i - 6*i - 2*i = -i. Let -4*b**2 + 16/3*b**3 + 2/3 - 2*b**4 + i*b = 0. What is b?
-1/3, 1
Let y(r) = -176*r + 22 - 167*r + 396*r + 5 + 25*r**2 - r**3. Let c be y(27). Factor 0*l**2 + c + 0*l - 4/7*l**5 - 8/7*l**4 + 0*l**3.
-4*l**4*(l + 2)/7
Suppose 3*b - 75 = -2*b. Suppose 3*s + 3 - 13 = a, -5*a = -2*s - b. Let -5*r - 1 + 7*r**4 + 13*r**3 - 6*r**2 + 4*r**s - r**5 - 11*r**3 = 0. Calculate r.
-1, -1/3, 1
Suppose 2*h = -0*h - h. Suppose -8*f + 16 + 0 = h. Factor 4/3 - 2/3*v - 2/3*v**f.
-2*(v - 1)*(v + 2)/3
Let z(y) = y**2 - 8*y + 7. Let h(m) = m - 1. Suppose 4*q + 13 = -3*j, -4*j = -0*j + 12. Let u(f) = q*z(f) - 3*h(f). Factor u(p).
-(p - 4)*(p - 1)
Suppose 0*s - 2*i + 4 = s, 4*s = i + 34. Determine y so that 8*y**3 - s*y - 1 - 3*y**4 + 5 - y**4 = 0.
-1, 1
Let d(p) be the third derivative of p**6/24 - 7*p**5/4 + 225*p**4/8 - 405*p**3/2 - 2*p**2 + 185*p. Solve d(c) = 0 for c.
3, 9
Factor 2/3*v**4 + 0 - 10/3*v**3 + 0*v + 0*v**2.
2*v**3*(v - 5)/3
Suppose -5*o + 24 + 1 = 5*q, 0 = -2*o - 4*q + 14. Factor 32*w**2 + 2*w**3 + 3*w - w**o - 35*w**2 - 1.
(w - 1)**3
Let l(o) = -o**2 - 4*o + 1. Let c be l(-3). Let y(j) = -j - 4. Let b be y(-7). Factor 5*p**3 - p**b - 3*p**3 - c*p**2 + 3*p**3.
4*p**2*(p - 1)
Let i be (6/141)/(6 - 1) + 0. Let n = 713/940 - i. Determine z, given that -3 + 3*z - n*z**2 = 0.
2
Let n(k) be the second derivative of 5*k**7/42 - 5*k**6/6 + 7*k**5/4 + 5*k**4/12 - 20*k**3/3 + 10*k**2 - 4*k + 9. Let n(c) = 0. Calculate c.
-1, 1, 2
Let f(i) = -i**3 + 11*i**2 - 8*i + 2. Let w(c) = -c**2 - 3*c - 1. Let h(u) = 2*f(u) + 4*w(u). Factor h(j).
-2*j*(j - 7)*(j - 2)
Let m(n) be the second derivative of n**7/42 + n**6/15 - n**4/6 - n**3/6 - 128*n. Factor m(d).
d*(d - 1)*(d + 1)**3
Let g be -1 + ((-50)/4)/(-5). Let d be (33/(429/(-130)))/((-10)/4). Factor 3*l**3 + 0 - g*l**2 - 3*l + 3/2*l**d.
3*l*(l - 1)*(l + 1)*(l + 2)/2
Let h be (-972)/(-72)*(-4)/(-3). Let v be 4*1/h + 46/36. Find x such that 0*x**3 - v*x**4 + 3/4*x + 3/2*x**2 + 0 - 3/4*x**5 = 0.
-1, 0, 1
Suppose 5*m - 4*o + 6 = 0, o - 4 = m - 2. Let r(p) be the second derivative of 1/2*p**m - 1/3*p**3 + 5/48*p**4 + 5*p + 0 - 1/80*p**5. Factor r(n).
-(n - 2)**2*(n - 1)/4
Let f(o) be the second derivative of -o**4/48 + 5*o**3/2 - 225*o**2/2 - 76*o. Find k such that f(k) = 0.
30
Let w(m) be the first derivative of -m**7/14 + 7*m**6/40 - m**5/10 + 8*m**2 + 8. Let j(n) be the second derivative of w(n). Factor j(f).
-3*f**2*(f - 1)*(5*f - 2)
Let i(n) be the second derivative of -n**5/20 + n**4/8 + n**3 - 35*n**2/2 - 22*n. Let u(j) be the first derivative of i(j). Solve u(c) = 0.
-1, 2
Let n(v) be the second derivative of 1/4*v**5 + 75/2*v**3 + 0 + 125*v**2 - 5*v + 5*v**4. Factor n(x).
5*(x + 2)*(x + 5)**2
Suppose 2*p + 0*p - 46 = t, -p = 4. Let h be -2 + ((-12)/t)/((-1)/(-12)). Suppose -2/3*n**2 + 0 + h*n - 2/3*n**3 + 2/3*n**4 = 0. Calculate n.
-1, 0, 1
Let h(s) be the third derivative of -s**8/1512 - 2*s**7/945 + s**6/180 + 281*s**2. Factor h(p).
-2*p**3*(p - 1)*(p + 3)/9
Suppose 5*q - 4*r = -6, 18 = -28*q + 33*q + 2*r. Let v = -205/3 + 69. Find j such that -2/3*j**q + 0 + v*j = 0.
0, 1
Let f(n) = n**3 + 5*n**2 + 2*n + 12. Let i be f(-5). Suppose 6*b - 3*b - 2*q = -4, i*b - 2*q = -4. Find v, given that -1/2 + 1/2*v**2 + b*v = 0.
-1, 1
Let q(r) be the first derivative of r**6/40 + 2*r**5/15 - r**4/8 + 23*r**2 + 48. Let p(b) be the second derivative of q(b). Factor p(m).
m*(m + 3)*(3*m - 1)
Let a(f) be the second derivative of -f**7/42 - f**6/15 + f**5/20 + f**4/6 - 363*f. Factor a(u).
-u**2*(u - 1)*(u + 1)*(u + 2)
Let u be -1 + 3/6 + (-84)/(-140). Let z(c) be the third derivative of 0*c + 0 - c**2 + c**3 - u*c**5 + 1/8*c**4 - 1/40*c**6. Suppose z(d) = 0. What is d?
-2, -1, 1
Let u(z) = z**3 - 11*z**2 + 22*z + 18. Let m be u(8). Factor 25/4 + 1/4*j**m - 5/2*j.
(j - 5)**2/4
Factor -10648/7 - 1716/7*t**2 + 8228/7*t - 4/7*t**4 + 20*t**3.
-4*(t - 11)**3*(t - 2)/7
Suppose -4*b = -69 + 45. Let d(o) = 3*o + 8 - 3 + 3*o**2 + 1. Let i(l) = -5*l**2 - 6*l - 11. Let v(c) = b*i(c) + 11*d(c). Factor v(r).
3*r*(r - 1)
Let f(b) = b**2 + 9*b + 16. Let q(c) = 2*c**2 + 17*c + 14. Let g be q(-7). Let m be f(g). Factor -m*t**3 + 2*t**2 - t + t**4 + 1/5 - 1/5*t**5.
-(t - 1)**5/5
Let o(n) be the third derivative of n**7/1470 + 13*n**6/840 + 11*n**5/140 - 11*n**4/24 - 7*n**3/3 - 7*n**2 + 14. Factor o(m).
(m - 2)*(m + 1)*(m + 7)**2/7
Let m(q) be the first derivative of 8 + 0*q**2 + 0*q + 0*q**3 - 1/5*q**4. Factor m(b).
-4*b**3/5
Let w(o) be the third derivative of -6*o**2 + 0*o - 1/27*o**3 - 1/54*o**4 + 0 - 1/270*o**5. Find v, given that w(v) = 0.
-1
Let o(q) = 1. Let d(h) = -h**2 - 2*h - 5. Let b = 13 + -15. Let t(v) = -4*v**2 - 8*v - 19. Let c(g) = b*t(g) + 9*d(g). Let p(x) = c(x) + 6*o(x). Factor p(a).
-(a + 1)**2
Find v such that 1411*v**2 + 509*v**2 - 3 + 1020*v + 2817*v**2 + 465*v**2 + 53 = 0.
-5/51
Factor -8/5*i**3 - 28/5*i + 46/5*i**2 - 2.
-2*(i - 5)*(i - 1)*(4*i + 1)/5
Let h = 2924/4865 + -1/973. Let d(t) be the first derivative of 7 + h*t**5 - 3*t**4 + 0*t + 3*t**3 + 0*t**2. Let d(w) = 0. Calculate w.
0, 1, 3
Let h(p) be the first derivative of p**3/2 - 81*p**2/2 + 2187*p/2 + 22. Suppose h(f) = 0. What is f?
27
Let g(a) be the second derivative of -a**6/105 - 13*a**5/70 - 23*a**4/21 - 4*a**3/7 + 72*a**2/7 + 37*a - 1. Let g(b) = 0. Calculate b.
-6, -2, 1
Factor 8/7*a - 2*a**2 + 24/7 + 2/7*a**3.
2*(a - 6)*(a - 2)*(a + 1)/7
Let t(s) = -2*s + 65. Let w be t(30). Suppose 8*n - 3*n + w = 0, -10 = -4*y + 2*n. Factor 1/2*v**y - v - 3/2.
(v - 3)*(v + 1)/2
Let j(c) be the third derivative of 1/8*c**6 + 0 + 11/16*c**4 + 3/140*c**7 + 5*c**2 + 0*c + 3/4*c**3 + 1/672*c**8 + 23/60*c**5. Factor j(n).
(n + 1)**3*(n + 3)**2/2
Let v = -283/195 - -80/39. Let m(g) be the second derivative of -2*g**3 + v*g**5 + 0 + 5*g - 2/15*g**6 - 1/3*g**4 + 4*g**2. Factor m(q).
-4*(q - 2)*(q - 1)**2*(q + 1)
Solve -640*m**3 - 162 + 1028*m**2 + 23*m**4 - 160*m - 107*m**4 + 18 = 0.
-9, -2/7, 2/3, 1
Let g(v) = 4*v**3 + 16*v**2 - 15*v + 5. Let d(a) = a**3 + a**2 - a + 1. Let y(n) = -15*d(n) + 3*g(n). Factor y(b).
-3*b*(b - 10)*(b - 1)
Let w(g) = 4*g**2 + g + 2. Let v = 5 - 6. Let f be w(v). Factor 6*x + 9*x**3 + 3*x**4 - 19*x**f + 28*x**5 - 15*x**2 - 12*x**5.
-3*x*(x - 1)**3*(x + 2)
Let w(f) = 2*f + 72. Let h be w(-36). Let y(u) be the third derivative of -1/60*u**5 - 1/6*u**4 + h - 2/3*u**3 - 4*u**2 + 0*u. Factor y(t).
-(t + 2)**2
Let v(r) = 2*r - 14. Let t be v(10). Factor 4*s**3 + 6*s + 14*s - 16*s + s**4 + 1 + t*s**2.
(s + 1)**4
Let i be (-19)/4 - (-740)/148. Let l(s) be the first derivative of 0*s + 0*s**2 - i*s**4 - s**3 - 6. Find o such that l(o) = 0.
-3, 0
Let x(n) be the second derivative of -12*n**5/35 - 2*n**4 + 111*n**3/14 - 135*n**2/14 + 295*n. Find s, given that x(s) = 0.
-5, 3/4
Suppose 3*l + 9 = -n + 24, -4*n = -4*l + 4. Let u(a) be the first derivative of -2*a + 1/3*a**n - 10 + 1/2*a**2. Determine k, given that u(k) = 0.
-2, 1
Suppose -28/5 - 4/5*w**2 + 32/5*w = 0. What is w?
1, 7
Let 609*f**2 - 610*f**2 - 4*f + 6*f = 0. What is f?
0, 2
What is z in 0 - 5/3*z**3 + 20/3*z + 20/3*z**2 - 5/3*z**4 = 0?
-2, -1, 0, 2
Let k = -1/18 + 13/18. Let v = k - 0. Suppose 2/3*h**2 + 0 + v*h = 0. What is h?
-1, 0
Solve 2/5*h**2 - 108/5 + 10*h = 0 f