0). Factor -2/15*t**4 + p*t + 0 + 2/5*t**3 - 2/5*t**2.
-2*t*(t - 1)**3/15
Let f(p) be the second derivative of -7*p**6/10 - 3*p**5/10 + 7*p**4/4 + p**3 - 19*p. Factor f(y).
-3*y*(y - 1)*(y + 1)*(7*y + 2)
Solve -22 + 4*p - 2/11*p**2 = 0 for p.
11
Let f(c) be the first derivative of 2*c**5/45 + 2*c**4/9 + 2*c**3/9 - 20. Solve f(b) = 0 for b.
-3, -1, 0
Let y = 325/28 + -45/4. Let x(i) be the second derivative of 3/2*i**4 + y*i**7 - 16/15*i**6 + 0 - 7/6*i**3 + 3*i - i**2 + 2/5*i**5. Factor x(j).
(j - 1)**3*(3*j + 2)*(5*j + 1)
Factor -6/5*b**2 - 1/5*b**4 - 4/5*b - 1/5 - 4/5*b**3.
-(b + 1)**4/5
Let n = 27 + -80/3. Let h(q) be the second derivative of 0 + n*q**3 + 1/12*q**4 + 1/2*q**2 - 2*q. Factor h(w).
(w + 1)**2
Let i be (-5)/10 - 81/(-6). Factor 10 + 3*u**3 - 10 + u**5 - 9*u**4 - i*u**5.
-3*u**3*(u + 1)*(4*u - 1)
Let k(d) be the first derivative of d**5 - 10*d**4 + 35*d**3 - 45*d**2 - 7. Find t, given that k(t) = 0.
0, 2, 3
Let z(p) = p**2 - 12*p - 19. Let d be z(13). Let m be (4/d)/((-6)/18). Factor 2*f**3 + 4/3*f**2 - m*f - 4/3.
2*(f - 1)*(f + 1)*(3*f + 2)/3
Let y(t) = -2*t**4 + 8*t**3 + 8*t**2 - 20*t. Let k(h) = 6*h**4 - 23*h**3 - 24*h**2 + 59*h. Let w(q) = 4*k(q) + 11*y(q). Factor w(m).
2*m*(m - 2)**2*(m + 2)
Let z be 2 + (-3 - (1 + -2)). Let u(d) be the second derivative of 0*d**4 - 1/12*d**3 - d + z*d**2 + 0 + 1/40*d**5. Determine j so that u(j) = 0.
-1, 0, 1
Let d(y) be the third derivative of 1/180*y**6 + 0*y**5 + 0*y**3 + 0*y**4 + 0 + 2*y**2 + 0*y. Let d(b) = 0. What is b?
0
Let a(g) be the first derivative of -3*g - 3*g**3 + 27/4*g**4 + 3 - 15/2*g**2. Factor a(d).
3*(d - 1)*(3*d + 1)**2
Let r(x) be the third derivative of -x**5/12 - 5*x**4/24 + 5*x**3/3 + 34*x**2. Factor r(q).
-5*(q - 1)*(q + 2)
Factor -3 - 32 + 20*a + 16*a**4 + 27 - 4*a**5 - 8*a**2 - 16*a**3.
-4*(a - 2)*(a - 1)**3*(a + 1)
Let b(m) be the third derivative of m**7/3360 - m**5/480 + m**3/6 + m**2. Let i(z) be the first derivative of b(z). Factor i(g).
g*(g - 1)*(g + 1)/4
Let r(l) be the first derivative of 0*l**2 + 4/9*l**3 + 5/6*l**4 + 1/9*l**6 + 8/15*l**5 + 3 + 0*l. Factor r(v).
2*v**2*(v + 1)**2*(v + 2)/3
Let w be 6/1*(-3)/6. Let k be w - (0 + (-39)/12). Determine h so that 0 - 1/4*h**4 + 0*h + 0*h**3 + k*h**2 = 0.
-1, 0, 1
Let q(g) = -g - 4. Let c be q(-4). Factor -16*m**2 + 4*m**3 + 3*m**2 - 4 - 3*m**2 + 14*m + 4*m**4 - 2*m**5 + c.
-2*(m - 1)**4*(m + 2)
Let f(j) = j**2 + 6*j + 1. Let w be -1*3/(-6)*-18. Let c(x) = 3*x**2 + 12*x + 3. Let y(l) = w*f(l) + 4*c(l). Factor y(v).
3*(v - 1)**2
Let b = -6/1225 + -23167/22050. Let k = b + 14/9. Determine m so that k*m**2 + 2 + 2*m = 0.
-2
Let z = 96396112/265 + -363760. Let t = 6/53 - z. Factor -6/5*u**2 - 2/5*u**3 - 2/5 - t*u.
-2*(u + 1)**3/5
Let a(j) be the second derivative of j**8/1680 - 2*j**7/315 + j**6/60 + j**4/12 + 11*j. Let m(n) be the third derivative of a(n). Find b, given that m(b) = 0.
0, 1, 3
Let s(a) = a**2 + a - 1. Let g(o) = 5*o**3 + 45*o**2 + 40*o - 25. Let x(p) = g(p) - 25*s(p). Factor x(l).
5*l*(l + 1)*(l + 3)
Let n(j) be the second derivative of 4*j + 5/24*j**3 - 1/12*j**4 + 1/80*j**5 - 1/4*j**2 + 0. Factor n(a).
(a - 2)*(a - 1)**2/4
Suppose -3*f - 4*b - 16 = 0, -3*b + 5 - 17 = 0. Solve f*p**3 + 0 - 3/5*p**2 + 1/5*p**4 - 2/5*p = 0 for p.
-1, 0, 2
Suppose 6*j - 5*k = 3*j + 6, 3*k - 6 = -3*j. Factor 0 + 1/3*d - 1/3*d**3 + 0*d**j.
-d*(d - 1)*(d + 1)/3
Let h(v) be the first derivative of 7*v**3/9 + 23*v**2/6 + 2*v + 3. Solve h(g) = 0 for g.
-3, -2/7
Let h = 7 - -11. Suppose -2*o - 2 = 4*f - h, -5*f - o + 14 = 0. Factor -2*q**4 + 3*q - 3*q + f*q**5 + 2*q**2 - 2*q**3.
2*q**2*(q - 1)**2*(q + 1)
Let r(v) be the second derivative of -v**6/45 - 2*v**5/15 - v**4/6 + 21*v. Determine k, given that r(k) = 0.
-3, -1, 0
Factor 0 - 14/5*x**5 - 32/5*x**4 + 0*x**2 + 0*x - 8/5*x**3.
-2*x**3*(x + 2)*(7*x + 2)/5
Let f(b) = b**2 + 1. Let x be f(3). Let v be x/(-15) + (0 - -1). Suppose -v*h**2 + 0*h + 0 = 0. What is h?
0
Let n(k) be the first derivative of 5 + 1/2*k**3 + 2*k + 2*k**2. Determine c, given that n(c) = 0.
-2, -2/3
Let a(s) be the first derivative of 2/9*s**3 + 0*s + 1/6*s**4 - 2/15*s**5 - 1/3*s**2 + 2. Factor a(o).
-2*o*(o - 1)**2*(o + 1)/3
Let b = -22/7 + 447/140. Let q(s) be the second derivative of s + 0 + 0*s**3 - b*s**5 + 0*s**2 - 1/12*s**4. Factor q(m).
-m**2*(m + 1)
Let q be 9/27 - ((-5)/3 + 2). Factor 0*y - y**2 + q*y**3 + 1/2*y**4 + 1/2.
(y - 1)**2*(y + 1)**2/2
Let p(l) be the second derivative of l**7/84 - l**6/15 + l**5/8 - l**4/12 + 2*l. Factor p(j).
j**2*(j - 2)*(j - 1)**2/2
Suppose -y - 2*y + 24 = 5*q, 2*y - q = 3. Factor g**3 - g**3 + 3*g - 4*g**2 + 2*g**y - g.
2*g*(g - 1)**2
Let y(s) be the third derivative of 0 - 1/30*s**5 + 2*s**2 + 0*s - 1/12*s**4 + 0*s**3. Factor y(n).
-2*n*(n + 1)
Let n(l) be the first derivative of 2/3*l**2 + 1/9*l**3 - 6 + l. Factor n(x).
(x + 1)*(x + 3)/3
Let n(k) be the first derivative of k**5/35 - k**4/14 + k**2/7 - k/7 + 2. Determine b so that n(b) = 0.
-1, 1
Let y(h) be the third derivative of 1/8*h**4 - 1/40*h**6 - 6*h**2 + 0*h**5 + 0*h + 0*h**3 + 0. Factor y(b).
-3*b*(b - 1)*(b + 1)
Let g(i) be the second derivative of i**7/294 + i**6/210 + i. Factor g(q).
q**4*(q + 1)/7
Let u(o) be the first derivative of -2*o**5/25 + o**4/10 + 2*o**3/15 - o**2/5 - 1. Let u(v) = 0. Calculate v.
-1, 0, 1
Let w = -302/115 - 4/23. Let g = -12/5 - w. Factor 2/5*c + 2/5*c**2 - 2/5*c**3 - g.
-2*(c - 1)**2*(c + 1)/5
Let s = -3 + 3. Suppose 5*w - 2*w = s. Suppose w + 0 - 2*h**2 = 0. Calculate h.
0
Let r be (-4)/10 - (-16)/40. Let s(n) be the first derivative of 3 + r*n - 2/3*n**2 + 2/9*n**3. Solve s(i) = 0.
0, 2
Factor 11*z - 8*z**2 + 8 - 12*z**3 + 16*z**2 + 17*z.
-4*(z - 2)*(z + 1)*(3*z + 1)
Let j(g) be the first derivative of -g**7/420 + g**6/240 + g**5/120 - g**4/48 - g**2 + 1. Let p(o) be the second derivative of j(o). Factor p(w).
-w*(w - 1)**2*(w + 1)/2
Let a(l) = -l**3 - 2*l**2. Let w be a(-2). Let d(y) be the third derivative of 0*y**5 + w + 1/315*y**7 + 1/180*y**6 + y**2 + 0*y**3 + 0*y**4 + 0*y. Factor d(s).
2*s**3*(s + 1)/3
Let y(k) = k**3 + 13*k**2 + 24*k + 22. Let i be y(-11). Factor i*q + 0 + 2/11*q**2.
2*q**2/11
Determine z, given that -11*z**2 + 69*z + 46*z - 30 + 31*z**2 = 0.
-6, 1/4
Suppose -11 = -2*f - 11. Factor 4/5*z**2 + f*z**3 + 0 - 4/5*z**4 + 2/5*z**5 - 2/5*z.
2*z*(z - 1)**3*(z + 1)/5
Let k = 2 - -1. Let s(j) be the first derivative of -1/4*j**2 + 1/10*j**5 + 0*j + 1/2*j**k - 3/8*j**4 + 2. Factor s(v).
v*(v - 1)**3/2
Let s(v) be the first derivative of v**4/14 + 10*v**3/21 + 6*v**2/7 + 9. Solve s(o) = 0.
-3, -2, 0
Let v be (42/3)/(3/((-18)/(-24))). Find r, given that 3/4*r**5 - 1/2 - v*r**4 - 6*r**2 + 11/4*r + 13/2*r**3 = 0.
2/3, 1
Find n, given that -2/5*n - 4/5*n**3 + 1/5*n**4 + 0 + n**2 = 0.
0, 1, 2
Let w = 331 + -331. Factor 2*g**3 - 3/2*g + 1 + w*g**4 - g**2 - 1/2*g**5.
-(g - 1)**3*(g + 1)*(g + 2)/2
Let r(i) be the second derivative of -i**6/60 - i**5/40 + i**4/8 + i**3/12 - i**2/2 + 15*i. Solve r(f) = 0.
-2, -1, 1
Let s(i) be the first derivative of i**8/1176 + 2*i**7/735 + i**6/420 - i**2 + 1. Let j(l) be the second derivative of s(l). Factor j(w).
2*w**3*(w + 1)**2/7
Let u(j) be the first derivative of -j**3/3 - 3*j**2 - 3*j + 3. Let x be u(-5). Suppose 2*q**x + q + 0 - 5 + 3 - q**2 = 0. What is q?
-2, 1
Let k(y) = -y**4 - 25*y**3 + 21*y**2 - 5*y. Let p(v) = -12*v**3 + 10*v**2 - 2*v. Let z(t) = -2*k(t) + 5*p(t). Find l, given that z(l) = 0.
0, 1, 4
Determine d, given that 18/7 + 57/7*d + 12/7*d**3 - 57/7*d**2 = 0.
-1/4, 2, 3
Let c(y) be the first derivative of y**4/2 + 2*y**3/3 - 2*y**2 + 16. Suppose c(p) = 0. What is p?
-2, 0, 1
Let k(u) = -u - 1. Suppose -10 + 6 = -4*q. Let x(l) be the second derivative of l**4 + 5*l**3/6 + l**2 + l. Let v(j) = q*x(j) + 2*k(j). Factor v(y).
3*y*(4*y + 1)
Let w(m) be the second derivative of -m**9/1008 + m**8/560 + m**3/2 - 4*m. Let v(f) be the second derivative of w(f). Factor v(l).
-3*l**4*(l - 1)
Let q(b) be the second derivative of -b**6/165 - 3*b**5/110 - b**4/33 - b. Factor q(r).
-2*r**2*(r + 1)*(r + 2)/11
Suppose -2*o = 2*o - 4*u - 28, 4*o - 23 = 3*u. Let 27*d**o - 18*d**2 + 6*d - 3*d - 12*d**4 = 0. What is d?
-1/2, 0, 1
Let h(v) = -2*v - 54. Let x be h(-28). Factor 0 + 2/5*i**3 - 4/5*i**x + 2/5*i.
2*i*(i - 1)**2/5
