**2*(v + 2)/4
Let h(j) be the third derivative of j**5/15 - 5*j**4/6 + 8*j**3/3 + 17*j**2. Factor h(a).
4*(a - 4)*(a - 1)
Let i(q) = 5*q**4 + 2*q**3 - 7*q**2 + 4*q + 4. Let b(u) = 4*u**4 + u**3 - 6*u**2 + 4*u + 4. Let f(j) = -4*b(j) + 3*i(j). Solve f(t) = 0 for t.
-1, 2
Let k(n) be the second derivative of -n**5/30 + n**4/9 + n**3/3 + 21*n. What is v in k(v) = 0?
-1, 0, 3
Let b(o) be the third derivative of 5/108*o**6 + 0 + 19/135*o**5 - 6*o**2 + 7/27*o**4 + 8/27*o**3 + 0*o + 8/945*o**7 + 1/1512*o**8. Factor b(d).
2*(d + 1)**2*(d + 2)**3/9
Let k(h) be the first derivative of 4*h**3/3 - 2*h**2 - 48*h + 60. Suppose k(i) = 0. What is i?
-3, 4
Let y(i) be the third derivative of 1/42*i**4 + 2*i**2 + 0*i + 1/21*i**3 + 1/210*i**5 + 0. Factor y(j).
2*(j + 1)**2/7
Let f(d) = -135*d**4 + 215*d**3 + 190*d**2 - 325*d + 55. Let x(a) = 5*a**4 - 8*a**3 - 7*a**2 + 12*a - 2. Let k(y) = -2*f(y) - 55*x(y). Factor k(o).
-5*o*(o - 2)*(o - 1)*(o + 1)
Let g = -13 - -13. Let u be 0 + g + -3 - -6. Solve u*o + 2 + 1/4*o**3 + 3/2*o**2 = 0.
-2
Suppose 5*c + 16 = -5*x - 4, 16 = -c - 4*x. Let n(q) be the first derivative of c*q**2 + 3/4*q**4 + q**3 - 1 + 0*q. Factor n(o).
3*o**2*(o + 1)
Let x(u) be the third derivative of 0 + 3*u**2 + 0*u + 1/4*u**6 - 3/8*u**4 + 3/10*u**7 + 9/112*u**8 + 1/2*u**3 - 3/10*u**5. Determine i so that x(i) = 0.
-1, 1/3
Let i = -4 - -4. Suppose -5*h + i*s + 9 = 3*s, 6 = 2*s. Find c such that c**4 + h + 1 - 2*c + 2*c**3 - 2*c**4 = 0.
-1, 1
Let f = 5 + -3. Let a be (1/(-6))/(28/(-126))*4. Factor 6/7*i**a + 2/7*i**f - 2/7 - 6/7*i.
2*(i - 1)*(i + 1)*(3*i + 1)/7
Suppose 12 - 47 = 5*r. Let u = r + 10. Factor 0*p**2 + 2*p**u - 2*p**2 - 2*p**2.
2*p**2*(p - 2)
Let t = -570 - -1714/3. Factor 0*b - t + 1/3*b**2.
(b - 2)*(b + 2)/3
Let m be 14 + -12 - 2*-1. Let u(t) be the first derivative of 0*t**3 - 3/5*t**5 + 0*t**2 + m + 0*t + 3/4*t**4. Suppose u(h) = 0. Calculate h.
0, 1
Let m(k) be the second derivative of 0 - 1/9*k**3 + 49/180*k**6 + 4/9*k**4 - 77/120*k**5 + k + 0*k**2. Determine r, given that m(r) = 0.
0, 2/7, 1
Let 64*q - 34*q - 4*q**2 + 16 - 42*q = 0. Calculate q.
-4, 1
Let d = -551 + 551. Factor -p + 1/2*p**2 + d.
p*(p - 2)/2
Suppose 0 = -5*p + 2*n + 23, 4*p - 2*n - 24 = n. Let k be (-4)/(-6) - 2/p. Let 2/7*w**5 + 0*w**4 - 4/7*w**3 + k + 2/7*w + 0*w**2 = 0. What is w?
-1, 0, 1
Let s(w) = w**2 - w. Let k(p) = p**3 + 4*p**2 - 5*p. Let j be (-1)/(-4 - (0 + -3)). Let q(r) = j*k(r) - 5*s(r). Factor q(t).
t**2*(t - 1)
Let o(u) be the second derivative of -1/5*u**5 - 4*u - 14/15*u**3 + 3/5*u**4 + 0 + 4/5*u**2 + 2/75*u**6. Factor o(n).
4*(n - 2)*(n - 1)**3/5
Let z(p) be the second derivative of -p**8/23520 - p**7/8820 + p**6/2520 + p**5/420 + p**4/6 - p. Let r(q) be the third derivative of z(q). Factor r(o).
-2*(o - 1)*(o + 1)**2/7
Let z = -28113443/120 + 234280. Let w = z - -1/40. Suppose w*k**3 + 1/3*k**2 + 0*k - 4/3*k**5 - 1/3*k**4 + 0 = 0. Calculate k.
-1, -1/4, 0, 1
Let a(k) = 5*k**2 - 4*k + 5. Let b(v) = 36*v**2 - 27*v + 36. Let s(h) = -15*a(h) + 2*b(h). Suppose s(x) = 0. What is x?
1
Find a such that a**2 - 49*a**2 - 24*a**4 + 29*a + 4 - 21*a + 4*a**4 + 56*a**3 = 0.
-1/5, 1
Let d = 46 + -43. Find n, given that -1/2*n**5 + 0*n + 0*n**2 + 0 + n**4 - 1/2*n**d = 0.
0, 1
Suppose -46 - 22 = -4*f. Let t(m) = -2*m**2 + 6*m + 6. Let k(v) = -6*v**2 + 17*v + 17. Let l(d) = f*t(d) - 6*k(d). Factor l(w).
2*w**2
Let h(c) be the third derivative of 0 + 1/3*c**3 + 0*c - 1/120*c**6 - 5/24*c**4 + 1/15*c**5 + 5*c**2. Factor h(x).
-(x - 2)*(x - 1)**2
Let z be (-403)/91 - (-5)/1. Factor -z - 2/7*d**2 + 6/7*d.
-2*(d - 2)*(d - 1)/7
Suppose 7 = -3*m + 3*s + 4, -3*m = 2*s - 2. Let i(x) be the first derivative of 1/8*x**4 + 0*x**2 + 0*x**3 - 1/20*x**5 + 3 + m*x. Find r such that i(r) = 0.
0, 2
Let s = 4 - 4. Let 5 - 2*t - 2*t - 2*t**2 - 7 + s*t = 0. Calculate t.
-1
Factor -2/3*u**2 + 0*u + 0 - 4/3*u**3 + 2*u**4.
2*u**2*(u - 1)*(3*u + 1)/3
Suppose 0 = 4*r - 0*q - 4*q - 380, 0 = 5*r + 3*q - 483. Let m be 2/11 + r/198. Let 0*k + 0 - m*k**3 - 2/3*k**2 = 0. Calculate k.
-1, 0
Let g(x) = 5*x**4 + 9*x**3 + 13*x**2 + 3*x + 2. Let n(p) = 5*p**4 + 10*p**3 + 12*p**2 + 2*p + 1. Let b(d) = -3*g(d) + 4*n(d). Factor b(v).
(v + 1)**3*(5*v - 2)
Let z(l) be the third derivative of 1/60*l**6 + 0 - 5/12*l**4 - 2/3*l**3 + 1/105*l**7 + 0*l - l**2 - 1/10*l**5. Factor z(u).
2*(u - 2)*(u + 1)**3
Let d(g) be the third derivative of g**5/300 - g**4/60 + g**3/30 - g**2. Factor d(m).
(m - 1)**2/5
Let f(o) be the first derivative of -o**6/1980 - o**3/3 + 6. Let u(g) be the third derivative of f(g). Suppose u(a) = 0. What is a?
0
Let x = 2296/33 - 582/11. Factor x*a**2 + 2/3 - 20/3*a.
2*(5*a - 1)**2/3
Let m(t) be the first derivative of -9/4*t - 4 + 15/4*t**2 + 9/8*t**4 - 3/20*t**5 - 3*t**3. Factor m(n).
-3*(n - 3)*(n - 1)**3/4
Let w(n) be the first derivative of 2/3*n**4 - 4/9*n**3 - 4/3*n**2 + 0*n + 4/15*n**5 - 10. Suppose w(x) = 0. Calculate x.
-2, -1, 0, 1
Let y(b) = -b**2 - 7*b + 6. Let g be y(-7). Let f(z) = 4*z. Let j be f(1). Let 5*d + 4*d**3 - 3*d + g*d**2 + 2*d**3 + 2*d**j = 0. Calculate d.
-1, 0
Factor 0*j**3 + 0*j + 3/5*j**4 + 0 + 0*j**2.
3*j**4/5
Let k + 25 - 9 + k**2 + 7*k = 0. Calculate k.
-4
Let j(c) = -c**2 + 3*c + 8. Let v(t) = 3*t + 9. Let n(a) = -3*j(a) + 2*v(a). What is q in n(q) = 0?
-1, 2
Let s = 22/3 - 41/6. Solve -2*o**2 + 0 - s*o = 0.
-1/4, 0
Let p be (-4)/(4/24*-2). Find x such that 0 - p*x**2 - 1 + 13*x**2 = 0.
-1, 1
Factor -5*b**5 + 0*b**5 + 3*b**3 - 4*b**3 + 6*b**5.
b**3*(b - 1)*(b + 1)
Suppose 2*h - 14 = -2*u + 5*u, -2*h = 4*u. Let q be ((-10)/28)/(-5)*h. Factor -4/7*a - q - 2/7*a**2.
-2*(a + 1)**2/7
Let a be (-28)/(-24) - 10/15. Suppose 0 = 2*o - 4*y - 24, -1 = -4*o - y + 2. Factor -a*c**3 + 1/2*c + 0 + 0*c**o.
-c*(c - 1)*(c + 1)/2
Factor 6/5*s**2 + 1/5*s**4 + 4/5*s**3 + 1/5 + 4/5*s.
(s + 1)**4/5
Let r be -4 + 1 + (6 - 1). Let w be 0 + (3 - (-2 + 1)). Factor -2*x**r + 4 + 2*x - w.
-2*x*(x - 1)
Suppose 5*s + 2*w + 3*w - 10 = 0, -w - 4 = -2*s. Suppose -2/5 - 32/5*t**s - 17/5*t - 16*t**5 + 43/5*t**3 + 88/5*t**4 = 0. What is t?
-2/5, -1/4, 1
Determine b so that -2*b**2 - 18 - 13 + 5*b**4 + 3*b + 28 + 4*b - b**5 - 6*b**3 = 0.
-1, 1, 3
Let h = 5 + -3. Factor h - 3 - 3*y**2 + 0*y + 4*y.
-(y - 1)*(3*y - 1)
Let s(f) = -f**2 - 13*f + 29. Let g be s(-15). Let v be (g/3)/((-10)/24). Solve v*t + 2/5*t**2 + 2/5 = 0.
-1
Let p(t) be the second derivative of t**4/60 + t**3/10 + t**2/5 + 3*t. Suppose p(r) = 0. What is r?
-2, -1
Let h(l) be the first derivative of -2/21*l**3 - 1/7*l**2 + 1/14*l**4 + 2/7*l - 1. Suppose h(i) = 0. What is i?
-1, 1
Factor -5/2*x**2 + 0 - 1/2*x**3 - 2*x.
-x*(x + 1)*(x + 4)/2
What is q in 2/7*q + 0 + 3/7*q**2 - 2/7*q**3 = 0?
-1/2, 0, 2
Let j(d) be the first derivative of -d**5/150 - d**4/60 - 3*d**2/2 - 3. Let c(m) be the second derivative of j(m). Factor c(h).
-2*h*(h + 1)/5
Let c(o) be the third derivative of -o**6/180 + 2*o**5/225 + o**4/180 - o**2. Factor c(r).
-2*r*(r - 1)*(5*r + 1)/15
Let i(r) = -r**3 + 6*r**2 + 7*r + 3. Let d be i(7). Factor 0*m + 2*m - 2*m + d*m**2.
3*m**2
Let j(q) = q + 3. Suppose -r + 15 = -6*r. Let n be j(r). Factor 0 + 10/11*g**4 + 0*g - 4/11*g**3 + n*g**2.
2*g**3*(5*g - 2)/11
Let f be 1/3 + 1/(-3). Factor -7*z**3 - 2*z**4 - z - 2*z**4 + z**4 - 5*z**2 + f*z**4.
-z*(z + 1)**2*(3*z + 1)
Find h such that -2/3*h + 0 + 1/3*h**2 = 0.
0, 2
Let c = 2 - 2. Factor 2*u + c*u**3 - 2*u**3 + 3*u**3 - 2*u**4 + 2*u**2 - 3*u**3.
-2*u*(u - 1)*(u + 1)**2
Let j(q) be the first derivative of 2*q**3/15 - q**2/5 - 12*q/5 + 19. Factor j(n).
2*(n - 3)*(n + 2)/5
Let x(b) be the first derivative of -b**3 - 3*b**2/2 - 5. Determine g, given that x(g) = 0.
-1, 0
Let g(s) be the first derivative of -s**5/70 - s**4/21 - s**3/21 - 2*s + 2. Let h(z) be the first derivative of g(z). What is k in h(k) = 0?
-1, 0
Let c = 6 + -6. Let c*m + 4/3*m**3 + 2/3*m**2 + 0 + 2/3*m**4 = 0. What is m?
-1, 0
Let a(s) be the second derivative of s**5/10 - s**3/3 + 3*s. Factor a(x).
2*x*(x - 1)*(x + 1)
Suppose 0*i + 2/3*i**2 - 2/3 = 0. Calculate i.
-1, 1
Let h be 10/(-15)*(-6)/8. Let y(x) be the second derivative of -h*x**4 - 1/10*x**5 + 2*x + 2*x**2 + 0 + 1/15*x**6 + 1/3*x**3. Factor y(q).
2*(q - 2)*(q - 1)*(q + 1)**2
Let t(n) = n**2 + 1 + 4*n - 4 + 0*n**2. Let u be t(-5). Factor 0*