rivative of -c**6/72 + 5*c**5/24 + 35*c**4/12 - 23*c**3/3 + 36. Let v(r) be the third derivative of s(r). Factor v(q).
-5*(q - 7)*(q + 2)
Let m be -4 - ((-1960)/36)/10. Let u = 2/9 + m. Let -1/3 - h**2 - 3*h**3 + u*h = 0. What is h?
-1, 1/3
Let q(p) be the first derivative of -p**6/10 + 7*p**5/20 - 5*p**4/12 + p**3/6 - 6*p + 11. Let k(g) be the first derivative of q(g). Factor k(j).
-j*(j - 1)**2*(3*j - 1)
Suppose 0 = -4*j + 4*y + 4, -j - 2*j = -y - 1. Suppose -2*d - 6 = j, 25 = 2*w - 5*d + 2. Factor w*b + 2 + 2 - 4*b**2 + 4*b**3 - 5*b - 3*b.
4*(b - 1)**2*(b + 1)
Let d(b) = -b**2 - 12*b - 32. Let f be d(-8). Solve -t**2 + t**3 - 2*t**2 - 4*t**3 + f*t**3 = 0 for t.
-1, 0
Let f(m) be the third derivative of 7*m**2 - 5/4*m**4 + 0*m**3 - 1/12*m**5 + 0 + 0*m. Find k, given that f(k) = 0.
-6, 0
Let a(g) be the third derivative of 0*g**4 - 1/60*g**5 + 0*g**3 + 0 + 0*g + 1/120*g**6 - 1/840*g**7 + 20*g**2. Find f such that a(f) = 0.
0, 2
Let w(x) be the first derivative of 125*x**6/18 - 370*x**5/3 + 7685*x**4/12 - 532*x**3/9 - 16072*x**2/3 - 21952*x/3 + 594. Factor w(t).
(t + 1)**2*(5*t - 28)**3/3
Let x(y) be the second derivative of -y**7/8820 + y**5/420 + 7*y**4/6 + 3*y. Let r(d) be the third derivative of x(d). Solve r(m) = 0.
-1, 1
Suppose x - 8 = -3*x. Let p(g) = -44*g - 1670. Let a be p(-38). Factor 1/4*q - 1/2 + 5/4*q**3 + x*q**a.
(q + 1)**2*(5*q - 2)/4
Let o = -23222 - -69671/3. Suppose -17/6*v + o - 1/6*v**3 + 4/3*v**2 = 0. What is v?
1, 2, 5
Let q = 6 + -2. Let 12*a**2 - 60*a**3 + 16*a**3 + 12*a**q + 216 + 44*a - 240 = 0. What is a?
-1, 2/3, 1, 3
Suppose -6 - 4 = -5*i. Factor -18*v**2 + 6*v**2 - 2*v**4 - i*v**4 - 24*v**3 + 8*v**3.
-4*v**2*(v + 1)*(v + 3)
Let m(n) be the third derivative of n**5/100 - n**4/20 - 3*n**3/2 - 6*n**2 + 11*n. Suppose m(g) = 0. Calculate g.
-3, 5
Let z be 27/(-18)*28/(-6). Suppose i = -z*i + 24. Solve 0 - 1/4*t + 1/4*t**i + 1/4*t**2 - 1/4*t**4 = 0.
-1, 0, 1
Let w = 181/3 + -359/6. Let x = -12 + 12. Factor w - 1/2*a**2 + x*a.
-(a - 1)*(a + 1)/2
Let k be (-5)/(-1) + (-1083)/95 + 8. Solve -1/5*y**3 - 4/5 - k*y - y**2 = 0 for y.
-2, -1
Let m be 12/18 - (-332)/6. Factor 15*z**2 + 12*z**4 + 60*z**2 + 32*z + 5*z**2 + m*z**3.
4*z*(z + 2)**2*(3*z + 2)
Let h(q) be the first derivative of -4*q - 8*q**2 - 7*q**3 - 11/4*q**4 - 2/5*q**5 + 19. Factor h(p).
-(p + 1)*(p + 2)**2*(2*p + 1)
Let f(l) be the third derivative of -7*l**6/180 + l**5/45 + 2*l**4/3 - 420*l**2. Suppose f(w) = 0. What is w?
-12/7, 0, 2
Let y(t) = 6 + 15 - 4 + 5*t + 3. Let o be y(-4). Factor -1/3*n**4 + 0 - 2/3*n**3 - 1/3*n**2 + o*n.
-n**2*(n + 1)**2/3
What is p in -8*p**2 + 10*p**4 - 190 + 190 + 20*p**3 + 18*p**4 = 0?
-1, 0, 2/7
Let q be ((-92)/414)/(8/(-12) - 1/(-6)). Factor -2/9*z**3 - q*z**2 - 2/9*z + 0.
-2*z*(z + 1)**2/9
Let a(p) be the third derivative of -p**7/140 + p**6/240 + p**5/15 + p**4/12 - 71*p**2. Let a(m) = 0. What is m?
-1, -2/3, 0, 2
Factor 43*r**2 - 103*r**2 + 45*r**2 + 33*r**2 - 33*r + 15.
3*(r - 1)*(6*r - 5)
Suppose 0 = -3*p + 101 - 95. Suppose -4 = -3*x + 4*k, -9 = -p*x - 3*k + 5. Factor x*j - 2/3*j**2 - 6.
-2*(j - 3)**2/3
Let q = -1313/2 - -670. Factor -3/2*y**4 + 0 + 9/2*y**3 + q*y**2 + 15/2*y.
-3*y*(y - 5)*(y + 1)**2/2
Let l(u) = 5*u**2 + u - 1. Let p be l(2). Suppose 2*b + 0*x = 3*x + p, -4*x - 20 = 0. Let 0*d**2 - 3*d**2 - d**2 + d**2 - d**4 + d + b*d**3 = 0. What is d?
0, 1
Let c = -2936 - -20579/7. Factor 0*i + c - 3/7*i**2.
-3*(i - 3)*(i + 3)/7
Let o be 16/5 - (-6)/(-30). Suppose o*d + 0 = 6. Let -2*s**d + 5*s**2 - 8 - 4 = 0. What is s?
-2, 2
Let q = -35 + 40. Find x such that -5*x - x**4 + 2*x**2 + 239*x**3 - 240*x**3 + q*x = 0.
-2, 0, 1
Let k(c) be the first derivative of -c**5/450 + c**4/10 - 9*c**3/5 - 25*c**2/2 - 38. Let j(w) be the second derivative of k(w). Find h, given that j(h) = 0.
9
Let l(u) be the first derivative of u**7/420 + u**6/144 - 7*u**5/240 - u**4/24 + 4*u**3/3 + 3. Let w(t) be the third derivative of l(t). Factor w(o).
(o - 1)*(o + 2)*(4*o + 1)/2
Let a(g) be the second derivative of -g**8/2240 - g**7/1120 + g**6/480 + g**5/160 - 8*g**3/3 - 16*g. Let x(l) be the second derivative of a(l). Factor x(i).
-3*i*(i - 1)*(i + 1)**2/4
Let g be (-2)/7*(-42)/6. Let z(a) be the second derivative of 1/40*a**6 + 1/8*a**3 + 0 - 1/168*a**7 - 1/24*a**4 - 4*a - 1/8*a**g - 1/40*a**5. Factor z(k).
-(k - 1)**4*(k + 1)/4
Let j(q) = q**4 + q**2 - q + 2. Let h(n) = -15*n**4 + 38*n**3 - 33*n**2 + 7*n - 6. Let v(i) = 2*h(i) + 6*j(i). Let v(c) = 0. What is c?
0, 1/6, 1, 2
Determine z so that -8 + 132*z**2 + 15*z**4 + 0 + 78*z**3 + 37*z**4 + 28*z + 70*z**3 = 0.
-1, 2/13
Let q(l) be the second derivative of 5/12*l**4 - 4*l + 5*l**2 + 0 - 5/2*l**3. Suppose q(z) = 0. Calculate z.
1, 2
Let t(s) be the second derivative of 1/30*s**6 + 15*s + 1/2*s**3 + 1/12*s**4 + 0 - s**2 - 3/20*s**5. Factor t(k).
(k - 2)*(k - 1)**2*(k + 1)
Let w(x) = -2*x**2 + 32*x - 53. Let j be w(14). Let l(k) be the third derivative of 1/210*k**5 - 1/84*k**4 + 0*k**j + 0 + 0*k - 5*k**2. Factor l(h).
2*h*(h - 1)/7
Suppose 0 = -5*w - 3*z - 3 + 53, -w - 4*z = -10. Suppose 0*f = -5*f + w. Let 2*i**4 + 2 + 0*i**2 + 0*i**2 - 3*i**2 - i**f = 0. Calculate i.
-1, 1
Let f(n) be the first derivative of -n**4/2 + 4*n**3/3 + n**2 - 4*n - 20. Factor f(z).
-2*(z - 2)*(z - 1)*(z + 1)
Factor 16/17*p + 0 + 2/17*p**3 - 18/17*p**2.
2*p*(p - 8)*(p - 1)/17
Suppose 0 = 2*o + 2, 3*o - 14 = -3*n + 2*o. Let h(y) be the second derivative of -1/30*y**6 - 2/3*y**3 + 9*y - 1/4*y**n + 0 - 2/3*y**4 + 0*y**2. Factor h(l).
-l*(l + 1)*(l + 2)**2
Let a(d) = -3*d**3 - 32*d**2 - 29*d. Let m(i) = i**3 + 11*i**2 + 10*i. Let k(v) = 6*a(v) + 21*m(v). Solve k(u) = 0 for u.
-12, -1, 0
Let f(y) = y + 9. Let r be f(-6). Let b = 0 + r. Solve 2/3*s**5 - 4/3*s**b + 8/3*s**2 - 4/3 + 2/3*s - 4/3*s**4 = 0.
-1, 1, 2
Let i(a) = a**3 + 4*a**2 - a + 1. Let o be i(-4). Suppose o*n**2 + 20 - 12*n - 22*n + 9*n = 0. Calculate n.
1, 4
Let x = -1895 + 1897. Factor 0 + 8/3*t**4 + 0*t + 0*t**x - 2*t**5 + 8/3*t**3.
-2*t**3*(t - 2)*(3*t + 2)/3
Let h = 3/179 + 167/716. Let w(j) be the second derivative of 2/15*j**6 + 11/20*j**5 - 12*j - h*j**4 + 0*j**2 + 0*j**3 + 0. Factor w(n).
n**2*(n + 3)*(4*n - 1)
Let c(b) = 4*b**3 + 8*b**2 - 12*b - 32. Let n(k) = k + 1 - 1 + 0. Suppose a = -4*w - 13, 3*w + 2*w + 5*a + 5 = 0. Let v(i) = w*n(i) + c(i). Factor v(j).
4*(j - 2)*(j + 2)**2
Suppose 0 = -112*j - 453 + 789. Let f = 1 + -1. Determine g so that 8/13*g**j + 2/13*g + f + 8/13*g**2 = 0.
-1/2, 0
Let m be -2 - (-1 - 22/1). Let a(h) = -2 + 3 - 2 + h**2. Let s(i) = -2*i**3 + 2*i**2 - 4*i - 8. Let r(d) = m*a(d) - 3*s(d). Factor r(n).
3*(n + 1)**2*(2*n + 1)
Let k be 2/(-11) - 1725/(-5313). Let b(a) be the second derivative of -1/42*a**4 - 2/7*a**2 + k*a**3 + 7*a + 0. Let b(i) = 0. What is i?
1, 2
Let u be (22 - 17) + (0 - 5). Suppose u = -10*g - 8 + 38. Factor -1/8*n**g + 0*n + 0 - 1/8*n**2.
-n**2*(n + 1)/8
Let k(n) = 5*n**2 - n + 15. Let x be k(4). Factor -4*c**3 + x*c - c**3 - 7*c**2 - 106*c - 13*c**2.
-5*c*(c + 1)*(c + 3)
Let s be (-1*1/2)/((-26)/3120*15). Find w such that 0*w + 2/3*w**3 - 1/3*w**2 - 1/3*w**s + 0 = 0.
0, 1
Let q = 2295/1534 + 3/767. Factor 0 + q*a**2 + 0*a.
3*a**2/2
Suppose -2*b + u + 8 = 0, 3*b + u - 10 = -3. Find w such that 531*w**3 + 6*w - 260*w**3 + 15*w**2 + 3*w**4 - 259*w**b = 0.
-2, -1, 0
Let r(y) be the first derivative of -2*y**6/9 - 24*y**5/5 - 104*y**4/3 - 64*y**3 + 288*y**2 + 1152*y + 104. Let r(x) = 0. What is x?
-6, -2, 2
Let q(n) be the third derivative of -n**5/90 + n**4/12 - 2*n**3/9 - 536*n**2. Find h, given that q(h) = 0.
1, 2
Let t(k) = 4*k**3 + 18*k**2 - 10*k - 84. Let d(b) = 8*b**3 + 37*b**2 - 21*b - 170. Let r(z) = 6*d(z) - 11*t(z). Find g, given that r(g) = 0.
-6, -2, 2
Let -2700 - 4/3*h**2 - 120*h = 0. What is h?
-45
Suppose g - 20 = -5*k, k - 5*k + 5 = 3*g. Suppose -k*y + 5*l - 13 = 2, -2*y + 4*l = 16. Factor -79*v + 79*v - y*v**2.
-2*v**2
Let a = 1156 - 1151. Let i(l) be the third derivative of 2/15*l**a + 0*l**3 + 0 - 1/30*l**6 + 0*l - 1/6*l**4 - l**2. Factor i(p).
-4*p*(p - 1)**2
Let r = 79298/45 + -1762. Let q(v) be the first derivative of 1/18*v**4 + 0*v - 1 - 1/9*v**2 - 8/27*v**3 + r*v**5. Determine p, given that q(p) = 0.
-1, -1/4, 0, 1
Let c(w) be the second derivative of w**6/30 - w**5/5 + w*