he third derivative of q(b). Find u such that k(u) = 0.
-2, 2
Let c(x) be the third derivative of -x**6/24 + 5*x**5/4 - 10*x**4 - 160*x**3/3 + x**2 + 46. Factor c(u).
-5*(u - 8)**2*(u + 1)
Let w(j) be the second derivative of 5/3*j**3 - 6*j - 5/12*j**4 + 0*j**2 + 0. Factor w(a).
-5*a*(a - 2)
Suppose -3*r - 3 = n, 4 - 26 = -4*n + 5*r. Solve 47 + n - 50*a**2 - 10 - 15*a**3 - 20*a = 0.
-2, 2/3
Factor -961/9 - 1/9*f**3 + 61/9*f**2 - 899/9*f.
-(f - 31)**2*(f + 1)/9
Let r = -107/26 - -60/13. Let n(z) be the first derivative of 3/5*z**5 - 2*z**3 - 3/2*z**4 + r*z**6 + 3*z + 1 + 3/2*z**2. Factor n(d).
3*(d - 1)**2*(d + 1)**3
Let 2/5 + 8/5*v + 8/5*v**2 = 0. What is v?
-1/2
Let w(u) be the first derivative of 5*u**3/3 + 35*u**2/2 - 150*u - 138. Factor w(n).
5*(n - 3)*(n + 10)
Let b(z) be the third derivative of -z**6/120 + 13*z**5/60 - 852*z**2. Find g such that b(g) = 0.
0, 13
Factor -1/5*h**2 - 17/5*h + 12.
-(h - 3)*(h + 20)/5
Let h be (1 - -2)/(((-21)/56)/(-1)). Let k be h + 708/(-90) + (-22)/(-60). Determine b so that -b**3 - 1/2*b**2 + 0 + b + k*b**4 = 0.
-1, 0, 1, 2
Let v(k) be the third derivative of -2*k**6/15 - 91*k**5/15 + 119*k**4/6 - 16*k**3 - 2*k**2 - 58. Find a, given that v(a) = 0.
-24, 1/4, 1
Let q(h) be the first derivative of 4*h**3/3 - 44*h**2 + 84*h + 237. Determine i, given that q(i) = 0.
1, 21
Suppose 0 = -3*g + 4*g + 3*z + 10, 3*z = 3*g - 6. Let b(o) = -o**3 + o + 1. Let m(i) = -6*i**3 + 56*i**2 - 98*i + 50. Let l(u) = g*m(u) + 2*b(u). Factor l(s).
4*(s - 12)*(s - 1)**2
Let k(c) be the first derivative of -1/7*c**2 - 1/21*c**3 - 19 + 1/28*c**4 + 0*c. Solve k(i) = 0.
-1, 0, 2
Let g = 97 - 128. Let v(f) = f**3 + 32*f**2 + 32*f + 35. Let j be v(g). Determine s, given that 0*s**2 + 0 + 2*s**3 - 2/3*s + 4/3*s**j = 0.
-1, 0, 1/2
Let s(q) = -4*q. Let u be s(-4). What is h in 51*h**4 + 34*h**4 + 112*h + 111*h**3 + 65*h**3 + 216*h**2 - 20*h**4 + u + 9*h**5 = 0?
-2, -1, -2/9
Suppose -21*s = -20*s + a + 1, -6 = 2*a. Let v(t) = -t**3 - 4*t**2 + 6*t + 5. Let w be v(-5). Factor w + 0*f**s + 0*f + 2/15*f**4 + 0*f**3.
2*f**4/15
What is q in 44/9*q + 70/9 + 2/3*q**2 = 0?
-5, -7/3
Let x(j) be the first derivative of j**5/20 - j**4/6 - j**3/2 - 5*j - 20. Let a(q) be the first derivative of x(q). Solve a(b) = 0.
-1, 0, 3
Let u = -7039/2 - -3522. Let 0*q**2 + 0*q**4 - 5/4*q**5 + 0 - 5/4*q + u*q**3 = 0. Calculate q.
-1, 0, 1
Let u(l) be the second derivative of l**4/27 + 11*l**3/27 - 2*l + 24. Determine d, given that u(d) = 0.
-11/2, 0
Factor 0*g - 35/3*g**3 + 5/3*g**4 + 50/3*g**2 + 0.
5*g**2*(g - 5)*(g - 2)/3
Let p(d) = 3*d**3 + 49*d**2 - 325*d + 753. Let w(n) = -10*n**3 - 148*n**2 + 976*n - 2256. Let y(z) = -16*p(z) - 5*w(z). Factor y(t).
2*(t - 8)**2*(t - 6)
Let t(a) = a**2 - 11*a + 12. Let j be t(10). Factor 4*b**2 + 10*b**2 + 320 - 9*b**j + 80*b.
5*(b + 8)**2
Let q(x) be the third derivative of -x**9/37800 + x**7/6300 - 13*x**4/24 - x**2. Let n(i) be the second derivative of q(i). Suppose n(s) = 0. Calculate s.
-1, 0, 1
Let z(f) be the second derivative of 42*f + 7/30*f**6 + 9/4*f**4 + 0 + 13/6*f**3 + 23/20*f**5 + f**2. Determine o so that z(o) = 0.
-1, -2/7
Factor 20/7*t**2 - 36/7 - 4/7*t**3 - 12/7*t.
-4*(t - 3)**2*(t + 1)/7
Suppose -v + 168 = 2*c - 6*v, -v = 0. Let j = c - 82. Solve -1 + m**j + 1/2*m - 1/2*m**3 = 0 for m.
-1, 1, 2
Let o(k) be the first derivative of 5*k**4/4 + 40*k**3/3 + 35*k**2/2 - 82. Factor o(a).
5*a*(a + 1)*(a + 7)
Let t(v) be the first derivative of 5*v**6/6 - 6*v**5 + 65*v**4/4 - 20*v**3 + 10*v**2 + 62. Suppose t(c) = 0. Calculate c.
0, 1, 2
Factor -184*t**3 + 186*t**3 + 4*t**4 + t**5 + 0*t**4 + t**5.
2*t**3*(t + 1)**2
Let f(s) = -2*s**5 - 6*s**4 + 11*s**3 - 19*s**2 + 9*s - 2. Let l(g) = -g**5 - 6*g**4 + 12*g**3 - 18*g**2 + 9*g - 2. Let x(a) = -2*f(a) + 3*l(a). Factor x(r).
(r - 2)*(r - 1)**4
Let h(k) = k**3 + 7*k**2 + k + 11. Let g be h(-7). Let b(w) be the second derivative of 2/3*w**2 - 2/9*w**3 + 1/36*w**g + 0 + 3*w. Solve b(f) = 0 for f.
2
Find k such that 56/3 - 5*k + 1/3*k**2 = 0.
7, 8
Suppose 0 = -2*l - 2*a - 4, -a = -3*l - 10 + 12. Let f be 4/(-10)*30/(-36). Factor l + f*x**2 + 1/3*x.
x*(x + 1)/3
Let x(l) = l**3 - l**2 + l + 1. Let w(s) = 2*s**3 + 3*s**2 - 5*s + 3. Let j(h) = 2*w(h) - 6*x(h). Factor j(i).
-2*i*(i - 4)*(i - 2)
Factor 56*z**3 - 58*z**3 + 201*z**2 + 273*z**2 - 37446*z + 986078.
-2*(z - 79)**3
Let m(p) = -6*p**3 + 14*p**2 - 2*p + 2. Let y(i) = 4*i**3 - 9*i**2 + i - 1. Suppose -50 = 13*c + 54. Let b(n) = c*y(n) - 5*m(n). Let b(j) = 0. What is j?
-1, 1
Let z(l) = -l**4 + l**3 - l**2 + 2*l - 1. Let d(w) = 3*w**4 - 8*w**3 + 8*w**2 - 4*w + 1. Let x(q) = -5*d(q) - 5*z(q). Factor x(t).
-5*t*(t - 2)*(t - 1)*(2*t - 1)
Let d be 7/(28/(-16)) - -6. Factor 270*q**d - 275*q**2 + 0*q + 0*q.
-5*q**2
Let x = -47 - -53. Let o(k) be the second derivative of -1/30*k**5 + 1/27*k**4 + 0*k**2 + 1/189*k**7 + 0 + 0*k**x + 0*k**3 - 3*k. Find h, given that o(h) = 0.
-2, 0, 1
Let b(h) be the third derivative of h**6/60 + 13*h**5/6 - h**4/12 - 65*h**3/3 - 11*h**2 + 2*h. Factor b(r).
2*(r - 1)*(r + 1)*(r + 65)
Let m be (-1 + 3)/((-34)/(-187)). Let s = 23/2 - m. Find b such that s*b - 1/4*b**2 + 0 = 0.
0, 2
Factor 2/7*g**3 - 48/7 + 12/7*g**2 - 8/7*g.
2*(g - 2)*(g + 2)*(g + 6)/7
Let w = -29 - -59. Suppose -3*g + w = 2*g. Factor -22*p + g*p**2 + 15 - 2 - 1.
2*(p - 3)*(3*p - 2)
Let n be 8/14 + 3160/2212. What is w in 0*w**3 + 0 - 2/9*w**4 + 0*w + 2/9*w**n = 0?
-1, 0, 1
Factor -t**4 + 7122 - 156*t - 13206 + 2*t**4 + 24*t**3 + 132*t**3 + 6083*t**2.
(t - 1)*(t + 1)*(t + 78)**2
Let k = 70 + -62. Let b = k - 5. Factor 0 + 0*u**2 - 2/5*u**b + 0*u**4 + 0*u + 2/5*u**5.
2*u**3*(u - 1)*(u + 1)/5
Let w(b) be the second derivative of 3*b**5/80 + 3*b**4/8 + 11*b**3/8 + 9*b**2/4 + 4*b - 2. Factor w(k).
3*(k + 1)*(k + 2)*(k + 3)/4
Let q be (-4)/3*(1 - 10/4). Let p = 7/12 - 1/3. Factor -p*s**q - 4 + 2*s.
-(s - 4)**2/4
Let u(j) be the third derivative of 4/15*j**5 + 2/3*j**3 + 7/12*j**4 + 0 + 1/30*j**6 + 0*j - 18*j**2 - 2/105*j**7 - 1/168*j**8. Let u(d) = 0. Calculate d.
-1, 2
Let u be -91 + 92 - 1/(0 - 1). Factor 49*s**u - 23*s**2 - 23*s**2.
3*s**2
Determine q so that q + 2120 - 2125 + q**2 + 3*q = 0.
-5, 1
Let n(i) = 3*i + 27. Let p(c) = -3*c - 26. Let g(h) = -4*n(h) - 5*p(h). Let r be g(-6). Let -1/6*k**5 + 0 + 2/3*k**r + 2/3*k**2 - 1/6*k - k**3 = 0. Calculate k.
0, 1
Let u = 3 + -3. Factor 0*d**5 + 8*d**3 + 2*d**5 + 4*d**2 + u + 69*d**4 + 4 - 77*d**4 - 10*d.
2*(d - 2)*(d - 1)**3*(d + 1)
Let c be (-1)/4 + 2/8. Suppose 12 = 4*p - c*p. What is j in -j**2 - j + 1 + 4*j**3 - 5*j + 5*j - p*j**3 = 0?
-1, 1
Let b be 1041/80 + (15 - 28). Let q(r) be the third derivative of -b*r**5 + 0*r**3 + 0 + 0*r + 14*r**2 + 1/48*r**4. Find v such that q(v) = 0.
0, 2/3
Let l = -6093 - -4283. Let t = -9002/5 - l. Suppose -64/5 + t*f + 1/5*f**3 - 12/5*f**2 = 0. Calculate f.
4
Let h(m) = m**2 + 4*m + 6. Let a be h(-4). Factor 64*p + 10*p**4 - 29*p - a*p**5 - 4*p**3 - 35*p.
-2*p**3*(p - 1)*(3*p - 2)
Let z(m) be the first derivative of -1/2*m**6 + 2/3*m**3 - 5 + 0*m**2 - 2/5*m**5 + 0*m + 3/4*m**4. Let z(c) = 0. Calculate c.
-1, -2/3, 0, 1
Let k be (-2 + 2)/3*1. Let j(m) be the third derivative of k*m - 4*m**2 + 0*m**5 + 1/168*m**8 + 1/30*m**6 + 0 + 0*m**4 - 1/35*m**7 + 0*m**3. Factor j(c).
2*c**3*(c - 2)*(c - 1)
Let c be (11 - 12) + 2/(5 - 3). Let n(d) be the second derivative of 1/10*d**2 + c - 3*d - 1/15*d**3 + 1/60*d**4. Factor n(j).
(j - 1)**2/5
Let f(t) be the first derivative of -9*t**4/32 - t**3/8 + 15*t**2/4 - 9*t/2 + 236. Factor f(k).
-3*(k - 2)*(k + 3)*(3*k - 2)/8
Let p be 2 - 3/5 - (-15)/25. Let -10*r - 65 - 5*r - 5*r**3 + 20 + 25*r**p = 0. What is r?
-1, 3
Determine k so that 1074*k**2 - 2136*k**2 + 18*k + 5*k**3 + 1071*k**2 - 4*k**3 = 0.
-6, -3, 0
Let q(w) be the first derivative of -3*w**4/4 + 222*w**3 - 24642*w**2 + 1215672*w - 58. Factor q(g).
-3*(g - 74)**3
Let d(l) = l**2 - 13*l - 3. Suppose -11 = -5*w - 36. Let c(s) = s**2 - 25*s - 5. Let x(b) = w*d(b) + 3*c(b). Factor x(r).
-2*r*(r + 5)
Suppose -61 = -3*b - 13. Suppose -3*k = -2*w - 0 - 4, 3*w - b = -k. Let q(r) = 3*r. Let n(y) = -y**2 - 2*y - 1. Let a(i) = w*q(i) + 3*n(i). Factor a(d).
-3*(d - 1)**2
Let r(c) be the third derivative of 11*c**6/30 - 26*c**5/15 + 19*c**4/6 - 8*c**3/3 + c**2 + 29. Facto