e of -4*n**3 + 2*n**2 + 3*n**4 - 4/5*n**5 + 0*n + 23. Factor b(k).
-4*k*(k - 1)**3
Let b(f) be the first derivative of 5*f**4/4 + 25*f**3/3 - 125*f**2/2 - 625*f - 310. Factor b(x).
5*(x - 5)*(x + 5)**2
Let l = -56 + 58. Suppose 3*m + m**2 + 3*m - l*m**2 + 3 - 4*m = 0. What is m?
-1, 3
Let s be 0/(50/(-5) + 8). Let i(t) be the second derivative of 1/6*t**3 + 0*t**4 + s*t**2 + 1/42*t**7 + 0 - 1/10*t**5 - 8*t + 0*t**6. Factor i(f).
f*(f - 1)**2*(f + 1)**2
Factor 5*r**5 - 22*r**3 + 14*r**4 + 14*r**4 + 0*r**5 + 23*r**4 + 2*r**4.
r**3*(r + 11)*(5*r - 2)
Factor 51*t + 14*t**3 - 25*t - 8 - 2*t**4 - 32*t**2 + 2*t**2.
-2*(t - 4)*(t - 1)**3
Factor 0 + 15/2*w**2 + 12*w + 3/4*w**3.
3*w*(w + 2)*(w + 8)/4
What is d in 3 + 13/2*d - 6*d**3 - 1/2*d**5 + d**2 - 4*d**4 = 0?
-6, -1, 1
Factor -87/4*h - 3/4*h**2 - 21.
-3*(h + 1)*(h + 28)/4
Let s be -2 + (-18)/45 + 12/5. Suppose 3/4*y**2 + s + 0*y = 0. Calculate y.
0
Factor 48*w**2 + 225/8 + 9/2*w**3 + 565/8*w.
(w + 9)*(6*w + 5)**2/8
Let l(j) be the third derivative of j**6/270 - j**5/30 + j**4/9 - j**3/6 + 12*j**2. Let v(g) be the first derivative of l(g). Determine n, given that v(n) = 0.
1, 2
Let a(w) be the third derivative of -1/1848*w**8 + 4/33*w**3 - 1/1155*w**7 - 10*w**2 - 2/33*w**4 + 0*w + 1/132*w**6 + 1/330*w**5 + 0. Factor a(u).
-2*(u - 1)**3*(u + 2)**2/11
Let o(q) = q**2 + 1. Let k(z) = 9*z**2 + 16*z + 17. Let b(f) = -k(f) + 5*o(f). Factor b(t).
-4*(t + 1)*(t + 3)
Suppose -5*q = 11*s - 9*s - 9, 5*s = 2*q + 8. Let -2/11*y**3 - 2/11*y**s + 0 + 4/11*y = 0. Calculate y.
-2, 0, 1
Let w(f) be the first derivative of -32 + 4*f**3 + 75/2*f**2 + 18*f. Factor w(r).
3*(r + 6)*(4*r + 1)
Let o = -118 + 116. Let u be (135/30)/((-3)/o). Factor -2/7*p**u - 6/7*p + 2/7 + 6/7*p**2.
-2*(p - 1)**3/7
Suppose 2*i + 2*d = i, 3*i - 2 = -4*d. Factor -54*t**2 - 18*t - 2*t**4 - 66*t**i - 14*t**3 + 154*t**2.
-2*t*(t - 1)**2*(t + 9)
Let l be -1 + -1 - 12/(-3). Find k, given that -25 - k**2 + 19*k - l*k - 7*k = 0.
5
Factor -52*o**4 - 10*o**3 + 22*o**4 + 21*o**4 + 10*o + 14*o**4 - 5.
5*(o - 1)**3*(o + 1)
Factor 81 + 3*z**2 - 27 + 30*z - 12 + 6.
3*(z + 2)*(z + 8)
Let d(s) be the second derivative of 1/18*s**3 + 6*s + 0 + 0*s**4 + 0*s**2 - 1/60*s**5. Factor d(b).
-b*(b - 1)*(b + 1)/3
Suppose -4*g = -3*z, 4 + 4 = 2*z. Factor 20*u**4 + 3*u**2 + 938*u**3 - 963*u**g + 2*u**2.
5*u**2*(u - 1)*(4*u - 1)
Determine t so that -230*t**3 + 75*t**4 + 640*t + 66*t**5 - 265 - 480*t**2 - 71*t**5 + 265 = 0.
-2, 0, 1, 8
Let f(o) = 2*o**2 - o. Let i(z) = -3*z**2 + 2*z + 12. Let x(c) = -3*f(c) - 3*i(c). Solve x(l) = 0 for l.
-3, 4
Let c(w) = 2*w**2 + 10*w + 8. Let y be c(6). Let m(n) be the first derivative of -1 + 68*n**2 - 16*n - 50*n**5 + 275/2*n**4 - y*n**3. Factor m(k).
-2*(k - 1)*(5*k - 2)**3
Let c(x) = 3*x**4 - 111*x**3 + 1070*x**2 - 768*x - 1946. Let k(r) = 2*r**2 + 6*r + 1. Let q(s) = c(s) + 2*k(s). Factor q(t).
3*(t - 18)**2*(t - 2)*(t + 1)
Suppose 4*k + n = -k + 4, 2*k - 4*n = -16. Suppose k = -3*v - 2*t - 4, 3*v = -2*t - 2*t - 14. Suppose -1/2*r + 0 - 5/4*r**v - 1/4*r**4 - r**3 = 0. Calculate r.
-2, -1, 0
Let -64*g - 16*g + 4*g**2 + 20 + 2*g**2 + 80 + 5*g**3 - g**2 = 0. Calculate g.
-5, 2
Let o = -45 - -5. Let x be (-64)/o*5/2. Determine y so that -4/9*y**2 + 2/9 + 10/9*y**5 - 20/9*y**3 + 10/9*y + 2/9*y**x = 0.
-1, -1/5, 1
Let r(w) = -32*w - 58. Let u be r(-4). Let b be 30/u + 1/(-7). Factor 0*z**3 - 32/7*z**2 - 32/7*z + 0 + 8/7*z**4 + b*z**5.
2*z*(z - 2)*(z + 2)**3/7
Let t(w) be the first derivative of -w**4/22 - 10*w**3/33 + 32*w**2/11 - 72*w/11 + 44. Let t(d) = 0. Calculate d.
-9, 2
Suppose 0 + 4*k**3 + 0*k - 4/3*k**4 + 0*k**2 = 0. Calculate k.
0, 3
Let l be 13/(-18) - (-18)/27. Let h = 23/90 + l. Factor 0 - 1/5*q**2 + h*q.
-q*(q - 1)/5
Let 2/13*q**3 + 48/13*q**2 + 288/13*q + 0 = 0. Calculate q.
-12, 0
Let z be (((-8)/14)/1)/((-4)/14). Let c = 37/6 - 167/30. Factor -c*u + 0 - 3/5*u**3 - 6/5*u**z.
-3*u*(u + 1)**2/5
Let z(m) be the first derivative of m**6/2 - 6*m**5/5 + 2*m**3 - 3*m**2/2 + 103. Factor z(f).
3*f*(f - 1)**3*(f + 1)
Find z, given that 6*z - 483/4*z**4 + 573/2*z**3 - 93*z**2 + 0 = 0.
0, 2/23, 2/7, 2
Suppose 1 + 3 = -4*o. Let y(p) = -5*p**3 - 2*p**2 + 1. Let g be y(o). Factor 0*i**2 + 3 - 2*i**2 + i**g - 2.
(i - 1)**2*(i + 1)**2
Let g(v) be the second derivative of -v**7/210 - 7*v**6/150 - 4*v**5/25 - 2*v**4/15 + 8*v**3/15 + 8*v**2/5 - 7*v + 12. Solve g(h) = 0 for h.
-2, 1
Let d(m) be the third derivative of m**7/3780 + m**6/405 + m**5/135 + 3*m**3 - 19*m**2. Let j(y) be the first derivative of d(y). Factor j(l).
2*l*(l + 2)**2/9
Suppose 139*z + 422 = 350*z. Suppose -4/5*k + 2/3*k**z + 2/15 = 0. What is k?
1/5, 1
Let t(q) be the first derivative of 1/10*q**5 + 1/4*q**4 + 1/4*q**2 + 1/3*q**3 - 5 - 2*q + 1/60*q**6. Let f(i) be the first derivative of t(i). Factor f(v).
(v + 1)**4/2
Solve 4*d**3 - 2*d**2 + 1348*d - 1348*d - 2*d**4 + 0*d**4 = 0 for d.
0, 1
Suppose 5*v + 3*z - 6 = 0, 4*z + 49 - 57 = -3*v. Suppose 1/6*x**3 - 1/3*x + 1/6*x**2 + v = 0. What is x?
-2, 0, 1
Let d = 2588 - 2585. Factor 3/5*k - 3/5*k**4 - 3/5*k**d + 0 + 3/5*k**2.
-3*k*(k - 1)*(k + 1)**2/5
Factor 69*r**2 + 24*r**3 + 84*r + 48 - 54 + 3*r**4 + 42.
3*(r + 1)*(r + 2)**2*(r + 3)
Let p(g) be the third derivative of g**6/60 + 77*g**5/30 + 380*g**4/3 + 1444*g**3/3 - 466*g**2. Find q, given that p(q) = 0.
-38, -1
Let p(k) be the first derivative of 8*k**5/5 + 275*k**4/2 + 4186*k**3 + 47081*k**2 - 24334*k + 186. Factor p(d).
2*(d + 23)**3*(4*d - 1)
Let q(l) be the third derivative of -l**9/12096 + l**8/1344 - l**7/336 + l**6/144 + 19*l**5/60 + 29*l**2. Let u(f) be the third derivative of q(f). Factor u(a).
-5*(a - 1)**3
Let o(u) be the first derivative of -5*u**3/18 + 25*u**2/4 + 40*u/3 - 123. Factor o(v).
-5*(v - 16)*(v + 1)/6
Let x(f) be the third derivative of -f**6/720 + 2*f**5/45 + f**4/144 - 4*f**3/9 - 178*f**2. Let x(m) = 0. Calculate m.
-1, 1, 16
Let k(p) be the second derivative of -p**3/6 - 8*p. Let a be k(-8). Factor 10*x - 4 + 20*x**4 - a*x**3 - 4*x**4 - 4*x**2 - 8*x**4 - 2*x**5.
-2*(x - 2)*(x - 1)**3*(x + 1)
Let l(q) be the third derivative of q**6/8 + 19*q**5/12 + 10*q**4/3 - 50*q**3/3 - 25*q**2. Factor l(j).
5*(j + 2)*(j + 5)*(3*j - 2)
Let r(c) be the first derivative of 14*c**5/45 - 5*c**4/9 - 2*c**3/27 + 4*c**2/9 + 252. Factor r(i).
2*i*(i - 1)**2*(7*i + 4)/9
Factor -2/19*i**2 + 150/19 - 148/19*i.
-2*(i - 1)*(i + 75)/19
Let j(h) be the third derivative of -h**6/600 - h**5/100 + h**4/30 + h**2 - 18*h. Solve j(b) = 0 for b.
-4, 0, 1
Let y(b) be the third derivative of b**8/336 - b**7/30 + b**2 + 3*b. Suppose y(p) = 0. What is p?
0, 7
Let h(v) be the third derivative of 1/6*v**4 + 8/3*v**3 - 8*v**2 + 0 - 4/15*v**5 + 0*v - 1/30*v**6. Factor h(o).
-4*(o - 1)*(o + 1)*(o + 4)
Suppose 0 = -r - 4 + 14. Factor r*b + 10*b - 18*b**2 - b - 5*b + 4.
-2*(b - 1)*(9*b + 2)
Factor -2/3*f**2 - 1058/3 - 92/3*f.
-2*(f + 23)**2/3
Let x(s) = -s**4 - 4*s**3 + 16*s**2 - 16*s + 5. Let n(d) = d**3 - d**2 - d + 1. Let l(m) = 3*n(m) + 3*x(m). Let l(f) = 0. What is f?
-6, 1
Factor 2/7*j + 2/7*j**2 + 0.
2*j*(j + 1)/7
Let v(m) = -m**3 + m**2 - 2*m + 3. Let u be v(0). Factor -3*x**5 + 6*x**4 + 3*x - 3*x**4 - u*x.
-3*x**4*(x - 1)
Let n(k) be the second derivative of -k**6/45 + k**5/75 + k**4/18 - 2*k**3/45 + 7*k + 2. Find j, given that n(j) = 0.
-1, 0, 2/5, 1
Let a(g) be the first derivative of -1/2*g - 1/4*g**2 + 1/8*g**4 + 1 + 1/6*g**3. Find u such that a(u) = 0.
-1, 1
Find m such that -26/3*m**4 + 0 + 4/3*m**2 - 22/3*m**3 + 0*m = 0.
-1, 0, 2/13
Let r(w) = w**3 + 6*w**2 - 11*w - 17. Let a be r(-7). Let c be (2/3)/(1/6). Factor -7 - 3*h + 8*h**c + 9*h**2 + 3*h**3 - a*h**4 + 1.
-3*(h - 2)*(h - 1)*(h + 1)**2
Let l be (2/3)/((-8)/(-36)). Suppose 4 - 14 = a + 3*t, 0 = 4*a - l*t - 35. Determine h so that 12*h**a + 0*h**2 - 4*h**3 + 2*h + 0*h**2 - 10*h**5 = 0.
-1, 0, 1
Let f(k) be the second derivative of -k**6/90 - k**5/12 - 2*k**4/9 - 2*k**3/9 - 14*k. Let f(p) = 0. What is p?
-2, -1, 0
What is q in -1426 - 72*q**2 + 343 + 114*q + 69*q**2 = 0?
19
Let v(w) be the second derivative of w**7/70 + 4*w**6/25 + 3*w**5/5 + 4*w**4/5 - 158*w. Suppose v(z) = 0. What is z?
-4, -2, 0
Let w be (-12 - 1014/(-84))*250. Factor w - 75/7*b - 1/7*b**3 + 15/7*b**2.
-(b - 5)**3/7
Let h be 24/(-6) + 9 - 238/4