4. Factor -7*b**4 + 18*b**3 - 14*b**2 - 3*b**4 + 6*b**w - 4*b**5 + 4*b.
2*b*(b - 2)*(b - 1)**3
Find g, given that 0*g**2 - 3/2*g + 3/4*g**4 + 3/2*g**3 - 3/4 = 0.
-1, 1
Let u be ((-40)/(-12))/(-5) + 520/78. Suppose -10*f - 2/3*f**3 - 14/3*f**2 - u = 0. Calculate f.
-3, -1
Let j(c) be the first derivative of -5*c**6/6 + 10*c**5 - 10*c**4 - 50*c**3/3 + 45*c**2/2 + 116. Let j(l) = 0. Calculate l.
-1, 0, 1, 9
Let j be -2 - (-12)/8 - 40/(-16). Let o(d) be the first derivative of 1/8*d**4 + 1/4*d**j + 0*d - 5/12*d**3 + 8. Factor o(r).
r*(r - 2)*(2*r - 1)/4
Factor -11/3*k**2 - 1/3*k**3 + 4*k + 0.
-k*(k - 1)*(k + 12)/3
Factor 25 + 190*u + 4*u**3 + 75 - 4*u**3 + 64*u**2 + 6*u**3.
2*(u + 5)**2*(3*u + 2)
Let k(v) be the third derivative of -1/50*v**5 - 16*v**2 - 17/60*v**4 + 2/5*v**3 + 0*v + 0. Factor k(j).
-2*(j + 6)*(3*j - 1)/5
What is g in 0*g + 0*g**2 - 1/3*g**4 + 0 + 2/3*g**3 = 0?
0, 2
Solve -2*t**2 + 62*t - 961/2 = 0.
31/2
Let o(c) be the third derivative of c**6/120 - 7*c**5/60 - 7*c**4/24 - 4*c**3/3 + 15*c**2. Let k be o(8). Solve -4/3*t**3 + 0*t - 4/3*t**4 + 0*t**2 + k = 0.
-1, 0
Suppose -42 + 24 = -3*r. Solve 20*q - 3 - 16*q**2 + r*q**4 + 45*q**5 - 7*q + 36*q**4 - 34*q**3 + 1 = 0 for q.
-1, 1/3, 2/5
Let x(u) be the first derivative of -u**4/10 + 8*u**3/15 - u**2 + 4*u/5 + 97. Determine a so that x(a) = 0.
1, 2
Let -15488/3 - 2/3*u**2 - 352/3*u = 0. What is u?
-88
Suppose 0*o - 4 = 4*o. Let l be (0/(o - 2))/(-2). Find u, given that l + 3/2*u + 3/4*u**3 + 9/4*u**2 = 0.
-2, -1, 0
Suppose 25*p = 29*p - 12. Find y such that 0 + 3/8*y**p - 1/4*y + 5/8*y**2 = 0.
-2, 0, 1/3
Let a = 11349/662 + -3/4634. Factor -2/7*s**4 - 74/7*s**2 - 20/7*s**3 - a*s - 72/7.
-2*(s + 2)**2*(s + 3)**2/7
Let h(f) be the second derivative of -5*f**8/336 + f**6/24 - 15*f**2/2 - 3*f. Let w(p) be the first derivative of h(p). Let w(x) = 0. What is x?
-1, 0, 1
Let w(r) be the first derivative of -7*r**5/15 + 5*r**4/6 + 4*r**3/3 + 15*r**2 - 1. Let z(k) be the second derivative of w(k). Factor z(p).
-4*(p - 1)*(7*p + 2)
Let m(i) be the second derivative of -i**4/4 + 13*i. Let u(w) = 7*w**2 + 4*w. Let y(v) = -6*m(v) - 3*u(v). Factor y(n).
-3*n*(n + 4)
Let l(r) = -56*r**5 + 100*r**4 - 78*r**3 - 34*r**2 - 34*r. Let v(a) = 5*a**5 - 9*a**4 + 7*a**3 + 3*a**2 + 3*a. Let f(j) = -6*l(j) - 68*v(j). Factor f(c).
-4*c**3*(c - 2)*(c - 1)
Let l(g) be the first derivative of 4/3*g + 0*g**2 + 3 - 1/9*g**3. Suppose l(r) = 0. Calculate r.
-2, 2
Let q = 32 + -35. Let z be 17/(-3) - -4 - q. Find v such that -4/3 + 8/3*v**2 - 4/3*v**3 + 2/3*v + 2/3*v**5 - z*v**4 = 0.
-1, 1, 2
Let w(a) be the second derivative of a**6/10 + 9*a**5/10 - 2*a**4 - 3*a**3 + 21*a**2/2 - 3*a - 5. Let w(s) = 0. Calculate s.
-7, -1, 1
Suppose -240/7 + 4/7*y**2 + 68/7*y = 0. What is y?
-20, 3
Factor 0 - 14*d + 4/3*d**2 + 2*d**3.
2*d*(d + 3)*(3*d - 7)/3
Let n(l) = -l + 8. Let f be n(8). Let s(b) be the first derivative of f*b**2 + 1 + 2/9*b**3 - 2/3*b. Factor s(q).
2*(q - 1)*(q + 1)/3
Factor -11*s**4 + 8*s**2 - 30*s**4 + 33*s**4 - 16*s**3 + 14*s - 2*s + 4*s**5.
4*s*(s - 3)*(s - 1)*(s + 1)**2
Let i(o) = 2*o + 19. Let v be i(15). Let s = 149/3 - v. Suppose 0 - s*w - 1/3*w**2 = 0. Calculate w.
-2, 0
What is p in 32*p + 3*p - 5*p - 4*p**2 + 7*p**2 = 0?
-10, 0
Let b(k) be the third derivative of k**5/90 - 5*k**4/3 - 124*k**3/9 + 558*k**2. Factor b(o).
2*(o - 62)*(o + 2)/3
Let g(a) = -5*a - 5. Let o(t) = -t**2 + t + 1. Suppose 2*z = -5*v + 27 - 5, -4*z + 2*v - 4 = 0. Let h(r) = z*g(r) + o(r). Determine w so that h(w) = 0.
-2
Let d(s) be the first derivative of s**4/5 + 4*s**3/15 - 8*s**2/5 - 16*s/5 + 150. Factor d(q).
4*(q - 2)*(q + 1)*(q + 2)/5
Let c = 12332 + -12330. Factor -75/2 - 3/8*u**c + 15/2*u.
-3*(u - 10)**2/8
Let f(n) be the third derivative of -n**5/120 + 13*n**4/24 - 25*n**3/12 + 406*n**2. Factor f(v).
-(v - 25)*(v - 1)/2
Let z = 1622 + -1620. Factor -8/5*j - 8/5 - 2/5*j**z.
-2*(j + 2)**2/5
Suppose 5*v - 21 = -2*v. Determine m, given that -m**v - 974*m**2 - m**4 + 974*m**2 = 0.
-1, 0
Let y(q) be the third derivative of -q**6/40 + 3*q**5/20 + 207*q**2. Factor y(v).
-3*v**2*(v - 3)
Let o be 2/(-8) + 63/12. Let j = o - 3. Find k, given that k**2 + 0*k - k + j*k + k = 0.
-2, 0
Let f(t) = 2*t**3 - t. Let d be f(1). Let 2*g**3 - 6*g**3 - 44*g + d + 28*g**2 + 3 + 16 = 0. What is g?
1, 5
Let o be (0 - (1 + 3)) + 9. Let i be ((-15)/9)/(o/(-6)). Find x, given that 2/3*x**i + 0 + 2/3*x = 0.
-1, 0
Let j(b) be the first derivative of 0*b**5 + 0*b**3 + 0*b**2 - 2/3*b**6 + b**4 - 6 + 0*b. Factor j(k).
-4*k**3*(k - 1)*(k + 1)
Let x = 4/3 + -5/6. Let r = 17/72 - -1/72. Suppose 3/4*t - r*t**2 - x = 0. Calculate t.
1, 2
Let p = -3/5752 + 23047/74776. Suppose 14/13*g - 16/13*g**2 + 4/13*g**4 + p*g**3 - 2/13*g**5 - 4/13 = 0. Calculate g.
-2, 1
Let w(j) = 13*j**3 + 29*j**2 + 15*j - 45. Let d(h) = 2*h**3 + h**2. Let k(q) = -4*d(q) + w(q). Solve k(t) = 0.
-3, 1
Let q(b) be the third derivative of -2*b**5/105 - 191*b**4/42 + 64*b**3/7 + 89*b**2 + 1. Determine u so that q(u) = 0.
-96, 1/2
Let v be 3/(-5) - (-16)/(-40). Let w be v - 1 - (12 + -17). Factor 31*k**2 - 40*k**2 + 9*k**3 + 8*k - 5*k - w*k**4.
-3*k*(k - 1)**3
Let q(s) = -2*s**4 + 10*s**3 + 42*s**2 + 104*s + 56. Let b(l) = -l**3 + 2*l**2. Let o(p) = -6*b(p) - q(p). What is j in o(j) = 0?
-2, -1, 7
Let t(r) be the third derivative of r**9/211680 + r**8/35280 + r**7/17640 - r**5/6 - 11*r**2. Let g(x) be the third derivative of t(x). Factor g(s).
2*s*(s + 1)**2/7
Let s = -28 - -24. Let x = 1 - s. Solve 20*h**x - 5*h**2 + 24*h**3 - 12*h + 8*h**2 + 13*h**2 - 48*h**4 = 0.
-3/5, 0, 1
Let r be 1/(297/54 + -5). Factor -3/11*i**r + 3/11*i - 1/11 + 1/11*i**3.
(i - 1)**3/11
Find b, given that 156/11*b - 64/11 - 162/11*b**3 + 86/11*b**4 + 6/11*b**5 - 2*b**2 = 0.
-16, -1, 2/3, 1
Let x(g) be the second derivative of g**7/147 + 11*g**6/105 + 23*g**5/70 - 47*g**4/42 - 8*g**3/7 + 36*g**2/7 - 82*g. Determine f so that x(f) = 0.
-6, -1, 1
Let y(j) be the first derivative of j**4/12 + 2*j**3/9 - j**2/6 - 2*j/3 - 246. Solve y(t) = 0.
-2, -1, 1
Determine m so that -2*m**5 - 76/3*m**4 - 52/3 + 12*m**3 + 128/3*m**2 - 10*m = 0.
-13, -1, -2/3, 1
Let d(w) be the second derivative of -w**6/6 - 4*w**5 - 75*w**4/4 + 135*w**3 + 51*w. Factor d(z).
-5*z*(z - 2)*(z + 9)**2
Suppose -y + 0*y = -4. Find p such that -5*p**y + p**4 + 22*p - 2*p**2 + 2*p**4 - 32 + 26*p - 12*p**3 = 0.
-4, 1
Factor 30*u**2 + 75*u + 120 + 2667*u**3 - 2670*u**3 + 49*u - u**4.
-(u - 6)*(u + 2)**2*(u + 5)
Suppose -31*r + 28*r = -99. Let h be 55/r - (-3)/(-9). Let 0 + 4*p**4 + 4*p**3 + 0*p + h*p**2 + 4/3*p**5 = 0. Calculate p.
-1, 0
Solve -4/19 + 2/19*v + 4/19*v**2 - 2/19*v**3 = 0.
-1, 1, 2
Let k(v) = -4*v**2 + 44*v - 22. Let j(i) = 2*i**2 - 20*i + 12. Let w(l) = 5*j(l) + 2*k(l). Factor w(b).
2*(b - 4)*(b - 2)
Let k(o) be the first derivative of -10 + 2/15*o**5 + 2/3*o - 2/3*o**4 - 4/3*o**2 + 4/3*o**3. Factor k(w).
2*(w - 1)**4/3
Factor 4/7*o**3 + 0 + 0*o - 4/7*o**4 + 0*o**2.
-4*o**3*(o - 1)/7
Let d(b) be the first derivative of -17 + 45/2*b**2 - 25*b - 5/4*b**4 - 5*b**3. Factor d(s).
-5*(s - 1)**2*(s + 5)
Let q be (0 - 0/6)/1. Let x(b) be the second derivative of q*b**4 + 0*b**3 + 4*b + 0*b**2 + 1/20*b**5 + 0. Find f such that x(f) = 0.
0
Let y be (72*1)/(14 + -12). Let o = -32 + y. Factor 4/3 + 16/3*r + o*r**2.
4*(r + 1)*(3*r + 1)/3
Factor -99 - 55*a**2 + 5*a**3 - 13*a + 108*a - 21 + 10*a**2 + 35*a.
5*(a - 4)*(a - 3)*(a - 2)
Let g(x) = -x**4 - 1. Let l(a) = 8*a**4 + 8*a**3 + 4*a**2 + 4. Let p be -1 - (-3)/(4/(-4)). Let y(h) = p*g(h) - l(h). What is b in y(b) = 0?
-1, 0
Let d be 0 + 7 - (728/(-20))/(-7). Let -11/10*u**2 - 4/5 + d*u + 0*u**3 + 1/10*u**4 = 0. What is u?
-4, 1, 2
Let q(n) be the third derivative of -5/84*n**8 - 2/15*n**7 + 0*n + 1/3*n**4 + 1/10*n**6 + 7/15*n**5 + 0 + 0*n**3 - n**2. Determine h, given that q(h) = 0.
-1, -2/5, 0, 1
Let m(f) be the first derivative of f**5/5 - 5*f**4/2 + 11*f**3 - 20*f**2 + 16*f - 54. Find x, given that m(x) = 0.
1, 4
Suppose -2*p + 30 = 20. Suppose 2*v - 4*h = -2*v, 27 = 4*v + p*h. Find l such that 2/9*l**4 + 0 + 0*l + 0*l**v - 2/9*l**2 = 0.
-1, 0, 1
Let j(b) be the second derivative of 5*b**9/756 - b**8/140 - b**7/105 + 5*b**3/6 + 5*b. Let h(y) be the second derivative of j(y). Factor h(f).
4*f**3*(f - 1