 6. Let j(r) = -12*r + 2 + 9*r - 50*r**2 + 2 + 5*r. Let p(u) = -5*j(u) - 2*n(u). Find f such that p(f) = 0.
-2/5, 2/5
Factor 3*v**4 + 7*v**5 + 5*v**5 - 9*v**5.
3*v**4*(v + 1)
Let d = -50715 + 50718. Factor -45/7*c**2 - 3/7*c**d - 27*c - 21.
-3*(c + 1)*(c + 7)**2/7
Factor -160*u - 1/3*u**4 - 1600/3 + 4*u**3 + 44/3*u**2.
-(u - 10)**2*(u + 4)**2/3
Let x(m) be the third derivative of -1/18*m**4 + 0*m + 1/90*m**6 - 4/9*m**3 + 2/45*m**5 + 0 - 12*m**2. Find p, given that x(p) = 0.
-2, -1, 1
Let d = 22 - 19. Factor 17*a + 4*a**d - 3*a**2 - 25*a - a**2.
4*a*(a - 2)*(a + 1)
Let g(m) be the first derivative of m**6/15 + 4*m**5/25 - 3*m**4/10 - 8*m**3/15 + 4*m**2/5 + 174. Factor g(f).
2*f*(f - 1)**2*(f + 2)**2/5
Suppose t = -t + 24. Suppose -5*g + 3 = -t. Factor 12*d**3 - 10*d**g - 3*d - 3*d - 4.
2*(d - 2)*(d + 1)**2
Let j(c) = -c**3 - 16*c**2 - 15*c + 2. Let s be j(-15). Suppose -2*y - s*y = -8. Solve -43*i - 2*i**3 - i**3 + i**y + 45*i + i**5 - i**4 = 0.
-1, 0, 1, 2
Let u(l) be the first derivative of 4 + 1/84*l**4 + 2*l + 0*l**3 + 0*l**2. Let y(s) be the first derivative of u(s). Let y(x) = 0. What is x?
0
Let c(b) = b**4 + 13*b**3 + 5*b**2 - 19*b + 7. Let i(t) = t**3 - t + 1. Let u(w) = -4*c(w) + 28*i(w). Factor u(q).
-4*q*(q - 1)*(q + 3)*(q + 4)
Let r(k) = 14*k**2 + 16*k + 22. Let a(o) = 20*o**2 + 17*o + 21. Let z(b) = 2*a(b) - 3*r(b). Factor z(h).
-2*(h + 3)*(h + 4)
Let d(o) be the third derivative of -1/40*o**5 - 1/480*o**6 + 0 - 5/96*o**4 + 0*o**3 + 0*o - 2*o**2. Factor d(n).
-n*(n + 1)*(n + 5)/4
Let h(f) be the third derivative of -f**8/1680 - f**7/315 - f**4/2 + 5*f**2. Let g(d) be the second derivative of h(d). Factor g(o).
-4*o**2*(o + 2)
Suppose -14*c = -0*c - 14. Suppose 3*k - 8 = -h, -2 = -0*k - k. Solve -38*f**3 + 26*f**3 + 3*f**4 - 1 + 9*f**h + c = 0 for f.
0, 1, 3
Let c(s) be the second derivative of -s**5/20 - s**4/4 + 5*s**3/3 - s - 27. Factor c(i).
-i*(i - 2)*(i + 5)
Let a be (-3 + 4)*5 - 1. Let b(n) be the first derivative of -7 - 1/10*n**a - 4/15*n**3 + 0*n - 1/5*n**2. Factor b(f).
-2*f*(f + 1)**2/5
Let u be ((-927)/54)/((-2)/(-6)). Let v = u - -207/4. Factor -1/4*p**4 + p**2 + p - v*p**3 + 0.
-p*(p - 2)*(p + 1)*(p + 2)/4
Factor -72/7*t + 68/7 + 4/7*t**2.
4*(t - 17)*(t - 1)/7
Let x(q) be the first derivative of 9*q**2 + 1/3*q**3 + 30 + 81*q. Factor x(m).
(m + 9)**2
Determine m, given that 2/3*m**2 + 32*m + 384 = 0.
-24
Let s be (-9540)/2968*(-5 + 2 + (-51)/18). Factor s*v - 35/4 + 5/4*v**3 - 45/4*v**2.
5*(v - 7)*(v - 1)**2/4
Let l(t) be the first derivative of -26*t**3/21 + 43*t**2 - 92*t/7 + 269. Determine s, given that l(s) = 0.
2/13, 23
Let f(k) be the second derivative of 2*k**3 + 1/35*k**5 + 1 - 8/21*k**4 + 14*k - 36/7*k**2. Factor f(d).
4*(d - 3)**2*(d - 2)/7
Let r(a) = -7*a - 103. Let v be r(-15). Suppose 4*t + 0 = 8. Find w, given that 0*w + 6*w**5 + 2/3*w**v + 0 - 10/3*w**3 + t*w**4 = 0.
-1, 0, 1/3
Suppose -5*w = y + 17, -6*w = -w - 5*y + 35. Let p be (0 - (-1)/w) + (-126)/(-56). Let 3/4 + 3/4*q**3 + 9/4*q**p + 9/4*q = 0. Calculate q.
-1
Let s(n) be the second derivative of -3/10*n**5 + 0 + 0*n**3 + 12*n + 0*n**2 - 1/4*n**4. Determine h, given that s(h) = 0.
-1/2, 0
Let o(g) = 7*g - 4. Let n be o(-2). Let v be (n/12)/(9/(-48)). Factor -4*p**3 - 16*p - 12*p**2 - v - 1/2*p**4.
-(p + 2)**4/2
Let l(h) be the second derivative of h**7/126 - 2*h**6/45 + h**5/20 + h**4/9 - 2*h**3/9 - 550*h. Suppose l(a) = 0. Calculate a.
-1, 0, 1, 2
Factor 8 + 69*u**2 + 372*u**3 + 4 + 11 + 4*u**2 + 93*u - 369*u**3.
(u + 1)*(u + 23)*(3*u + 1)
Let m be 663/117 - (5 - 4). Factor 0 - 2/3*r**5 - 4/3*r - 6*r**3 - m*r**2 - 10/3*r**4.
-2*r*(r + 1)**3*(r + 2)/3
Let d(p) be the first derivative of 2*p**6/15 - 8*p**5/25 + p**4/5 - 69. Factor d(l).
4*l**3*(l - 1)**2/5
Let r(i) be the second derivative of 3*i**5/40 + 7*i**4/4 + 53*i**3/4 + 30*i**2 - i + 80. Let r(c) = 0. Calculate c.
-8, -5, -1
Suppose -n - n - 16 = -5*f, 0 = -2*f + 3*n + 13. Let u be (-2)/8 + (-17)/(-4). Determine s, given that s**4 + 3*s**u + 2*s**3 - f*s**4 = 0.
-1, 0
Let u(h) = h**3 + 8*h**2 + 8*h + 10. Let m be u(-7). Suppose z - 12 = -m*z. Suppose z + b**2 - 12*b - 21 - 3*b**2 = 0. What is b?
-3
Let f(d) be the second derivative of 5/9*d**5 + 2*d**2 + 0 - 14/9*d**3 + 6*d - 5/27*d**4. Factor f(w).
4*(w + 1)*(5*w - 3)**2/9
Let m(o) be the second derivative of -2/45*o**6 + 0*o**4 + 2/3*o**2 + 18*o - 4/9*o**3 + 0 + 2/15*o**5. Factor m(k).
-4*(k - 1)**3*(k + 1)/3
Let i(s) = -s - 14. Let d be i(-14). Suppose -4*b = -d*b - 32. Factor 8*z + 8 - b*z**2 - 6*z + 5*z - 20*z**3 + 13*z.
-4*(z - 1)*(z + 1)*(5*z + 2)
Let f(c) be the first derivative of -c**4/4 - 3*c**3 - 15*c**2/2 - 7*c + 14. Find d, given that f(d) = 0.
-7, -1
Suppose 8/7*s**2 - 2/7*s**5 + 0 - 16/7*s**3 + 10/7*s**4 + 0*s = 0. Calculate s.
0, 1, 2
Determine k, given that -140/3*k**3 - 44/3*k**4 + 1096/3*k**2 - 2/3*k**5 + 676/3 - 1586/3*k = 0.
-13, 1, 2
Let v(a) be the third derivative of a**5/30 + 19*a**4/3 + 1444*a**3/3 - 6*a**2 + 1. Suppose v(l) = 0. What is l?
-38
Let d be ((-17 - -3) + -3)/(0 - 1). Suppose -20*b = -d*b - 6. Factor 10/9*n**3 + 14/9*n - 2/9*n**4 - 4/9 - 2*n**b.
-2*(n - 2)*(n - 1)**3/9
Let v(c) be the second derivative of c**7/1120 - c**6/80 + c**5/32 - 5*c**3/2 - 17*c. Let k(h) be the second derivative of v(h). Find y such that k(y) = 0.
0, 1, 5
Let q(b) be the second derivative of b**5/60 + 17*b**4/36 - b**3/18 - 17*b**2/6 - b + 251. Solve q(h) = 0.
-17, -1, 1
Let j(p) be the third derivative of -p**6/600 - p**5/75 + 7*p**4/120 + p**3/3 - 3*p**2 - p. Factor j(b).
-(b - 2)*(b + 1)*(b + 5)/5
Factor 1035*n**2 + 18250500 + 238050*n + 3/2*n**3.
3*(n + 230)**3/2
Let r(l) = 10*l - 14*l - 5*l - 5 - l**2. Let x be r(-8). Find f, given that 11*f + 3*f**2 + 5 + x*f**2 - f - f**2 = 0.
-1
Let r(g) = 25*g - 10. Let w be r(1). Suppose w*a = 14*a. Suppose a - 1/3*c**2 + 1/3*c**3 + 0*c = 0. What is c?
0, 1
Suppose -97*r + 315 = -34*r. Factor 2*h**4 + 4 + 1/2*h**3 - r*h**2 - 2*h + 1/2*h**5.
(h - 1)**2*(h + 2)**3/2
Let g(x) = -x**3 + 5*x**2 - 2*x + 43. Let t be g(7). Let s be 18/(-4)*(7 + t/9). Determine i so that 0*i**s - 4/5*i**2 + 0 - 1/5*i**5 + 3/5*i**4 + 0*i = 0.
-1, 0, 2
Let a be -4*(-3)/(-18)*3. Let u be 6/28*(-7)/a. Let 0 + u*w**2 - 3/2*w = 0. Calculate w.
0, 2
Let z = 1815 + -23689/13. Let t = -742/117 - z. Suppose -16/9 + 4*r**2 - t*r + 4/9*r**4 - 22/9*r**3 = 0. What is r?
-1/2, 2
Let a be 108/(-162)*-6*3/102*1. Factor 16/17*l**2 + a*l**4 + 0 - 10/17*l**3 - 8/17*l.
2*l*(l - 2)**2*(l - 1)/17
Let c(d) = 88*d**2 + 12*d + 40. Let v(k) = k**2 + 2. Let x(t) = -c(t) + 20*v(t). Suppose x(l) = 0. What is l?
-3/17, 0
Find a, given that -2/3*a**2 - 8/3*a - 8/3 = 0.
-2
Suppose -u = 0, 4 = -y + u + 3*u. Let b be (3/6)/((-25)/y - 4). Find p such that -4/9*p - 2/9*p**2 + 0 + b*p**3 = 0.
-1, 0, 2
Let h = -261 + 261. Let q(s) be the third derivative of 0*s**3 + 1/540*s**6 + h + 0*s**5 + 0*s + 0*s**4 - 4*s**2. Solve q(x) = 0 for x.
0
Let g(w) be the first derivative of w**5/3 + 17*w**4/6 + 4*w**3 - 11*w**2/2 - 11. Let h(n) be the second derivative of g(n). Find d, given that h(d) = 0.
-3, -2/5
Let a be 900/6000 + 6/(-40). Factor -16/11*p**4 - 32/11*p**3 + 0 - 2/11*p**5 + a*p**2 + 0*p.
-2*p**3*(p + 4)**2/11
Let u(o) be the third derivative of o**8/336 - o**7/84 + o**6/80 + o**5/120 - o**4/48 - 8*o**2. Factor u(b).
b*(b - 1)**3*(2*b + 1)/2
Let v(g) be the first derivative of 5*g + 19 - 5/3*g**3 - 35/4*g**4 + 35/2*g**2. Factor v(o).
-5*(o - 1)*(o + 1)*(7*o + 1)
Factor 0 - 10*a**3 + 22/7*a**4 + 0*a - 2/7*a**5 + 50/7*a**2.
-2*a**2*(a - 5)**2*(a - 1)/7
Let y(f) = 4*f**2 - 4*f - 8. Let t = 82 - 83. Let c(z) = z**2 - 1. Suppose -4*r + 25 = -l, 3*r = 2*l + 2*l + 22. Let i(q) = r*c(q) + t*y(q). Factor i(x).
2*(x + 1)**2
Let v(q) be the second derivative of q**4/30 + 2*q**3 - 31*q**2/5 + 80*q. Let v(t) = 0. What is t?
-31, 1
Suppose -p = -7*p + 12. Let a(r) be the first derivative of 2/3*r**3 + 0*r + p*r**2 - 8. Factor a(z).
2*z*(z + 2)
Let i(x) be the third derivative of x**7/210 + x**6/40 + x**5/60 - x**4/8 - x**3/3 - 114*x**2. Factor i(h).
(h - 1)*(h + 1)**2*(h + 2)
Let z = 3482/15 + -232. Let f(w) be the first derivative of -1/6*w**6 - z*w**5 - 1/6*w**2 + 2/9*w**3 + 0*w + 1/3*w**4 + 3. Find k such that f(k) = 0.
-1, 0, 1/3, 1
Let d(l) be the thi