6). Let w be 3 + 4 + v/6. Factor 4*r - w*r**2 - 2 + 1/2*r**3.
(r - 2)**2*(r - 1)/2
Let x = -35/12 + 13/4. Suppose -x*c**4 + 0 - 1/3*c**3 + 1/3*c + 1/3*c**2 = 0. Calculate c.
-1, 0, 1
Let l(u) be the third derivative of 1/210*u**5 + 1/42*u**4 + 0*u**3 + 0*u + 0 - 4*u**2. Determine w, given that l(w) = 0.
-2, 0
Let q(w) = -w**5 + w**3 + w. Let u(g) = -g**5 - 6*g**4 + 9*g**3 - 2*g**2 + 3*g. Let y(i) = 6*q(i) - 2*u(i). Factor y(d).
-4*d**2*(d - 1)**3
Let -2*l**3 - l**3 - 3*l**5 + 21*l**4 - 27*l**4 = 0. What is l?
-1, 0
Let z(p) be the third derivative of -p**8/294 - 22*p**7/735 - 23*p**6/210 - 23*p**5/105 - 11*p**4/42 - 4*p**3/21 + 14*p**2. Solve z(g) = 0.
-2, -1, -1/2
Let a be (-4 + -1*21)*-1. Solve -12*v**3 + 0*v + 32*v**2 - a*v + 8 - 3*v + 0*v = 0 for v.
2/3, 1
Let b(t) be the first derivative of -t**4 - 16*t**3/3 - 8*t**2 + 58. Determine z so that b(z) = 0.
-2, 0
Let b(r) be the third derivative of -1/120*r**5 + 0 - 1/96*r**4 + 1/420*r**7 - 7*r**2 + 0*r**3 + 0*r + 1/1344*r**8 + 0*r**6. Factor b(k).
k*(k - 1)*(k + 1)**3/4
Let n = -44 - -65. Suppose -4*h = 5*x - 23, 0 = -3*x - 2*x - 3*h + n. Factor 7*i**3 - 6*i**3 - 3*i**x - 4*i**2.
-2*i**2*(i + 2)
Find x, given that -3*x - 1/2*x**2 - 5/2 = 0.
-5, -1
Suppose l - 3 = -4. Let v be l + 8/(-1 + 3). Suppose -u**4 - 4*u**v - u**2 + u**3 - u**5 - 2*u**4 = 0. What is u?
-1, 0
Suppose -72*r**3 + 0 + 96*r**4 + 27/2*r**2 + 0*r = 0. What is r?
0, 3/8
Suppose -26*y = -27*y + 5. Let d(v) be the third derivative of 1/12*v**4 + 2/15*v**3 + 0 + 1/50*v**y + 2*v**2 + 0*v. Let d(l) = 0. Calculate l.
-1, -2/3
Let h = 3589/1436 - -1/1436. Factor 1/2*p**5 + h*p**2 - 1/2*p**4 - p + 0 - 3/2*p**3.
p*(p - 1)**3*(p + 2)/2
Let o(n) be the first derivative of -n**6/10 - 9*n**5/20 - 3*n**4/4 - n**3/2 + n - 7. Let l(i) be the first derivative of o(i). Factor l(y).
-3*y*(y + 1)**3
Let p(l) = 2*l**2 - 3*l + 4. Let w be p(4). Let u be (-3)/1*(-16)/w. Factor 0*m - 2/5 + 2/5*m**u.
2*(m - 1)*(m + 1)/5
Let j = -49 + 69. Suppose 5*y + k = 6*k + 30, 0 = 5*k + j. Factor -u**3 - 13 + u**y + 13 + 0*u**2 + u - u**4.
-u*(u - 1)*(u + 1)**2
Let s be -1 + -2 + 9 + 2. Let v be s/(-24) + 14/6. Factor -2*z - z**v + 5*z**2 + 4*z.
2*z*(2*z + 1)
Let o(j) be the third derivative of -7*j**6/480 - j**5/120 + 14*j**2. Factor o(p).
-p**2*(7*p + 2)/4
Suppose -11 + 1 = -5*h. Let 8*n**2 - 10*n**3 + 8*n**4 - 4*n**2 + 4*n**2 - 4*n**2 - h*n**5 = 0. Calculate n.
0, 1, 2
Suppose 2*y - 12 = -3*a, 2*a - y + 0*y = 1. Let z(v) be the first derivative of -1 + 2/3*v - 2/9*v**3 + 1/6*v**4 - 1/3*v**a. Factor z(l).
2*(l - 1)**2*(l + 1)/3
Factor -8/7 - 4/7*q**2 - 12/7*q.
-4*(q + 1)*(q + 2)/7
Let l = -40/7 + 87/14. Let u(a) be the second derivative of -a + 1/6*a**3 - 1/20*a**5 - 1/12*a**4 + 0 + l*a**2. Factor u(q).
-(q - 1)*(q + 1)**2
Factor 1 + 160*v - v**2 - 160*v.
-(v - 1)*(v + 1)
Let z(o) be the second derivative of 5*o**7/189 + 7*o**6/135 - 13*o**5/90 - 11*o**4/54 + 8*o**3/27 + 4*o**2/9 - 6*o. Let z(w) = 0. Calculate w.
-2, -1, -2/5, 1
Let v(f) = f**3 - f**2 + f + 1. Let n(i) = 3*i**3 - 5*i**2 + 3*i + 2. Let s(d) = -n(d) + 2*v(d). Let t be s(2). Factor 4*l - 2 - 2*l**t + l - l.
-2*(l - 1)**2
Let u(g) be the first derivative of -g**6/9 + 4*g**5/5 - 7*g**4/3 + 32*g**3/9 - 3*g**2 + 4*g/3 - 29. Factor u(j).
-2*(j - 2)*(j - 1)**4/3
Suppose 0 = -g - 2 + 4. Factor -y**2 + 8*y**3 - 2*y**g - 7*y**2 - 2*y**4 + 4*y.
-2*y*(y - 2)*(y - 1)**2
Let -2/5*c**4 + 0*c + 2/5*c**2 - 7/5*c**5 + 7/5*c**3 + 0 = 0. Calculate c.
-1, -2/7, 0, 1
Let n(q) be the second derivative of -q**7/210 + q**6/150 + q**5/50 - 8*q. Factor n(i).
-i**3*(i - 2)*(i + 1)/5
Let a be (-10 + 5 + -5)*4/(-10). Suppose 3 = 2*q - 1. Solve 0*s + 0 + 70/9*s**5 + 8/9*s**q - 40/9*s**3 + 22/9*s**a = 0 for s.
-1, 0, 2/7, 2/5
Let u be 14*2/4 + -3. Let b - 5/2*b**2 + 7/2*b**5 + 5/2*b**u + 0 - 9/2*b**3 = 0. Calculate b.
-1, 0, 2/7, 1
Suppose -w = -0*w. Suppose -3*p + 5*x = p - 10, w = 5*p - 4*x - 8. Determine n so that p + 2/5*n**3 + 4/5*n**2 + 2/5*n = 0.
-1, 0
Let h(m) be the first derivative of -m**4/12 + 7*m**3/9 - 5*m**2/2 + 3*m - 40. What is i in h(i) = 0?
1, 3
Let p(z) = -2*z**2 + 17*z - 15. Let o(r) = 3*r**2 - 25*r + 22. Let s(v) = -5*o(v) - 8*p(v). Find b, given that s(b) = 0.
1, 10
Let x(b) be the third derivative of 1/1050*b**7 + 0*b - 1/150*b**5 + 0 + 1/30*b**3 - 1/120*b**4 - 1/1680*b**8 + 1/300*b**6 + 4*b**2. Solve x(q) = 0 for q.
-1, 1
Suppose -10*m**4 - 2*m**5 - 28*m**2 + 9 + 16*m + 19*m**2 - 14*m**3 - 1 + 11*m**2 = 0. What is m?
-2, -1, 1
Let z(d) be the second derivative of d**5/20 + d**4/6 + d**3/6 - 7*d. Factor z(k).
k*(k + 1)**2
Let b be 5 - 9/(-6)*-2. Let d(c) be the first derivative of b - 1/10*c**4 - 1/5*c**2 - 4/15*c**3 + 0*c. Suppose d(w) = 0. What is w?
-1, 0
Let u(h) be the first derivative of -h**3/6 + h/2 + 7. Let u(o) = 0. Calculate o.
-1, 1
Let z(l) be the second derivative of 2/3*l**2 + 1/15*l**5 + 0 + l + 2/3*l**3 + 1/3*l**4. Find k such that z(k) = 0.
-1
Suppose 3*w + 7 + 11 = 0. Let h be (8/30)/(w/(-9)). Determine g, given that -h*g**2 + 0 + 2/5*g = 0.
0, 1
Factor -154 + 154 + 2*a + 2*a**3 + 4*a**2.
2*a*(a + 1)**2
Let m(n) = -n**3 - 11*n**2 - 14*n - 36. Let q be m(-10). Factor 4/5*j**3 - 6/5*j**q + 2/5*j**5 - 6/5*j + 4/5*j**2 + 2/5.
2*(j - 1)**4*(j + 1)/5
Let l = -2/33999 + 4805194/33999. Let u = l + -140. Factor -1/3*i**2 - u*i - 4/3.
-(i + 2)**2/3
Suppose i + 4*i = -30. Let c(x) = -x - 3. Let m be c(i). Factor 2*d**2 + d + m*d**2 - d**2.
d*(4*d + 1)
Let u(s) = -5*s**3 - 5*s**2 + 35*s - 25. Let x(m) = -m + 1. Let n(o) = -u(o) - 30*x(o). Find v such that n(v) = 0.
-1, 1
Let m = -18 - -109/6. Let r(h) be the first derivative of -1 + 1/8*h**4 + 0*h + 0*h**2 - m*h**3. Determine j, given that r(j) = 0.
0, 1
Let w be (-3)/10*(-1 - (-1)/(-3)). What is x in -6/5*x**2 + 4/5*x + w*x**3 + 0 = 0?
0, 1, 2
Let k(f) be the first derivative of -4*f**3 - 21*f**2/2 + 6*f - 15. Factor k(y).
-3*(y + 2)*(4*y - 1)
Suppose -n = n - 12. Factor 27*p**4 - 4 - 9*p**4 + 36*p**3 + 42*p**2 + n*p + 14*p**3 + 0.
2*(p + 1)**3*(9*p - 2)
Let v = 9 + -13. Let d be 1/v*(-128)/72. Factor -d*j + 2/9 + 2/9*j**2.
2*(j - 1)**2/9
Let p be 9/6*(-4)/(-6). Let o be (-2 - p*-3) + 1. Factor -4*b**4 - o*b**3 + b - b - 2*b**5.
-2*b**3*(b + 1)**2
Let i = 18 + -12. Let h be 4/(-6) - (-7)/i. Find p, given that -1/2*p**2 + 0 + h*p = 0.
0, 1
Factor z**2 - z - z - 3*z - 2 + 4*z.
(z - 2)*(z + 1)
Let -6 - 2*w + 2*w**3 - 3*w**3 + 9*w = 0. Calculate w.
-3, 1, 2
Let t be 60*(15/10 - 2). Let f = t - -32. Factor 0 - 3/5*m**3 + 4/5*m + 0*m**f - 1/5*m**4.
-m*(m - 1)*(m + 2)**2/5
Let u(d) = -6*d**2 - 2*d + 4. Suppose 4*i = -0*i + 16. Let n(s) = -5*s**2 - s + 4. Let g(p) = i*n(p) - 3*u(p). Let g(h) = 0. Calculate h.
-1, 2
Factor 4*s + 3 - 6*s**2 - 8 + 7.
-2*(s - 1)*(3*s + 1)
Let q(p) be the second derivative of 5*p**7/42 - p**6/6 - p**5/4 + 5*p**4/12 - 5*p. Find b, given that q(b) = 0.
-1, 0, 1
Suppose 0 = -2*a + 3*d - 0*d - 15, 5*a - 10 = -2*d. Factor a + 0*f + 1/2*f**3 + 1/2*f**2.
f**2*(f + 1)/2
Let l(d) be the second derivative of 0 - 1/9*d**3 + 4*d - 1/36*d**4 + 0*d**2. Determine b so that l(b) = 0.
-2, 0
Suppose z = -3*z + 24. Suppose -z*t + 8 + 10 = 0. Factor -1/5 - 1/5*c**t - 3/5*c**2 - 3/5*c.
-(c + 1)**3/5
Suppose 0 = -2*r + 10, 0*r = -5*f + 3*r + 5. Factor -2*z**5 - 2*z**3 + 3*z**5 + 4*z**4 - 4*z**4 - z**f.
z**3*(z - 2)*(z + 1)
Let a(j) be the second derivative of -3/70*j**5 - 1/42*j**4 + 0*j**3 - 1/35*j**6 - 2*j - 1/147*j**7 + 0 + 0*j**2. Find b, given that a(b) = 0.
-1, 0
Let w be (32/14)/((-2)/(-7)). Suppose -3*t = t - w. Find o such that 2/11*o + 2/11*o**t + 0 = 0.
-1, 0
Suppose 4*u - 4 - 4 = 0. Let x(z) be the second derivative of 0 - 1/40*z**5 - 1/12*z**3 + 1/12*z**4 + 0*z**u + 2*z. Factor x(v).
-v*(v - 1)**2/2
Suppose -31 = 3*s + 3*t + 2, 59 = -5*s - t. Let i be (-3)/s - (-14)/8. Factor -4*y + 4*y - y**2 + 3*y**i + 2*y.
2*y*(y + 1)
Let u(l) be the first derivative of -l**7/105 + l**6/45 - l**5/90 + 2*l**2 - 2. Let x(c) be the second derivative of u(c). Let x(r) = 0. What is r?
0, 1/3, 1
Let d(y) = -y**2 + y - 1. Let l(x) = -3*x**5 + 12*x**4 - 18*x**3 + 15*x**2 - 6*x + 3. Let j(k) = 3*d(k) + l(k). Factor j(w).
-3*w*(w - 1)**4
Let z(g) be the first derivative of -1/4*g**4 + 1/2*g + 4 + 0*g**3 + 1/2*g**2 - 1/10*g**5. Factor z(d).
-(d - 1)*(d +