b). Suppose v(f) = 0. Calculate f.
0, 2/5
Let w = 336 + -336. Factor 2/5*v**3 + w*v + 0 - 4/5*v**2.
2*v**2*(v - 2)/5
Let j(k) be the third derivative of -1/36*k**4 - k**2 + 0*k + 1/180*k**5 + 0*k**3 + 0. Determine g, given that j(g) = 0.
0, 2
Find r, given that 10/3 - 5/3*r**2 + 5/3*r = 0.
-1, 2
Let k(s) = -s**3 + 13*s**2 + s - 13. Let b(w) = -w**3 + 25*w**2 + w - 25. Let u(d) = -2*b(d) + 5*k(d). Let u(a) = 0. Calculate a.
-1, 1, 5
Let y be 48/32 + 6/4. Factor 0 + 4/5*j**y + 2/5*j**4 + 0*j**2 + 0*j.
2*j**3*(j + 2)/5
Solve -8/3*b**2 - 50/9*b**5 - 8/9*b + 22/9*b**3 + 0 + 20/3*b**4 = 0 for b.
-2/5, 0, 1
Let y(j) be the third derivative of -2/5*j**5 + 0*j**3 + 0 + 3/40*j**6 + 1/2*j**4 + 0*j - 2*j**2. Find o, given that y(o) = 0.
0, 2/3, 2
Let c(o) = -o**3 - 9*o**2 - 4*o. Let m(a) = -a**2 + a + 1. Suppose 3*r + 39 = 12. Let t be (-3)/r*3*-1. Let p(j) = t*c(j) + 4*m(j). Factor p(v).
(v + 1)*(v + 2)**2
Let w be (1 + 14)/(3/(-6)). Let k be (w/40)/((-9)/40). Solve k*l - 2*l**2 - 2/3 - 10/3*l**3 + 8/3*l**4 = 0 for l.
-1, 1/4, 1
Factor 0*n**2 + 0*n + 0 - 1/3*n**4 - 1/3*n**3.
-n**3*(n + 1)/3
Let y(i) be the second derivative of 2*i + 1/7*i**3 - 1/42*i**4 - 2/7*i**2 + 0. Factor y(b).
-2*(b - 2)*(b - 1)/7
Let q = 5 + -6. Let w(m) be the first derivative of -m**2/2 - 2. Let y(z) = -2*z**2 - 4*z. Let l(c) = q*y(c) + 6*w(c). Let l(a) = 0. Calculate a.
0, 1
Suppose 4*q = 4 + 4. Let c be 5/(-25)*0 + q. Factor 0 + 1/2*h**c - h.
h*(h - 2)/2
Let a(t) be the third derivative of 0*t + 0 - 1/6*t**4 - 5*t**2 + 4/15*t**5 - 8/45*t**6 + 1/18*t**3. Find y, given that a(y) = 0.
1/4
Suppose 0 = -2*x + 6, -7*l - 4*x = -3*l - 20. Suppose y - 3*t - 8 = 4, 5*y = -5*t. Factor -1/4*w**4 + 1/4*w**y - 1/4*w + 1/4*w**l + 0.
-w*(w - 1)**2*(w + 1)/4
Let s be (-22)/(-77) - (-74)/(-14). Let v be (-16)/(-72) - s/18. Factor 3/2*g - 1 - v*g**2.
-(g - 2)*(g - 1)/2
Let f be (-280)/40 - (-110)/14. Solve 0 + 0*i - 3/7*i**2 - 3/7*i**4 + f*i**3 = 0 for i.
0, 1
Let l(s) be the second derivative of 0*s**2 + 1/2*s**5 + 0 - 4/15*s**6 + 7/6*s**4 - 2/3*s**3 - s. Factor l(f).
-2*f*(f - 2)*(f + 1)*(4*f - 1)
Let l be (-84)/(-140) + (-7)/(-5). Factor 1/2*w**l + 0*w - 1/2.
(w - 1)*(w + 1)/2
Suppose -4*x + 0*x + 48*x**2 + 20*x - 28*x**3 = 0. Calculate x.
-2/7, 0, 2
Let q(f) be the third derivative of -f**8/1512 - f**7/135 - 4*f**6/135 - 4*f**5/135 + 4*f**4/27 + 16*f**3/27 - 15*f**2. Solve q(w) = 0.
-2, 1
Let u = 263 + -261. Solve -2/5*s**u + 0*s + 0 + 2/5*s**3 = 0 for s.
0, 1
Let s(g) be the third derivative of -1/4*g**4 - 5*g**2 + 0 + 0*g - 1/60*g**6 - 1/10*g**5 - 1/3*g**3. Solve s(j) = 0.
-1
Solve -3/5*y**3 + 0*y + 0 - 6/5*y**4 + 0*y**2 = 0 for y.
-1/2, 0
Let f be (3/(-2))/(8/(-16)). Let w(p) = p - 3. Let i be w(f). Determine c, given that -4/9*c**2 + 4/9*c**4 - 2/9*c**5 + 2/9*c + i + 0*c**3 = 0.
-1, 0, 1
Let u(r) be the first derivative of 9*r**5/10 + 3*r**4/2 + 2*r**3/3 + 10. Factor u(b).
b**2*(3*b + 2)**2/2
Suppose 20 = 4*i, -5*a = i + 3*i. Let p be a + 3 - -4 - -1. Factor -2/7*j**p + 0 + 2/7*j**2 + 2/7*j - 2/7*j**3.
-2*j*(j - 1)*(j + 1)**2/7
Let w(b) be the second derivative of -b**7/4 - b**6/4 + 27*b**5/40 + 5*b**4/8 - b**3/2 + 6*b. Determine n so that w(n) = 0.
-1, 0, 2/7, 1
Let s be 5*(0 - 2/(-5)). Suppose v + 0*v - s = 0. Factor 2*l**3 + l**2 - 4*l**2 + l**v.
2*l**2*(l - 1)
Let k(p) be the third derivative of -p**8/224 - p**7/140 + p**6/80 + p**5/40 - 21*p**2. Let k(f) = 0. What is f?
-1, 0, 1
Suppose 1 = -2*v + 13. Suppose -2*u = -3*u + v. Factor -u*a**3 - a**2 - 5*a**2 - 10*a**2 - 14*a - 4.
-2*(a + 1)**2*(3*a + 2)
Let p be 8/(-9)*66/(-88). Solve -p*f**2 + 0 + f - 1/3*f**3 = 0.
-3, 0, 1
Let n(f) be the third derivative of 0 + 1/72*f**4 - 1/90*f**5 - 1/1008*f**8 + 0*f + 1/315*f**7 - f**2 + 0*f**3 + 0*f**6. Factor n(w).
-w*(w - 1)**3*(w + 1)/3
Let u(y) be the second derivative of y**4/12 + 7*y**3/6 - 5*y**2/2 + 4*y. Let q be u(-8). Factor -5/4*w**2 - 7/4*w**q + 0 + 1/2*w.
-w*(w + 1)*(7*w - 2)/4
Let u(g) be the first derivative of -g**6/2 - 6*g**5/5 + 3*g**4/4 + 2*g**3 - 11. Determine x so that u(x) = 0.
-2, -1, 0, 1
Suppose -p = -4*p - 42. Let z = p - -20. Factor -z*f**3 + f - f**5 - f**4 - 3*f**4 - 4*f**2 - 2*f.
-f*(f + 1)**4
Find i, given that 0*i**3 + 6*i**3 - 2*i**4 - i**4 = 0.
0, 2
Let y(h) = -h**5 - h**3 + h**2 - h + 1. Let t(f) = 4*f**4 + 7*f**3 - 6*f**2 + 3*f - 4. Let a(l) = 5*t(l) + 20*y(l). What is u in a(u) = 0?
-1/2, 0, 1
Suppose 4*w = -5*v + 26, -3*w + 8 = -0*v - 2*v. Let -4/3*u**v + 2/3*u + 2/3 = 0. Calculate u.
-1/2, 1
Suppose 4*j = 3*w - j - 29, -5*w + 41 = -j. Suppose 0*k + w = 2*k. Solve 2*t**2 - 8*t**k - 4*t**2 + 10*t**3 - 2*t**3 = 0.
0, 1/2
Let q(z) be the second derivative of -z**5/120 + z**4/8 - 3*z**3/4 - 2*z**2 + 4*z. Let n(l) be the first derivative of q(l). Factor n(b).
-(b - 3)**2/2
Let j(v) = -10*v**4 - 7*v**3 + 3*v**2 + 7*v - 7. Let y(z) = -3*z**4 - 2*z**3 + z**2 + 2*z - 2. Let i(b) = 6*j(b) - 21*y(b). Factor i(l).
3*l**2*(l - 1)*(l + 1)
Factor -60*a - 38*a**2 - 12 - 31*a**2 - 21*a**3 + 0*a**2.
-3*(a + 1)*(a + 2)*(7*a + 2)
Let f(u) be the second derivative of u**4/36 + 5*u**3/18 + 2*u**2/3 + u. Factor f(q).
(q + 1)*(q + 4)/3
Let h be (-1)/(-7) - (-204)/42. Factor 0*f**3 + f**4 - 1/2*f + 1/2*f**h + 0 - f**2.
f*(f - 1)*(f + 1)**3/2
Let z(x) be the second derivative of x**4/96 - x**3/24 + 4*x. Determine j, given that z(j) = 0.
0, 2
Let s(q) be the first derivative of -1 - 1/15*q**5 + 1/3*q**3 + 5/6*q**2 - 1/12*q**4 + 2/3*q. Factor s(f).
-(f - 2)*(f + 1)**3/3
Factor -2*r - 25*r**2 - r + 27*r**2 + r.
2*r*(r - 1)
Let y = 608/5 + -120. Factor -2/5*x**2 - y*x - 8/5.
-2*(x + 2)**2/5
Let v(k) be the third derivative of k**6/540 - k**5/135 + 8*k**2. Let v(i) = 0. What is i?
0, 2
Determine j so that 0*j + 0*j**2 + 0*j**4 + 3/2*j**3 - 3/2*j**5 + 0 = 0.
-1, 0, 1
Let u(m) = 2*m**4 - 2*m**3 + 4*m**2 + 2*m - 6. Let t(x) = 6*x**4 - x + 5*x + 7*x**2 - 17 + 4*x**2 - 6*x**3 + 2*x. Let i(l) = 6*t(l) - 17*u(l). Factor i(a).
2*a*(a - 1)**2*(a + 1)
Let i = -2 + 4. Suppose -37 = -3*f - 16. Factor 3*p**2 + 3*p**i - f*p**2 + p + 1 - p**3.
-(p - 1)*(p + 1)**2
Let g(u) be the second derivative of 2/39*u**3 - 1/78*u**4 + 0*u**2 + 0 - 6*u. Factor g(y).
-2*y*(y - 2)/13
Suppose 0 = 6*g - 7*g + 3. Let k(v) be the second derivative of 0 + 1/12*v**g + 3/40*v**5 + 2*v + 1/8*v**4 + 0*v**2 + 1/60*v**6. Find x, given that k(x) = 0.
-1, 0
Factor 1/2*y**3 - 3/4*y + 3/4*y**4 - 1/2*y**2 + 1/4*y**5 - 1/4.
(y - 1)*(y + 1)**4/4
Let y(h) = h**2 + 3*h - 5. Let p be y(5). Let o = p - 104/3. Factor 1/3*d**4 + 0 + 0*d + 1/3*d**5 - o*d**2 - 1/3*d**3.
d**2*(d - 1)*(d + 1)**2/3
Factor 90 - 55/3*c**3 + 75*c**2 + 5/3*c**4 - 135*c.
5*(c - 3)**3*(c - 2)/3
Let g(h) = 5*h**2 + 3*h - 2. Let r(f) = -1 + 4*f**2 + 2*f + 2*f - 2*f - 1. Let b(x) = 2*g(x) - 3*r(x). Factor b(d).
-2*(d - 1)*(d + 1)
What is l in l - 2*l**4 - l**5 - l - 2*l**3 + 3*l**5 + 2*l**2 = 0?
-1, 0, 1
Suppose 0 = 3*a, i + 4*a - 3*a + 14 = 0. Let c be (-10)/(-35) - 80/i. Determine r so that r**4 + 4*r**3 + r**4 - c*r**3 = 0.
0, 1
Let c(x) = -x**3 + 4*x**2 + 20*x + 9. Let a be c(7). What is i in 2*i - 18/7*i**a - 4/7 + 10/7*i**3 - 2/7*i**4 = 0?
1, 2
Let u(p) be the second derivative of -p**6/30 - p**5/10 - 6*p. Factor u(v).
-v**3*(v + 2)
Let n(z) be the second derivative of -3*z - 1/7*z**2 - 1/105*z**6 + 0*z**3 + 0 + 0*z**5 + 1/21*z**4. Factor n(o).
-2*(o - 1)**2*(o + 1)**2/7
Let i be (2/(-6))/((-19)/228). Let r(t) be the third derivative of -1/240*t**6 + i*t**2 + 0 - 1/30*t**5 - 1/6*t**3 + 0*t - 5/48*t**4. Factor r(d).
-(d + 1)**2*(d + 2)/2
Let x(y) = y**2 + y + 8. Let j be x(7). Solve 23*s**2 + 73*s**2 - 21*s - 15*s - j*s**3 = 0.
0, 3/4
Let d(o) be the third derivative of o**5/210 - o**4/42 - o**2. Determine r, given that d(r) = 0.
0, 2
Suppose 150 = 3*d + 594. Let k = d - -448/3. Solve -2*c + 2/3*c**2 + k = 0 for c.
1, 2
Let v = 30 - 31. Let n be (125/15)/5 + v. What is z in 7/3*z**3 + 5/3*z**4 + n*z**2 + 0*z + 0 = 0?
-1, -2/5, 0
Factor 1/2*t**2 + 0 + 1/4*t + 1/4*t**3.
t*(t + 1)**2/4
Let m(n) be the third derivative of n**6/240 + 7*n**5/60 - 31*n**4/48 + 4*n**3/3 + 15*n**2. Factor m(z).
(z - 1)**2*(z + 16)/2
Let b(v) = 5*v**2 - 5*v. Let a(g) = 21*g**2 - 19*g. Let d(p) = -6*a(p) + 26*b(p). Find m such that d(m) = 0.
0, 4
Suppose q - 4 = -q. Let a(y) be the second 