b).
b*(b - 1)*(b + 1)**2
Let y be (-8)/(-28) + 38/14. Suppose -3*j - 7 = -5*z, -4*j = -y*z + z. Find t such that 1/2*t - 1/4*t**z - 1/4 = 0.
1
Factor -2 - 12/5*y - 2/5*y**2.
-2*(y + 1)*(y + 5)/5
Let i = 471 + -461. Factor -21/2*g**2 - 2 + i*g.
-(3*g - 2)*(7*g - 2)/2
Let u(s) be the third derivative of s**6/300 - s**5/150 - s**4/15 + 4*s**3/15 - 4*s**2. Solve u(g) = 0 for g.
-2, 1, 2
Let l = 2684/399 + -8/133. Let w(y) be the second derivative of -2*y**2 + 8/5*y**5 - l*y**4 + 17/3*y**3 + 0 + 2*y. Determine d, given that w(d) = 0.
1/4, 2
Let s = -120 - -1441/12. Let v(z) be the first derivative of -1/3*z - s*z**4 + 1/9*z**3 + 2 + 1/6*z**2. Factor v(f).
-(f - 1)**2*(f + 1)/3
Let r = 30 + -24. Let q = 29 + -85/3. Solve -r + 4*c - q*c**2 = 0.
3
Let d = 8 - 7. Let s(l) = l**2 + l. Let a be s(d). Factor 0 - 3/4*c**3 + 0*c - 1/4*c**a.
-c**2*(3*c + 1)/4
Suppose 3*c - 14 + 2 = 0. Factor 0*g + g + 3*g**2 - g**2 + g**2 - c*g**4.
-g*(g - 1)*(2*g + 1)**2
Let a be (2/(2/(-7)))/(-1). Let i = a - 5. Factor -2 + 2 - 2*w + 4*w**2 + 5*w**i - 7*w**3.
-w*(w - 1)*(7*w - 2)
Let p(n) be the first derivative of 1 + 0*n**3 - 1/4*n**6 - 3/4*n**2 + 3/4*n**4 + 0*n**5 + 0*n. Factor p(a).
-3*a*(a - 1)**2*(a + 1)**2/2
Factor 7*h + 0*h - 2 + 8*h**3 - 11*h - 2*h.
2*(h - 1)*(2*h + 1)**2
Let l(q) = -2*q**2 + 6*q + 10. Let x(v) = 3*v**2 - 13*v - 21. Let r(m) = -5*l(m) - 2*x(m). Solve r(j) = 0.
-1, 2
Factor -j**3 + 2*j**2 + 0*j**2 + 3*j**2 - 4*j**2.
-j**2*(j - 1)
Let g = 9/86 - -2173/602. Let w = g - 22/7. Factor 2/7*i**2 - w*i + 2/7.
2*(i - 1)**2/7
Let f(d) be the third derivative of 0*d + d**2 - 1/1344*d**8 + 1/24*d**3 + 1/120*d**5 + 1/32*d**4 - 1/280*d**7 + 0 - 1/240*d**6. Let f(v) = 0. What is v?
-1, 1
Suppose 2*j = 1 - 3, 4*t - 45 = 5*j. Suppose 5*z = -0 + t. Factor 2/7*x**z - 2/7*x + 0.
2*x*(x - 1)/7
Let s(i) = -i**2 - 1. Let r(t) = -3*t**3 + 13*t**2 - 9*t + 7. Let m(p) = -r(p) - 4*s(p). Factor m(z).
3*(z - 1)**3
Find s, given that 8*s + 13*s**3 + 11*s**3 + 5*s**2 - 12 - 25*s**3 = 0.
-2, 1, 6
Let f = -44 + 91/2. Let t(m) be the second derivative of -f*m**2 + 3/80*m**5 - 2*m + 0 + 3/16*m**4 + 0*m**3. Suppose t(o) = 0. What is o?
-2, 1
Factor -2/5*y**2 - 2/5*y + 0.
-2*y*(y + 1)/5
Let r be 934/(-13) + (-2)/13. Let q be (-2)/(-4) + (-28)/r. Factor 8/9*y - 2/9*y**2 - q.
-2*(y - 2)**2/9
Let s = 55 - 51. Let a(d) be the third derivative of 0 - 1/210*d**7 + 2*d**2 + 1/60*d**6 + 0*d - 1/6*d**3 - 1/24*d**s + 1/30*d**5 - 1/336*d**8. Factor a(j).
-(j - 1)**2*(j + 1)**3
Suppose 4*n - 26 = -3*d, -4*d - 8 = -4*n + 4. Let u(a) be the first derivative of -1/3*a**3 - 4*a + 1 + d*a**2. Solve u(f) = 0 for f.
2
Let x = 26 + -103/4. Let h = x - 0. Factor -1/4*i**2 + 1/4 + 1/4*i**3 - h*i.
(i - 1)**2*(i + 1)/4
Let w(v) be the second derivative of -1/6*v**3 - v**2 - 1/30*v**6 + 1/20*v**5 - 2*v + 0 + 1/4*v**4. Suppose w(x) = 0. Calculate x.
-1, 1, 2
Let q(i) = i**4 - i**3 + i + 1. Let k(l) = -9*l**4 - 18*l**3 - 28*l**2 - 12*l - 4. Let w(v) = k(v) + 4*q(v). Factor w(r).
-r*(r + 2)**2*(5*r + 2)
Let h be (-20)/24 + (-43)/(-30). Factor h*a**2 - 6/5*a + 0.
3*a*(a - 2)/5
Let s(m) = -m**5 - 2*m**4 - 6*m**3 + m + 2. Let g(v) = 5*v**5 + 9*v**4 + 25*v**3 - v**2 - 3*v - 8. Let k = -28 + 10. Let o(p) = k*s(p) - 4*g(p). Factor o(y).
-2*(y - 2)*(y - 1)*(y + 1)**3
Let b be (-6)/(-2)*(-20)/30. Let d be 2*-1*b/2. Let -2/3*t + 4/9*t**3 - 4/9*t**d - 2/9 + 2/3*t**4 + 2/9*t**5 = 0. What is t?
-1, 1
Let r(a) = a**2 + 2*a - 3. Let z be r(-4). Let f = 8 - 0. Find t such that -4*t + f*t**3 + 3*t + t**2 - t + z*t**2 = 0.
-1, 0, 1/4
Let y be 0/18*(-2 - -1). Let a(c) be the third derivative of 0*c + 1/480*c**6 + 0*c**5 + 0 - 1/96*c**4 - 2*c**2 + y*c**3. Solve a(h) = 0.
-1, 0, 1
Let a = -10104/5 - -2030. Let q be 3/(-9) - (-46)/30. Solve a*v**2 + 24/5*v**3 - q*v - 4/5 = 0.
-2, -1/4, 1/3
Let r(j) be the first derivative of 0*j**5 + 0*j**3 + 1/9*j**6 + 1/3*j**2 + 0*j - 4 - 1/3*j**4. Factor r(p).
2*p*(p - 1)**2*(p + 1)**2/3
Let z(v) = -v**3 - 10*v**2 + 11*v + 3. Let n be z(-11). Suppose -j**5 + j**2 + j**n - j**2 = 0. Calculate j.
-1, 0, 1
Let d = -8 - -5. Let i = 6 + d. Solve 4/5*j + 54/5*j**i + 14/5*j**5 - 46/5*j**4 - 26/5*j**2 + 0 = 0.
0, 2/7, 1
Let m = -15 - -19. Suppose 0 + 1/3*s**m - 1/3*s + 1/3*s**3 - 1/3*s**2 = 0. What is s?
-1, 0, 1
Let b(w) = w**2 - 6*w. Let v be b(6). Let d = v + 2. Find z, given that 1/4*z**3 + 1/2 - 1/4*z - 1/2*z**d = 0.
-1, 1, 2
Let h(o) = -9*o - 16*o + 53 - 62*o - o**3 + 36*o**2 + 10*o. Let v(m) = 2*m**3 - 54*m**2 + 115*m - 79. Let u(s) = -7*h(s) - 5*v(s). Find k such that u(k) = 0.
2
Let n(y) = y**3 + 1. Let r(q) = 50*q**3 - 35*q**2 - 40*q + 45. Let j(p) = 25*n(p) - r(p). Let j(o) = 0. What is o?
-1, 2/5, 2
Let f(x) = x + 3. Let l be f(9). Factor -2*h + 0*h - h**3 + 0*h + 9*h**2 - l*h**2.
-h*(h + 1)*(h + 2)
Let z(s) be the first derivative of s**5/55 - s**3/33 - 23. Let z(x) = 0. What is x?
-1, 0, 1
Let b(f) = 8*f**3 + 3*f**2 - f - 2. Let a(x) = 9*x**3 + 2*x**2 - 2*x - 3. Let o(c) = -4*a(c) + 6*b(c). Solve o(k) = 0 for k.
-1/2, -1/3, 0
Let r be (-4)/(-10) - 46/(-10). Let d(n) be the third derivative of 1/180*n**r + n**2 + 0 + 0*n - 1/72*n**4 - 1/18*n**3 + 1/360*n**6. Solve d(x) = 0.
-1, 1
Let k = 3 - -2. Suppose k*m = q + 13, 0*m = -4*q - 3*m + 17. Factor -q*f**3 + 2 - 7*f + 0*f + 9*f**3 - 2*f**2.
(f - 1)*(f + 1)*(7*f - 2)
Let m(a) = -3*a**2 + 2*a - 3. Suppose 0*r + 4 = -2*r. Let u(o) = 4*o**2 - 2*o + 4. Let i(z) = r*u(z) - 3*m(z). Find y, given that i(y) = 0.
1
Let l(t) be the first derivative of -t**5 + 15*t**4/4 - 5*t**3 + 5*t**2/2 + 6. Solve l(p) = 0.
0, 1
Let g = 664/3 + -220. Solve -2/3*x**4 + 2/3*x**2 + 4/3*x**3 - g*x + 0 = 0 for x.
-1, 0, 1, 2
Let u(n) be the third derivative of -n**8/84 + 2*n**7/105 + n**6/30 - n**5/15 + 2*n**2. Factor u(j).
-4*j**2*(j - 1)**2*(j + 1)
Let n = 120 - 120. Find s, given that n - s**4 + 5/4*s**3 - 1/2*s**2 + 0*s + 1/4*s**5 = 0.
0, 1, 2
Factor 0 + 1/6*l**2 - 1/6*l.
l*(l - 1)/6
Find n such that 0*n - 2/5*n**2 + 8/15 + 2/15*n**3 = 0.
-1, 2
Let v(y) be the second derivative of y**4/78 - 10*y**3/39 - 2*y + 24. Solve v(z) = 0.
0, 10
Suppose -2 = -5*n - 4*k, -4*n + 2*k + 16 = -2*k. Factor 4 + 5*y**2 + n*y**3 - 6*y + 14*y - y**3 + 0*y**2.
(y + 1)*(y + 2)**2
Let w(t) = 2*t**2 - 3*t**3 + 4*t - 4*t**2 + 4 - 5*t + 6*t**3. Let v(n) = 4*n**3 - 2*n**2 - n + 5. Let y(u) = 4*v(u) - 5*w(u). Solve y(k) = 0 for k.
-1, 0
Let c(v) be the third derivative of v**8/10080 - v**7/13860 + v**5/60 + v**2. Let q(p) be the third derivative of c(p). Factor q(y).
2*y*(11*y - 2)/11
Let a(m) be the second derivative of 0 + 6*m - 1/28*m**4 + 1/14*m**2 - 1/21*m**3. Suppose a(u) = 0. What is u?
-1, 1/3
Let p(s) be the second derivative of -s**7/105 - s**6/45 + s**5/75 + s**4/15 + s**3/45 - s**2/15 + s. Let p(c) = 0. Calculate c.
-1, 1/3, 1
Factor 3 - 6*s**3 + 25*s**4 + 5*s - 155*s**2 + 37 + 66*s**3 + 25*s.
5*(s - 1)**2*(s + 4)*(5*s + 2)
Let v(x) be the second derivative of -x**9/68040 - x**8/30240 + x**4/2 + 2*x. Let c(k) be the third derivative of v(k). Factor c(l).
-2*l**3*(l + 1)/9
Let w = -1/46 - 21/92. Let c = 1/4 - w. Determine i, given that -1/2*i**3 + c - 1/2*i**2 + 1/2*i = 0.
-1, 1
Let u = -4 + 10. Suppose 3*q + 6 - 4*q**2 + u*q**2 - 5*q**2 = 0. Calculate q.
-1, 2
Let l be 0 - 1 - 15/(-28)*4. Factor -14*u**2 + 0*u + l.
-2*(7*u - 2)*(7*u + 2)/7
Suppose -l + 3 = 2*l, -3*j + 20 = 5*l. Suppose -j = -o + 2*q, -3*o + 4*q = q - 15. Factor 4*g**5 + 6*g**3 - g**5 - 2*g**5 - 6*g**4 + g**o - 2*g**2.
2*g**2*(g - 1)**3
Let t(d) be the first derivative of -d**3/18 - d**2/6 - d/6 + 11. Factor t(m).
-(m + 1)**2/6
Find j, given that -1 + 3/4*j**2 + 0*j + 1/4*j**3 = 0.
-2, 1
Let q(k) be the first derivative of -5*k**4 - 25*k**3 - 30*k**2 + 20*k + 23. Factor q(v).
-5*(v + 2)**2*(4*v - 1)
Factor -12/5*w**3 + 8/5*w**2 - 2/5*w + 0 - 2/5*w**5 + 8/5*w**4.
-2*w*(w - 1)**4/5
Let n(j) be the third derivative of 0 + 3*j**2 - 1/12*j**3 - 1/240*j**5 - 1/32*j**4 + 0*j. Factor n(z).
-(z + 1)*(z + 2)/4
Let w(o) be the second derivative of 3*o**7/7 + 7*o**6/5 + 7*o**5/10 - 17*o**4/6 - 16*o**3/3 - 4*o**2 + 3*o. What is p in w(p) = 0?
-1, -2/3, 1
Determine g, given that -18*g**2 + 7*g**4 - 6*g**3 - 5*g**4 - 6*g**3 - 8*g - 4*g**4 = 0.
-4, -1, 0
Let 4/15*y - 2/15*y**5 + 2/5*y**3 - 2/3*y**2 + 0 + 2/15*y**4 = 0. Calculate y.