b). Factor r(s).
-2*(s + 1)**3/3
Solve 8/7 + 2*o**4 - 2/7*o**5 - 32/7*o - 38/7*o**3 + 50/7*o**2 = 0.
1, 2
Let c(o) be the first derivative of 1/9*o**2 + 4/27*o**3 + 1/18*o**4 + 0*o + 21. Find w, given that c(w) = 0.
-1, 0
Let q be (-1540)/(-130) - ((-4)/(-26))/(-1). Let v be (18/q)/(3/10). Factor 0*l + 2/3*l**4 - 1/3*l**v + 0 - 1/3*l**3 + 0*l**2.
-l**3*(l - 1)**2/3
Let w(d) = -50*d**2 + 48*d + 83. Let u(x) = 123*x**2 - 120*x - 207. Let n(f) = 5*u(f) + 12*w(f). Factor n(j).
3*(j + 1)*(5*j - 13)
Let n be (6095/212)/((-51)/12) + 7. Find x such that -n*x + 2/17*x**3 + 0 + 2/17*x**2 = 0.
-2, 0, 1
Find d, given that -16/3*d + 2/3*d**2 + 8 = 0.
2, 6
Let h(i) be the third derivative of i**7/56 - 5*i**6/96 + i**5/24 + 60*i**2. Let h(x) = 0. What is x?
0, 2/3, 1
Let x = -18299/30 + 610. Let w(k) be the second derivative of 0 + 10*k - 1/4*k**4 + 0*k**2 - x*k**6 + 0*k**3 + 1/5*k**5. Factor w(z).
-z**2*(z - 3)*(z - 1)
Factor 125*m**3 + 7*m**5 - 190*m**2 + 170*m - 2*m**5 - 40*m**4 - 30*m - 40.
5*(m - 2)**3*(m - 1)**2
Let a(g) be the first derivative of 2*g**6/21 - 8*g**5/35 + 8*g**3/21 - 2*g**2/7 + 44. Factor a(r).
4*r*(r - 1)**3*(r + 1)/7
Let w be (4 - 3) + 1*(-3 + 2). Suppose -14*u + 12*u + 8 = w. Factor 6/5*b**2 + 3/5*b**u - 9/5 + 12/5*b**3 - 12/5*b.
3*(b - 1)*(b + 1)**2*(b + 3)/5
Let l(g) = 139*g**3 - 235*g**2 - 92*g - 18. Let a(y) = 70*y**3 - 118*y**2 - 46*y - 8. Let p(m) = -5*a(m) + 2*l(m). Factor p(s).
-2*(s - 2)*(6*s + 1)**2
Let l = -19 + 22. Solve 4*g - 4*g**l + 8*g**4 - 10*g**4 + 3 - 1 = 0.
-1, 1
Suppose -4*r - 45 = -13. Let z be -1*3*r/12. Find k such that 1/3*k + 1 - 2/3*k**z = 0.
-1, 3/2
Let i(q) = -q**3 - q**2 + 1. Let a(d) = 4*d**5 + 16*d**4 + 12*d**3 - 12*d**2 - 20*d - 4. Let y = -60 - -56. Let n(k) = y*i(k) + a(k). Let n(w) = 0. What is w?
-2, -1, 1
Let k(a) be the second derivative of 5*a**7/189 + 79*a**6/135 + 3*a**5/5 - 47*a**4/27 - 59*a**3/27 + 5*a**2/3 + 71*a - 4. Suppose k(b) = 0. Calculate b.
-15, -1, 1/5, 1
What is d in 5/3*d**2 - 80*d + 960 = 0?
24
Let m = 111 + -87. Suppose -5*v + 3*a + 25 = 0, 4 = 4*v - 4*a - m. Let 1/3*t**v - 1/3 - 1/3*t + 1/3*t**3 = 0. What is t?
-1, 1
Let v(c) be the first derivative of -c**6/27 - 28*c**5/45 - 11*c**4/6 + 224*c**3/27 - 64*c**2/9 + 81. Solve v(n) = 0.
-8, 0, 1
Factor -20/3*r - 2/9*r**2 + 0.
-2*r*(r + 30)/9
Let v be (2 - 32/12)*-9. Let y(z) be the third derivative of 0 - 1/12*z**3 + 1/96*z**4 + 0*z + 1/30*z**5 + 1/96*z**v + 7*z**2. Factor y(b).
(b + 1)**2*(5*b - 2)/4
Let z(t) = -17*t + 134. Let u be z(8). Let d be (-1 - 1)/(u/9*7). Suppose 3/7*m**4 + 3/7*m + d*m**3 + 0 + 9/7*m**2 = 0. What is m?
-1, 0
Let y = -19950 - -19952. Factor -1/3*g**y + 5/3*g - 5/3*g**3 - 2/3 + g**4.
(g - 1)**2*(g + 1)*(3*g - 2)/3
Let q(g) = -g**3 - 6*g**2 + 15*g - 6. Let n be q(-8). Suppose -5*w = n*w. Find r, given that 1/4*r**3 + w*r**2 - 1/4*r**4 + 0 + 0*r = 0.
0, 1
Let b(u) = u**4 - u**2 - u - 1. Let y(q) = -q**5 + 8*q**4 + 2*q**3 - 10*q**2 - 7*q - 4. Let s = 47 + -53. Let p(o) = s*b(o) + y(o). Factor p(x).
-(x - 2)*(x - 1)**2*(x + 1)**2
Let m(j) be the second derivative of j**6/180 + j**5/90 - j**4/18 + 3*j**2 - 4*j. Let f(t) be the first derivative of m(t). Factor f(i).
2*i*(i - 1)*(i + 2)/3
Let p(q) be the first derivative of -49/4*q**4 - 46/3*q**3 - 2*q - 17/2*q**2 - 18/5*q**5 - 8. Determine h so that p(h) = 0.
-1, -1/2, -2/9
Let l(c) be the first derivative of -c**4/46 + 20*c**3/69 + 11*c**2/23 + 184. What is h in l(h) = 0?
-1, 0, 11
Suppose 9 = 2*y + 3. Suppose 4*g + 2 = -3*o - 2*o, -6 = y*o. Suppose 3*q + g*q + 4*q**3 + q**4 + 5*q**2 + 0*q**3 - 3*q = 0. What is q?
-2, -1, 0
Let s(t) = -29*t + 92. Let y be s(3). Let g(q) be the second derivative of 8*q**3 - 16*q**2 + 0 - 3/2*q**4 + 1/10*q**y - 5*q. Determine c, given that g(c) = 0.
1, 4
Determine z, given that -2*z**4 - 4*z**2 + 0*z**4 + 6*z**3 + 0*z**2 + 2*z - 2*z**2 = 0.
0, 1
What is n in 10976*n**2 + 42*n**4 + 1176*n**3 + 1/2*n**5 + 0*n + 0 = 0?
-28, 0
Let v(o) be the first derivative of o**4/34 + 2*o**3/51 - o**2/17 - 2*o/17 + 99. Factor v(z).
2*(z - 1)*(z + 1)**2/17
Let o(k) = k**2 - 6*k + 12. Let p be o(5). Suppose p*l - 35 = -0*l. Factor -8*u**2 - 4*u - 4*u**l + 10*u**4 + 4*u**5 + 4*u**5 - 2*u**4.
4*u*(u - 1)*(u + 1)**3
Let b(l) be the second derivative of l**6/360 + l**5/120 + 3*l**3/2 - 2*l. Let d(w) be the second derivative of b(w). Suppose d(i) = 0. Calculate i.
-1, 0
Let s(i) be the first derivative of -i**8/1680 + i**6/180 - i**4/24 + 13*i**3/3 - 28. Let x(g) be the third derivative of s(g). Find m, given that x(m) = 0.
-1, 1
Suppose 65 = t + 4*t. Suppose t = g + h, 5*g - h - 38 = 3*h. Let 53*l**2 - 4 + 2 - 84*l - 200*l**2 - g = 0. Calculate l.
-2/7
Let u(f) = 5*f - 16. Let d be u(4). What is n in 11*n**2 - 32*n**2 + 15*n**3 - 5*n**d + 11*n**2 = 0?
0, 1, 2
Let x(z) be the third derivative of 0*z + 1/72*z**6 - 1/1008*z**8 - 2/315*z**7 + 0*z**5 + 13*z**2 + 0 + 0*z**4 + 0*z**3. Solve x(b) = 0.
-5, 0, 1
Suppose -s - 30 = 5*o, 0 = -2*o + 12 - 24. Let p be 2/(2 - 0)*0. Factor s*z + p*z**4 + 0*z**2 + 2/13*z**5 - 2/13*z**3 + 0.
2*z**3*(z - 1)*(z + 1)/13
Let -a**2 + 6*a**3 + a**2 - 3*a**4 - 3*a**2 = 0. What is a?
0, 1
Let n(z) = -6*z - 46. Let f be n(-11). Factor -38*a - 8*a**2 - 39*a + f*a**3 + 65*a.
4*a*(a - 1)*(5*a + 3)
Let y = -37/10 - -673/90. Let t(r) be the first derivative of -y*r**3 + 7 + 0*r - 5/6*r**4 - 2*r**2. What is l in t(l) = 0?
-3, -2/5, 0
Let x = 40/269 + 189/538. Factor x*u**3 + u + 0 - 3/2*u**2.
u*(u - 2)*(u - 1)/2
Find g, given that -4 + 5*g**4 - 8*g**3 + 17/2*g - g**2 - 1/2*g**5 = 0.
-1, 1, 8
Find f such that 9*f**2 - 162*f - 1/6*f**3 + 972 = 0.
18
Let d(u) be the first derivative of u**6/6 - 3*u**5/5 - u**4/2 + 4*u**3 - 4*u**2 - 93. Factor d(z).
z*(z - 2)**2*(z - 1)*(z + 2)
Factor -9*p**3 - 11*p**5 - 12*p - 2*p**4 - 4*p**4 + 24*p**2 + 14*p**5.
3*p*(p - 2)*(p - 1)**2*(p + 2)
Let i = 53278/5 + -10650. Solve -12/5 + 8/5*b**3 + 3/5*b**4 - 11/5*b**2 - i*b = 0.
-3, -1, -2/3, 2
Suppose -4*j = -0*j - 3*t - 177, 207 = 4*j + 3*t. Factor -4*l**2 + 15*l**2 + l**3 + 36 + j*l + 2*l**2.
(l + 1)*(l + 6)**2
Let h be 7 + 8/(-4) + 551/(-116). Suppose h*d**2 + 0 - 1/4*d = 0. What is d?
0, 1
Let s = 149 - 127. Let p(h) = 5*h - 110. Let g be p(s). Factor -1/2*j**2 - 3/4*j**3 - 1/4*j**4 + 0 + g*j.
-j**2*(j + 1)*(j + 2)/4
Let o(m) = -m**3 + 16*m**2 - 12*m - 18. Let q be o(14). Let j = 3 - 1. Factor q*c**2 + 2*c**4 + 4*c**3 - 2 - 4*c - 206*c**j.
2*(c - 1)*(c + 1)**3
Suppose -4*d + 1 = 3*h - 0*h, -5*d + 5 = 5*h. Suppose -3*m**3 + 3*m**3 - 4 + 4*m**2 - 4*m**h + 5*m - m = 0. Calculate m.
-1, 1
Suppose -3*l + l = -38. Determine h, given that 10*h**3 + 13*h + 15 + 5*h - 24*h**2 - l = 0.
2/5, 1
Let d(n) be the first derivative of -2*n**3/33 + 158*n**2/11 - 12482*n/11 - 22. Factor d(k).
-2*(k - 79)**2/11
Let z = 7 + -5. Suppose -w = -0*w - z. Factor 1 + 2*r**w - r + r**2 - 4*r**2 + r**3.
(r - 1)**2*(r + 1)
Let n(d) = -d**2 - 6*d + 11. Let o be n(-5). Let q(z) = 3*z - 1. Let t be q(1). Factor 0 - j**2 - 22*j - o*j**2 - 4 - j**t.
-2*(j + 1)*(9*j + 2)
Let p = -66 + 73. Let k(u) be the second derivative of -1/70*u**5 + 1/42*u**3 + 0*u**2 + 0 + 0*u**4 + 0*u**6 - 3*u + 1/294*u**p. Determine n so that k(n) = 0.
-1, 0, 1
Let x(k) = 152*k**2 - 465*k + 29. Let l be x(3). Factor -9/5*g - 3/5 - 9/5*g**l - 3/5*g**3.
-3*(g + 1)**3/5
Let m(l) be the first derivative of l**6/39 - 4*l**5/65 + l**4/26 - 64. Suppose m(t) = 0. Calculate t.
0, 1
Let y(v) be the third derivative of -v**6/20 + 28*v**5/15 + 79*v**4/12 + 20*v**3/3 - 786*v**2. Find j such that y(j) = 0.
-1, -1/3, 20
Let o(c) be the first derivative of -c**8/420 - c**7/105 - c**6/90 - 10*c**3 - 12. Let v(t) be the third derivative of o(t). Factor v(z).
-4*z**2*(z + 1)**2
Let z(p) be the second derivative of -7/15*p**3 + 0 + 2/25*p**5 + 19*p + 2/5*p**2 + 2/15*p**4. What is u in z(u) = 0?
-2, 1/2
Let g(l) be the third derivative of l**5/300 + 7*l**4/120 - 127*l**2. Factor g(h).
h*(h + 7)/5
Suppose 4*v + 0*j - 10 = j, 0 = -5*v - 5*j. Factor 6*c + 16 - 288*c**v + 14*c + 292*c**2.
4*(c + 1)*(c + 4)
Let n(v) be the third derivative of 1/3*v**4 - 1/20*v**5 - 1/60*v**6 - 2/3*v**3 - 18*v**2 + 1/210*v**7 + 0*v + 0. Factor n(k).
(k - 2)*(k - 1)**2*(k + 2)
Factor 73*z**2 - 85*z**2 + 7*z**2 - 585*z**3.
-5*z**2*(117*z + 1)
Let n(f) b