32. Let t(o) = 8*b(o) + 5*c(o). Factor t(x).
2*(x - 1)*(x + 4)
Let y(x) be the first derivative of -x**4/8 - x**3/6 + x**2/4 + x/2 - 126. Factor y(q).
-(q - 1)*(q + 1)**2/2
Let t = 16 + -4. Suppose -t = -5*q + 3. Factor -6*l**2 - 6*l + 4*l**3 - l**3 + q*l**2.
3*l*(l - 2)*(l + 1)
Let r(j) be the first derivative of j**8/560 + j**7/280 - 13*j**3/3 + 1. Let y(s) be the third derivative of r(s). Factor y(o).
3*o**3*(o + 1)
Let j be -8 - 37/(370/(-120)). Let f(u) be the second derivative of 0*u**2 + 0*u**3 + 0 - 1/84*u**j - 14*u. Suppose f(s) = 0. What is s?
0
Let f = -281 - -283. Let d(s) be the first derivative of 0*s + 2 + 1/2*s**4 - 2/3*s**3 - 2*s**f. Factor d(l).
2*l*(l - 2)*(l + 1)
Let t be 25/(-30) - (-28)/24. Suppose 2/3*f**2 + 0*f + 0*f**3 - t - 1/3*f**4 = 0. What is f?
-1, 1
Suppose -3*b + 43 = -0*b + 5*h, b - 26 = -4*h. Let r be 2 + b/(-4) + 3/(-12). Let -1/2 - r*q + 1/4*q**3 + 1/2*q**2 = 0. Calculate q.
-2, -1, 1
Factor -97*s**3 + 625 + 450*s**2 - 5*s**3 + 22*s**3 + 5*s**4 - 1000*s.
5*(s - 5)**3*(s - 1)
Let i(s) be the first derivative of 6/25*s**5 + 0*s**2 + 8 + 3/5*s**3 + 3/4*s**4 + 0*s. Determine r so that i(r) = 0.
-3/2, -1, 0
Factor -69/2 - 3/4*y**2 + 75/4*y.
-3*(y - 23)*(y - 2)/4
Let c(h) be the first derivative of h**5/30 - h**4/6 + h**3/6 + h**2/3 - 2*h/3 - 343. Find n, given that c(n) = 0.
-1, 1, 2
Let s = -23749/29232 + 75/464. Let g = -3/7 - s. Solve g*u**2 + 0 + 2/9*u = 0 for u.
-1, 0
Let x(g) be the third derivative of 0 - 9*g**2 + 0*g + 1/105*g**5 + 10/21*g**3 - 1/7*g**4. Solve x(z) = 0.
1, 5
Let f(g) be the second derivative of 0*g**2 + 1/10*g**5 - 1/63*g**7 - 2*g + 0 - 2/45*g**6 + 2/9*g**4 - 4/9*g**3. Factor f(o).
-2*o*(o - 1)**2*(o + 2)**2/3
Let w = 87 - 84. Factor 3*c**4 - c**5 - 8*c**w - 4 - 2*c**2 + 9*c + 3*c**4 + 3*c**2 - 3*c**2.
-(c - 4)*(c - 1)**3*(c + 1)
Let k(d) be the second derivative of 0*d**3 + d + 0*d**2 - 1/4*d**5 + 0*d**4 + 0. Factor k(m).
-5*m**3
Suppose -12*p + 17*p - 25 = 0. Let v be 4/p + (-5)/((-150)/21). Determine s, given that 12*s - 15/2*s**2 + v*s**3 - 6 = 0.
1, 2
Let k be (-24)/(-20)*(-4 + 34). Determine y so that -k*y**5 + 4*y**2 - 3 + 2 + 20*y**3 + 1 + 12*y**4 = 0.
-1/3, 0, 1
Let k(a) be the second derivative of -a**6/10 - 3*a**5/20 + a**4/4 + a**3/2 - 113*a. Factor k(b).
-3*b*(b - 1)*(b + 1)**2
Let t(m) be the first derivative of 0*m**3 + 5/4*m**4 + 0*m + 0*m**2 - 7. Factor t(v).
5*v**3
Let o be -3 + 2/(-2 + 264/129). Suppose 44 - o = t. Solve 0 + 0*j + 3/4*j**2 + 3/4*j**t + 3/2*j**3 = 0 for j.
-1, 0
Let n(o) = 11*o**2 + 66*o + 55. Let y(f) = 31*f**2 + 198*f + 167. Let b(w) = 17*n(w) - 6*y(w). Factor b(g).
(g - 67)*(g + 1)
Let s(r) = r**3 + 13*r**2 + 11*r - 12. Let b be s(-12). Let j = 4/33 + 10/99. Suppose 2/9*g**2 - j*g**3 + b - 2/9*g**4 + 2/9*g**5 + 0*g = 0. Calculate g.
-1, 0, 1
Solve -11/3*n**4 + 233/3*n**2 - 151*n - 30 + 3*n**3 = 0 for n.
-5, -2/11, 3
Let v(x) be the first derivative of 10/11*x**2 + 50/11*x + 9 + 2/33*x**3. Factor v(m).
2*(m + 5)**2/11
Let t(o) = -3*o**2 + 31*o + 24. Let v be t(11). Let r(j) be the first derivative of 1 + v*j**2 - 4/3*j**3 - j**4 + 4*j. Factor r(d).
-4*(d - 1)*(d + 1)**2
Factor -5*a**4 - 108*a - 3*a**3 + 9*a**3 - 3662*a**2 + 3707*a**2 + 2*a**4.
-3*a*(a - 3)**2*(a + 4)
Let d(y) = y**3 - 4*y**2 - y + 6. Let k be d(4). Suppose 4*p + 5*j - 28 = j, -k*p + j = -2. Factor -1/4*h + 0 - 12*h**3 - 16*h**4 - p*h**2.
-h*(4*h + 1)**3/4
Let j be 559/86 + 3*1 - (-117)/(-13). Factor -j*m**2 - 1/4*m + 1/4.
-(m + 1)*(2*m - 1)/4
Let c(m) be the second derivative of -m**8/5880 - m**7/2940 + m**6/1260 + m**5/420 + 7*m**3/6 + 6*m. Let k(s) be the second derivative of c(s). Solve k(a) = 0.
-1, 0, 1
Let b be ((-12)/16)/(2*1/(-288)). Let i = 111 - b. Find x, given that 0 + 21/4*x**2 + 3*x**i - 3/2*x = 0.
-2, 0, 1/4
Let x = 115 - 4139/36. Let k(n) be the second derivative of 2*n + 0 + 1/3*n**2 + 1/18*n**3 - x*n**4. Let k(u) = 0. What is u?
-1, 2
Let l(v) = -2*v**2 + 10*v + 3. Suppose 6*p - 9 = 3*p. Let r(z) = -3*z**2 + 10*z + 2. Let n(y) = p*r(y) - 2*l(y). Factor n(k).
-5*k*(k - 2)
Let c(t) be the first derivative of 2*t**3/39 - 3*t**2/13 + 4*t/13 - 53. Factor c(v).
2*(v - 2)*(v - 1)/13
Let k(y) be the third derivative of 0 - 5/24*y**4 - 1/120*y**5 - 18*y**2 - 25/12*y**3 + 0*y. Factor k(d).
-(d + 5)**2/2
Let t be 0 - 1/1*-2. Let c be (-115)/(-69)*(1 + 2). Solve 4*r**t + 0*r**3 + 4*r - c*r**3 + 0*r**4 - 4*r**4 + r**3 = 0 for r.
-1, 0, 1
Let k be ((-2)/(-12))/(5/10 - 0). Suppose -2/3 + a**2 - k*a**4 + 1/3*a**3 - 1/3*a = 0. What is a?
-1, 1, 2
Suppose 1111 = -7*f + 237*f - 1189. Determine t so that 0 + f*t**2 + 35/6*t**3 - 10/3*t = 0.
-2, 0, 2/7
Find s such that -57/4*s**3 - 3/2 + 51/4*s**4 + 57/4*s - 45/4*s**2 = 0.
-1, 2/17, 1
Suppose 0 = -5*d - 432 + 447. Let s(a) be the second derivative of 1/14*a**d - 1/84*a**4 - 1/7*a**2 + 0 - a. Let s(l) = 0. What is l?
1, 2
Let a(m) be the first derivative of -2*m**5/55 + 25*m**4/22 - 26*m**3/3 - 169*m**2/11 - 5. Determine x, given that a(x) = 0.
-1, 0, 13
Let i = -44 - -47. Factor -16000*p - 144*p**3 - 947*p**2 - 16*p**i + 0*p**4 + 40000 + 4*p**4 + 3347*p**2.
4*(p - 10)**4
Let a(h) be the first derivative of h**3/3 - 858. Let w(q) = 8*q**2 - 2*q. Suppose 3*u - 1 = 2*u. Let l(k) = u*w(k) - 6*a(k). Factor l(x).
2*x*(x - 1)
Determine w, given that 87/4*w - 45/4 - 3/4*w**3 - 39/4*w**2 = 0.
-15, 1
Let l(g) be the second derivative of -1/9*g**3 + 12*g - 1/36*g**4 + 1/2*g**2 + 0. Let l(v) = 0. Calculate v.
-3, 1
Let p(k) = 6*k**3 - 5*k**2 - 11*k + 4. Let i(g) = 18*g**3 - 13*g**2 - 34*g + 11. Let f(u) = 2*i(u) - 7*p(u). Factor f(n).
-3*(n - 2)*(n + 1)*(2*n - 1)
Factor 1/3*k**2 - 8/3*k + 4.
(k - 6)*(k - 2)/3
Suppose -15*j - 159 = -279. Let l(s) be the first derivative of -9/8*s**4 + j + 0*s + 7/10*s**5 - 1/6*s**6 - 1/4*s**2 + 5/6*s**3. Factor l(n).
-n*(n - 1)**3*(2*n - 1)/2
Let r be 837/(-12) + 9/(-36). Let m = r + 72. What is w in 0*w - 2/3 + 2/3*w**m = 0?
-1, 1
Suppose 24 = -25*c + 74. Let i(l) be the second derivative of -2*l + 1/105*l**6 + 0*l**c + 0 - 1/70*l**5 + 1/21*l**3 - 1/42*l**4. Let i(r) = 0. Calculate r.
-1, 0, 1
Suppose -18*x - 4 = -19*x. Factor -x*i - 4*i**2 + 10 + 6 - 8.
-4*(i - 1)*(i + 2)
Let u be 10/(5*17/34) - 4/(-5). Solve 2/5*n**4 + u*n - 6/5*n**3 - 16/5 - 4/5*n**2 = 0.
-2, 1, 2
Suppose 463 = -7*r + 85. Let i = -6 - r. Find t, given that -3*t**2 + 24*t**3 - 139 - i*t**4 + 139 = 0.
0, 1/4
Let z(h) be the first derivative of 0*h**2 - 3/5*h**5 + 21 - 3*h**4 + 0*h - 4*h**3. Factor z(o).
-3*o**2*(o + 2)**2
What is g in -68*g**3 - 176*g + 20*g**4 - 84*g**4 + 40 + 2 - 10 + 28*g**5 + 248*g**2 = 0?
-2, 2/7, 1, 2
Let u(x) be the first derivative of -x**4/10 + 16*x**3/3 - 22. Let u(r) = 0. Calculate r.
0, 40
Factor 61/3*g**3 + 92/3*g - 10/3*g**4 - 8/3 - 42*g**2.
-(g - 2)**3*(10*g - 1)/3
Let y be ((-4)/7)/(6/(-21)). Factor 15*w**y - 10*w - w**3 - 4 - w**3 - 23*w**2 + 0*w**3.
-2*(w + 1)**2*(w + 2)
Suppose 22*z - 13*z - 18 = 3*z. Factor -1/3*t - 1/3*t**z + 0 - 2/3*t**2.
-t*(t + 1)**2/3
Let s(c) = -c**2 + 8*c + 13. Let t(h) = -2*h**2 + 8*h + 12. Let l(y) = -3*s(y) + 2*t(y). Factor l(r).
-(r + 3)*(r + 5)
Find z, given that 17/7*z**2 + 19/7*z**3 - 3*z**4 - 24/7*z + 4/7 + 5/7*z**5 = 0.
-1, 1/5, 1, 2
Let x be 3/(-6)*(-16)/2. Determine q so that -3*q**2 - 50*q**x + 12*q**3 - 12*q + 7*q**2 + 54*q**4 - 8 = 0.
-2, -1, 1
Determine w so that 20*w**2 - 22*w - 27*w**3 + 24*w**3 + 5*w**3 = 0.
-11, 0, 1
Suppose 0 = 2*n - 3*n + 15. Let t = n - 9. Factor -24*j + 0*j**2 + t*j**2 + 48 - 3*j**2.
3*(j - 4)**2
Suppose 5*j - 40 = -4*u, 4*u - 40 = j - 0*j. Factor -3*b**3 + u + 4*b**2 + 5*b**2 + 0*b**3 - 7 - 9*b.
-3*(b - 1)**3
Let -8/7*s**5 - 26/7*s**4 + 58/7*s**3 + 16*s**2 - 104/7*s - 32/7 = 0. Calculate s.
-4, -2, -1/4, 1, 2
Let m(v) = -8*v**2 - 31*v - 21. Let s be m(-3). Let -5/4*d**4 + 1/2*d**2 + 0*d - 3/4*d**3 + s = 0. What is d?
-1, 0, 2/5
Suppose 0 = 4*z + q - 9, 0*z + z = -q. Factor -y**5 + 43*y**2 - y**5 + 2*y**4 + 11*y**3 - 45*y**2 - 9*y**z.
-2*y**2*(y - 1)**2*(y + 1)
Let m(q) be the third derivative of -q**7/504 + q**6/18 - 2*q**5/3 + 13*q**4/24 + 10*q**2. Let x(l) be the second derivative of m(l). Factor x(h).
-5*(h - 4)**2
Factor 2*i**3 + 2/5*i**2 + 0 - 2*i - 2/5*i**4.
-2*i*(i - 5)*(i - 1)*(i + 1)/5
Let f(h) be the third derivative of h**8/672 - h**