. Factor w(a).
-(a - 1)*(a + 2)/2
Factor -4*v**2 + 18*v + 24*v - 44 - 79*v + 13*v + 12.
-4*(v + 2)*(v + 4)
Let z(w) = 7*w**2 + 6*w - 7. Let l(o) be the first derivative of 5*o**3 + 13*o**2/2 - 15*o - 17. Let h(q) = 6*l(q) - 13*z(q). Factor h(i).
-(i - 1)*(i + 1)
Let t(o) be the third derivative of o**6/600 - 11*o**5/300 - 7*o**4/15 - 2*o**3 + 26*o**2. Factor t(m).
(m - 15)*(m + 2)**2/5
Let d(v) be the third derivative of -v**7/42 + 7*v**6/8 - 49*v**5/4 + 1715*v**4/24 - 25*v**2. Determine w, given that d(w) = 0.
0, 7
Let b(s) = -13*s**3 + 11*s**2 + 8*s - 11. Let k(n) be the first derivative of 3*n**4/2 - 2*n**3 - 2*n**2 + 6*n + 13. Let x(f) = -2*b(f) - 5*k(f). Factor x(z).
-4*(z - 2)*(z - 1)*(z + 1)
Let s = -10 + 15. Suppose 4*f - 3*a - 24 = s, -4*f + 23 = -a. Factor -2*q**3 - q + f*q**3 - 2*q.
3*q*(q - 1)*(q + 1)
Factor -24*l + 17027 - 10*l**3 - 41*l**2 + 13*l**2 - l**4 - 17027.
-l*(l + 2)**2*(l + 6)
Let b(l) be the third derivative of -l**5/140 + 5*l**4/56 - 2*l**3/7 + 3*l**2 + 10*l. Factor b(x).
-3*(x - 4)*(x - 1)/7
Let l(c) = 1. Let g(n) = -n**2 - 9*n + 31. Let f(x) = -3*g(x) - 15*l(x). Let f(b) = 0. Calculate b.
-12, 3
Let k be 1/(-5*(-6)/90). Determine i, given that 3/2*i**2 - 3/4*i**k + 3/4*i - 3/2 = 0.
-1, 1, 2
Let u = -117/4 - -123/4. Let w(n) be the first derivative of -6*n**3 + 3*n + 3*n**5 - 3/2*n**4 + 5 - u*n**2 + 3/2*n**6. Find p, given that w(p) = 0.
-1, 1/3, 1
Let d(w) = 108*w**2 - 396*w - 136. Let z(f) = 79*f + 6 - 22*f**2 + 26 - 5. Let p(j) = -3*d(j) - 16*z(j). Find l, given that p(l) = 0.
-2/7, 3
Suppose 3*q - 17 = -0*i - 2*i, -3*q - i + 13 = 0. Suppose -q*k - 9 = -3*t, -2*t - 2*k - 10 = -5*t. Factor 4 + 2*r**2 + 4*r + 6*r + t*r**2 + 0*r.
2*(r + 1)*(3*r + 2)
Factor 8*y**3 + 10 - 70 + 6*y**3 - 19737*y**2 + 19957*y**2 + 146*y.
2*(y + 1)*(y + 15)*(7*y - 2)
Solve 9*s**2 + 12*s + 21*s**2 - 35*s**2 = 0 for s.
0, 12/5
Let r(k) be the first derivative of k**4/20 - 2*k**3/5 + 9*k**2/10 - 8*k + 15. Let t(u) be the first derivative of r(u). Factor t(q).
3*(q - 3)*(q - 1)/5
Let j(r) be the first derivative of -6 - 1/20*r**5 - 2*r**2 + 0*r**4 + 0*r + 1/2*r**3. Let l(s) be the second derivative of j(s). Factor l(o).
-3*(o - 1)*(o + 1)
Let b be (1/9)/(2/24*2). Let i be 5*(26/(-30) + 1). Suppose 2/3*z**3 - 2/3*z**2 + i - b*z = 0. What is z?
-1, 1
Let n(d) be the second derivative of d**7/1365 - d**6/390 + d**5/390 - 12*d**2 + 24*d. Let g(m) be the first derivative of n(m). What is s in g(s) = 0?
0, 1
Solve 50*g + 792 - 792 - 35*g**3 + 165*g**2 = 0.
-2/7, 0, 5
Suppose 3*s + 10 = -2*t, 227*s - 226*s - 5 = t. Factor -2/5*p**5 + s*p**3 + 0 + 6/5*p**4 + 0*p - 8/5*p**2.
-2*p**2*(p - 2)**2*(p + 1)/5
Solve -4/9 + 0*r**3 - 4/9*r**4 + 0*r + 8/9*r**2 = 0.
-1, 1
Let c be 7/105 - (1 - (-267)/(-45)). Solve -4/5*r - 2/5*r**4 - 6/5*r**3 + 0 + 2/5*r**c + 2*r**2 = 0.
-2, 0, 1
Let t(y) be the third derivative of y**5/180 - 13*y**4/36 + 25*y**3/18 - 291*y**2. Suppose t(l) = 0. What is l?
1, 25
Suppose -27*o + 9 = -24*o. Let h(j) be the first derivative of 1 + 1/24*j**6 + 0*j**2 + 0*j**o + 1/16*j**4 - 1/10*j**5 + 0*j. Suppose h(t) = 0. Calculate t.
0, 1
Let d(m) be the first derivative of 3*m**4/28 + 4*m**3/7 + 11. Factor d(o).
3*o**2*(o + 4)/7
Let f(a) be the first derivative of -5*a**3/3 - 60*a**2 - 220*a - 174. Factor f(j).
-5*(j + 2)*(j + 22)
Let f(v) be the first derivative of 0*v**2 + 1/18*v**4 + 1/30*v**5 + 0*v**3 + 6 + 7*v. Let l(i) be the first derivative of f(i). Solve l(w) = 0 for w.
-1, 0
Let w be (1 + -5 - -10)*(-4)/(-12). Let d(h) be the first derivative of -1/5*h**5 + 3/4*h**4 - 2/3*h**3 + 0*h**w - 5 + 0*h. Factor d(t).
-t**2*(t - 2)*(t - 1)
Let z(w) = w**3 + 13*w**2 - 31*w - 12. Let o be z(-15). Factor 0 + 3/2*k**2 - 2/3*k - k**o + 1/6*k**4.
k*(k - 4)*(k - 1)**2/6
Let u(l) be the second derivative of -1/2*l**2 + 6*l + 1/48*l**4 + 0 + 1/8*l**3. Factor u(p).
(p - 1)*(p + 4)/4
Let k(x) be the first derivative of 4*x**6/33 - 24*x**5/55 + x**4/2 - 2*x**3/11 - 392. Solve k(l) = 0 for l.
0, 1/2, 1, 3/2
Let f(v) be the second derivative of -v**4/7 + 23*v**3/14 + 9*v**2/7 - 7*v + 8. Let f(w) = 0. What is w?
-1/4, 6
Suppose 5*x = h - 50, -4*x + 167 = 3*h - 2*x. Let n = h - 53. Factor -9/5*s - 3/5*s**n + 0.
-3*s*(s + 3)/5
Let z(q) be the third derivative of -2*q**7/105 - 3*q**6/20 - 2*q**5/5 - 5*q**4/12 - q**2 - 85*q. Solve z(l) = 0.
-5/2, -1, 0
Let x(s) be the first derivative of 2*s**3/9 - 22*s**2 + 145. Factor x(m).
2*m*(m - 66)/3
Suppose -2*s + 2*q + 24 = 0, -3*q = -5*s - 7*q + 69. Find t such that -10*t**3 + 3 + 5*t + 5*t**4 - s*t**5 + 18*t**5 - 10*t**2 + 2 = 0.
-1, 1
Let v be (-1)/6 + (-55)/(-66). Factor -2/3*u**2 + 8 + v*u**3 - 16/3*u.
2*(u - 2)**2*(u + 3)/3
Let i(q) = 5*q**3 + 70*q**2 - 61*q - 140. Let r(n) = 9*n**3 + 69*n**2 - 60*n - 141. Let x(k) = 3*i(k) - 2*r(k). Suppose x(z) = 0. What is z?
-1, 2, 23
Suppose 2*j - 3*j = -5. Suppose 16*q**4 - 15*q**2 - q**5 - q**2 + 6*q**j - 4*q - 3*q**3 + 2*q**5 = 0. What is q?
-2, -1, -2/7, 0, 1
Let p(v) = -11 + 0 - v - 9 + 3. Let g be p(-17). Factor 0 + g*m**2 - 1/2*m**4 + 2*m - 3/2*m**3.
-m*(m - 1)*(m + 2)**2/2
Let i be (1/(-3))/(-8 - 470/(-60)). Determine p, given that -2/3 + 2/3*p**3 - 2*p**2 + i*p = 0.
1
Let v(x) be the third derivative of x**11/1496880 + x**10/170100 + x**9/68040 - 4*x**5/15 - 15*x**2. Let f(t) be the third derivative of v(t). Factor f(j).
2*j**3*(j + 2)**2/9
Let k(s) be the second derivative of 0*s**2 - 11*s + 0*s**4 - 1/285*s**6 + 0 + 1/190*s**5 + 0*s**3. Determine b, given that k(b) = 0.
0, 1
Let j(g) = 2*g**4 + 16*g**3 + 14*g**2 - 204*g - 220. Let l(p) = 7*p**4 + 48*p**3 + 41*p**2 - 609*p - 661. Let c(u) = 13*j(u) - 4*l(u). Factor c(f).
-2*(f - 6)**2*(f + 1)*(f + 3)
Let c(x) be the third derivative of 7/32*x**4 + 0 - 18*x**2 + 1/4*x**3 + 3/160*x**6 + 1/10*x**5 + 0*x. Determine a so that c(a) = 0.
-1, -2/3
Let g(b) be the second derivative of -b**7/189 - b**6/15 + 11*b**5/45 - b**4/27 - 7*b**3/9 + 11*b**2/9 - 96*b. Suppose g(c) = 0. Calculate c.
-11, -1, 1
Let t(g) be the first derivative of -g**5/5 + 9*g**4/4 - 10*g**3 + 22*g**2 - 24*g + 63. What is p in t(p) = 0?
2, 3
Let t(m) = -2*m - 15. Suppose -d + 50 = -5*p, -3*d = -3*p - 18 - 24. Let u be t(p). Factor 14/9*f**u + 0 - 4/9*f - 10/9*f**2.
2*f*(f - 1)*(7*f + 2)/9
Let t(r) = -2*r + 25. Let i be t(12). Let u = i - -12. Factor -u*w + 2*w + w**2 + 8*w.
w*(w - 3)
Let -118 + 2*p**4 + 228 - 2*p - 106 + 2*p**3 - 6*p**2 = 0. Calculate p.
-2, -1, 1
Let q(w) = -18*w**2 - 63*w - 13. Suppose -4*r = -r + 33. Let h(i) = 89*i**2 + 314*i + 64. Let a(c) = r*q(c) - 2*h(c). Factor a(u).
5*(u + 3)*(4*u + 1)
Let z(f) be the second derivative of 3*f**5/20 + 3*f**4 + 41*f**3/2 + 45*f**2 - 175*f. Solve z(h) = 0 for h.
-6, -5, -1
Let a(c) = c**3 - c**2 - 2*c - 2. Let h(q) = q**3 - 21*q**2 - 46*q - 30. Let l(m) = -6*a(m) + 2*h(m). Factor l(d).
-4*(d + 1)*(d + 2)*(d + 6)
Let r = 5 + -2. Let j = -250 - -752/3. Factor -j*a**r + 1/3*a**2 + 2/3*a - 1/3.
-(a - 1)*(a + 1)*(2*a - 1)/3
Let s be 2/1*5/2. Suppose -3*u = 3*v - 99, -s*u + 161 = -3*v - 4. Solve u*m**3 - 6 - 9 + 3 - 6*m**4 + 48*m - 63*m**2 = 0 for m.
1/2, 1, 2
Suppose 0 = y - m + 1 - 0, -2*y + 3 = 3*m. Suppose 2*j = 6 - y. Solve -3*f - f**5 + 3*f**4 - 45*f**j - 11*f**5 - 42*f**4 + 6*f**2 - 27*f**2 = 0.
-1, -1/4, 0
Let f(u) = 12*u. Let t be f(0). Let d(y) be the third derivative of -1/150*y**5 - 1/60*y**4 + 0*y**3 + t + 0*y + 12*y**2. Find a, given that d(a) = 0.
-1, 0
Let f(t) be the first derivative of t**6/96 - 17*t**5/240 + t**4/6 - t**3/6 + 10*t**2 - 12. Let w(a) be the second derivative of f(a). Factor w(b).
(b - 2)*(b - 1)*(5*b - 2)/4
Suppose -w = -h + 2, -13*w = -4*h - 16*w + 15. Let g(f) be the first derivative of 1/34*f**4 + 3 - 4/17*f**2 + 16/17*f - 4/51*f**h. Factor g(i).
2*(i - 2)**2*(i + 2)/17
Suppose -2*u = q + 12, -q = -2*u - 1 - 15. Factor 2*t - 1/2*t**2 - q.
-(t - 2)**2/2
Suppose 3 - 31 = 14*t. Let f be (t/3)/(-22 - -21). Factor -f*w**4 - 2/3*w - 2*w**2 + 0 - 2*w**3.
-2*w*(w + 1)**3/3
Suppose 4*h - 25 = -3*c - 3, 3*h - 21 = -3*c. Let k = c - 1. Let 2/7*w**3 - 3/7*w**4 + 2/7*w**2 + 1/7 + 1/7*w**k - 3/7*w = 0. Calculate w.
-1, 1
Let r = 28741 + -28741. Solve 0 + 1/3*p**3 + r*p + p**2 = 0.
-3, 0
Let b be (18/(-15))/((-12)/15 + 1). Let s be 0/(-3 + b/(-1)). Find q, given that 2/5*q**3 + 