f 2*q**3/45 - 41*q**2/15 - 172*q/15 + 162. Factor r(w).
2*(w - 43)*(w + 2)/15
Let a(k) be the second derivative of -26*k - 8/11*k**2 + 1/110*k**5 + 4/11*k**3 + 0 - 1/11*k**4. Factor a(w).
2*(w - 2)**3/11
Let v = 842 - 830. Let s(j) be the third derivative of 1/3*j**5 + 0 - 5/42*j**7 + 0*j + 5/336*j**8 + 1/4*j**6 - 5/3*j**4 + 0*j**3 + v*j**2. Factor s(a).
5*a*(a - 2)**3*(a + 1)
Find r, given that -3*r + 33*r**3 - 64*r**3 - 9*r**2 + 22*r**3 - 3*r**4 = 0.
-1, 0
Let i be (-28)/16*444/(-168). Let u(y) be the first derivative of -1/4*y**6 - 13/2*y**3 - 2*y - 17/10*y**5 - 5*y**2 - i*y**4 + 5. Solve u(o) = 0 for o.
-2, -1, -2/3
Let m(z) be the third derivative of z**6/360 - z**5/36 + 7*z**4/72 - z**3/6 - 60*z**2. Factor m(i).
(i - 3)*(i - 1)**2/3
Let w(z) be the first derivative of z**7/168 + z**6/30 + 3*z**5/40 + z**4/12 + z**3/24 + 6*z + 7. Let x(m) be the first derivative of w(m). Factor x(v).
v*(v + 1)**4/4
Suppose 4 + 10 = 3*h - 5*r, 5*r + 2 = -h. Determine y so that -12*y - 3*y**5 - 28*y**4 - 9*y**5 + 8*y**5 - 20*y - 80*y**2 - 72*y**h = 0.
-2, -1, 0
Let i(t) be the third derivative of t**7/1785 + 4*t**6/255 + 23*t**5/255 - 12*t**4/17 + 27*t**3/17 - 33*t**2. Determine q so that i(q) = 0.
-9, 1
Determine g, given that 2/15*g**4 - 2/15*g**3 + 8/15*g - 8/15*g**2 + 0 = 0.
-2, 0, 1, 2
Let r(x) be the third derivative of x**8/84 + 2*x**7/21 - 3*x**6/10 - 13*x**5/15 + 14*x**4/3 - 8*x**3 - 131*x**2 + 2. Solve r(k) = 0.
-6, -2, 1
Suppose 3*m + 11 = 5*u, 0*u + 2*u - 4*m = -4. Suppose 8*z - 2 = u*z + 3*h, -h = 5*z - 12. Factor 1 - 5/2*r**z + 3/2*r.
-(r - 1)*(5*r + 2)/2
Suppose -h - h = -6. Suppose y + 1 = h. Factor -k + 0*k**2 + 3*k**y + 2*k**3 - 7*k**2 + 3*k.
2*k*(k - 1)**2
Let p(y) = y**3 + 12*y**2 + 10*y + 4. Let u be p(-11). Let n be ((-12)/u)/(2/(-115)). Factor -59*k**2 + 16*k - n*k**3 + 83*k**2 + 10*k**4 + 10*k**3.
2*k*(k - 2)**2*(5*k + 2)
Let o = 334 - 331. Suppose 2*l = -l + o*w + 3, 2*w = 5*l - 2. Factor l - 2/9*z**3 + 0*z - 2/9*z**4 + 0*z**2.
-2*z**3*(z + 1)/9
Factor 1/9*c**5 + 2/3*c**3 + 8/9*c**4 + 25/9*c + 0 - 40/9*c**2.
c*(c - 1)**2*(c + 5)**2/9
Let f(n) be the second derivative of n**8/588 - 4*n**7/735 + 2*n**5/105 - n**4/42 - 11*n**2/2 - 5*n. Let a(s) be the first derivative of f(s). Solve a(r) = 0.
-1, 0, 1
Let v(d) = -8*d**3 - 4*d**2 + 28*d + 84. Let n(g) = g**3 - g**2 + g - 7. Let m(w) = -6*n(w) - v(w). Solve m(o) = 0.
-7, -1, 3
Let v = 412/165 - -28/165. Solve -2/3*l**5 + 16/3*l - 10/3*l**4 + v*l**2 + 0 - 4*l**3 = 0 for l.
-2, 0, 1
Let s(q) be the second derivative of q**5/180 - q**4/18 + q**3/6 + 23*q**2/2 + 26*q. Let w(p) be the first derivative of s(p). Let w(l) = 0. Calculate l.
1, 3
Let a(x) = -x**3 + x**2 - 1. Let k(g) = -8*g**3 - 67*g - 32. Let u(b) = 44*a(b) - 4*k(b). Let u(w) = 0. Calculate w.
-3, -1/3, 7
Suppose 0 = -5*t + 5*r + 20, 0 = -5*t + 2*t - r + 24. Let -11*p**2 + 0*p - 4 + t*p**2 - 8*p = 0. Calculate p.
-1
Let b be (2 - 4)*(489/(-48) + 10). Let -9/8*t + 3/8 + 9/8*t**2 - b*t**3 = 0. Calculate t.
1
Let x(f) = -f**2 + 17*f - 12. Let i be x(18). Let r be (-30)/4*(-6)/i - -3. Find l, given that l**2 + 0 - r*l + 1/2*l**3 = 0.
-3, 0, 1
Let c(z) be the first derivative of -5/8*z**2 + 5/4*z**3 + 1/4*z**5 - 15/16*z**4 + 0*z + 7. Factor c(t).
5*t*(t - 1)**3/4
Let d(w) be the second derivative of 0*w**2 + 1/84*w**4 - 1/6*w**3 + 0 - 7*w. Factor d(k).
k*(k - 7)/7
Suppose -32 = -10*r + 8. Factor -5*d**3 + 2*d - 7 - 9*d**3 + r*d**4 + 7 + 12*d**2 - 4.
2*(d - 2)*(d - 1)**2*(2*d + 1)
Factor 2577 - 39*i**4 + 444*i**2 - 1809 + 42*i**4 - 1152*i - 63*i**3.
3*(i - 8)**2*(i - 4)*(i - 1)
Let s(l) = l**4 + 7*l**3 + 2*l**2 - 4. Let c = 64 + -68. Let a(q) = 2*q**4 + 8*q**3 + q**2 - 5. Let w(f) = c*a(f) + 5*s(f). Factor w(k).
-3*k**2*(k - 2)*(k + 1)
Suppose -7794*f**2 + 160*f - 5*f**5 - 22*f**3 - 8*f**3 - 35*f**4 + 7954*f**2 = 0. Calculate f.
-4, -1, 0, 2
Let i(c) be the second derivative of c**7/21 + c**6/3 - 3*c**5/5 - 16*c**4/3 + 32*c**3/3 - 445*c. Factor i(r).
2*r*(r - 2)*(r - 1)*(r + 4)**2
Let c(h) be the first derivative of -5*h**3/3 + 410*h**2 - 33620*h - 477. Factor c(n).
-5*(n - 82)**2
Suppose 2*v - 88 = -5*u, -v = 4*u - 15 - 41. Solve 3072 + 3/4*j**4 + 288*j**2 - 1536*j - v*j**3 = 0.
8
Let a(x) be the second derivative of x**7/105 - x**6/15 + 2*x**5/25 + 8*x**4/15 - 32*x**3/15 + 16*x**2/5 - 149*x + 2. Factor a(t).
2*(t - 2)**3*(t - 1)*(t + 2)/5
Let y(x) = 148*x - 888. Let p be y(6). Factor 0*t**2 - 1/4*t**3 + 0*t + p - 1/4*t**4.
-t**3*(t + 1)/4
Suppose 6*d + 2 = 20. Suppose -8 = -2*s - 3*f + 2*f, 4*f - 20 = -4*s. Let d*a**2 - s*a**3 + 47 - 47 = 0. What is a?
0, 1
Let p(r) be the first derivative of -2*r**3/3 + r**2 + 12*r + 81. Factor p(v).
-2*(v - 3)*(v + 2)
Let b = 852 - 848. Let l(x) be the second derivative of -b*x + 0*x**4 + 1/20*x**6 + 0 + 1/20*x**5 + 0*x**3 + 0*x**2 - 5/84*x**7. Find c such that l(c) = 0.
-2/5, 0, 1
Suppose -5*m = 2*r + 6, 0 = 2*r - 23*m + 20*m - 10. Find h such that -2/7*h**3 + 2/7*h + 0*h**r + 0 = 0.
-1, 0, 1
Let i(z) = -3*z - 12. Let c be i(-5). Factor 19*v**c - 17*v**3 - v**4 + 1 + v - 3*v.
-(v - 1)**3*(v + 1)
Suppose -11 = t - 1. Let h(y) = -y - 8. Let x be h(t). Factor -8*w**3 + 6*w**x + 8*w**4 - 5*w**4 - w**3.
3*w**2*(w - 2)*(w - 1)
Let w(h) = -h**2 + 10*h - 13. Let n be w(8). Suppose 29 = 3*p - 3*r - r, -p + 18 = -n*r. Let 0*b**2 + 0 - 2/7*b + 2/7*b**p = 0. What is b?
-1, 0, 1
Let g(v) = 30*v**5 - 54*v**4 + 24*v**3 - 2. Let k(d) = -59*d**5 + 107*d**4 - 48*d**3 + d**2 - d + 5. Let u(h) = 5*g(h) + 2*k(h). Solve u(r) = 0 for r.
-1/4, 0, 1/2, 1
Let p = -124 + 124. Let b(v) be the second derivative of 1/42*v**4 - 1/70*v**5 + 1/21*v**3 + 0*v**2 - 1/105*v**6 + p + 2*v. Determine s, given that b(s) = 0.
-1, 0, 1
Let u(q) be the first derivative of q**4/2 - 16*q**3/3 - 44*q**2 - 96*q + 116. Factor u(j).
2*(j - 12)*(j + 2)**2
Let d(p) = -p**2 + 18*p + 24. Let w(m) = -3*m**2 + 36*m + 48. Let z(h) = -9*d(h) + 4*w(h). Suppose z(n) = 0. Calculate n.
-4, -2
Suppose -4*y + y = -i + 11, i + 7 = -3*y. Let w be (-906)/(-126) + (-5)/(-35). Factor -5/3*u**3 - 8/3 - w*u**i - 28/3*u.
-(u + 2)**2*(5*u + 2)/3
Let l(x) be the third derivative of -1/4*x**4 - 1/10*x**5 - 1/3*x**3 + 11*x**2 + 0*x + 0 - 1/60*x**6. Solve l(z) = 0 for z.
-1
Let o be -207 + 207 + 6/14 + 4/(-14). Determine k so that 0 - 1/7*k**3 + 2/7*k + o*k**2 = 0.
-1, 0, 2
Suppose -47*y = -30*y - 51. Let a(f) be the second derivative of -1/36*f**4 + 0*f**y + 0 + 0*f**2 - 3*f - 1/90*f**6 - 1/30*f**5. Suppose a(g) = 0. Calculate g.
-1, 0
Let f(o) be the first derivative of 4*o**5/35 - 3*o**4/7 + 8*o**3/21 + 672. Solve f(p) = 0.
0, 1, 2
Let l(c) be the third derivative of c**5/120 + 33*c**4/16 - 25*c**3/3 - c**2 + 136*c. Find r, given that l(r) = 0.
-100, 1
Let g(y) be the third derivative of 5*y**8/336 + 2*y**7/21 + 5*y**6/24 + y**5/6 + 12*y**2. Factor g(n).
5*n**2*(n + 1)**2*(n + 2)
Let v be 7/(-27 + (-5319)/(-162)). Find t, given that -2/5*t + 0 - 2/5*t**4 - 6/5*t**3 - v*t**2 = 0.
-1, 0
Let s(b) be the first derivative of -b**8/420 + b**7/70 - b**6/30 + b**5/30 - 17*b**3/3 - 21. Let x(j) be the third derivative of s(j). Factor x(m).
-4*m*(m - 1)**3
Let c(s) = -11*s**3 + 116*s**2 - 269*s + 124. Let z(l) = -9*l**3 + 119*l**2 - 267*l + 125. Let v(t) = -4*c(t) + 5*z(t). Find j, given that v(j) = 0.
1, 129
Factor -2/15*k**2 + 4/3 - 6/5*k.
-2*(k - 1)*(k + 10)/15
Suppose -5*o + 4 = -6. Suppose o = -2*y + 6. Factor y - 3*t**2 + 2*t**2 + 2*t**2 - 3*t.
(t - 2)*(t - 1)
Let p be -1 - ((-1105)/260 + 5/4). Suppose 2/19*y**5 + 4/19*y**p + 0 + 0*y**3 - 2/19*y - 4/19*y**4 = 0. What is y?
-1, 0, 1
Suppose -2*k = -2*f, -93*f - 4*k = -95*f - 4. Find y such that 0*y + 1/5*y**f + 0 = 0.
0
Let o(c) be the second derivative of -6*c - 1/30*c**4 + 2/15*c**3 - 1/5*c**2 + 0. Let o(z) = 0. Calculate z.
1
Suppose -7*q + 5*q = -22. Suppose -24*d + 48 + q*d**2 - 9*d**2 + d**2 = 0. What is d?
4
Find p, given that 20/3 + 22/3*p + 2/3*p**2 = 0.
-10, -1
Let v be ((-40)/36)/(-5) + (-238)/(-63). Let p(u) be the second derivative of 0*u**2 + 0*u**3 - v*u + 0*u**5 + 0*u**4 + 0 - 1/30*u**6 + 1/42*u**7. Factor p(i).
i**4*(i - 1)
Find i, given that 4*i**2 + 0*i + 24 + 22*i - 2*i = 0.
-3, -2
Suppose 0 = -4*m - 3 + 15. Suppose -3*l = -5*f + 4, 0 = 2*f + m*l + l - 12. Factor -24*w**2 + 4*w + 15*w**2 + 1 + 1 + 11