*4/9 - 200*z**3/9 - 23*z**2. Factor u(j).
-(j - 20)**2/3
Let a(w) be the first derivative of -2*w**7/735 + 2*w**5/105 - 2*w**3/21 + 2*w**2 - 2. Let d(s) be the second derivative of a(s). Determine p so that d(p) = 0.
-1, 1
Suppose -5*r - 9 = -3*l, -3*r = l - 7 + 4. Let u(s) be the third derivative of 0*s**3 + r*s - 1/30*s**5 + 1/12*s**4 + 0 + s**2. Suppose u(x) = 0. Calculate x.
0, 1
Let f be (4/60)/(4/24). Suppose 0*o + 0 + 4/5*o**4 - 2/5*o**3 + f*o**5 - 4/5*o**2 = 0. Calculate o.
-2, -1, 0, 1
Let b(h) be the second derivative of -h**5/10 - h**4/6 + h**3/3 + h**2 + h. Factor b(w).
-2*(w - 1)*(w + 1)**2
Factor 3*x**5 + 144*x**2 - 71*x**2 - 73*x**2.
3*x**5
Let f(t) be the second derivative of -1/48*t**4 + 2*t + 0 + 0*t**2 - 1/24*t**3. Factor f(x).
-x*(x + 1)/4
Suppose -2*y + 3 = -1. Let o be (1 - y)/(2/(-6)). Factor 6*a**2 + 4*a**o + 0 + 4 + a**4 + 4*a - 3.
(a + 1)**4
Let s = 18 + -18. Let t(p) be the third derivative of 2*p**2 + s*p**4 - 1/360*p**6 + 0*p**3 + 0 + 0*p**5 + 0*p. Factor t(v).
-v**3/3
Let i be 2/15 - 232/(-60). Let a(s) be the third derivative of -2*s**2 + 0 + 3*s**3 + 0*s - 1/2*s**i + 1/30*s**5. Suppose a(f) = 0. Calculate f.
3
Let i(t) be the third derivative of -3*t**6/20 + t**5/2 - 7*t**4/12 + t**3/3 + 12*t**2. Find u such that i(u) = 0.
1/3, 1
Let p(x) be the first derivative of x**3/3 - x**2 - 11. Factor p(s).
s*(s - 2)
Let l(f) be the third derivative of -f**6/240 + f**4/48 + f**2. Solve l(o) = 0 for o.
-1, 0, 1
Suppose -4*w + 12 = -0. Factor 0 + 2/3*x**2 - 1/3*x**5 - 2/3*x**4 + 1/3*x + 0*x**w.
-x*(x - 1)*(x + 1)**3/3
Let j = 37 + 5. Suppose 2*n - 19 = -2*u + 5, 0 = 5*u - 4*n - j. Solve 6*r**2 - 1 + r**3 - u*r + 5 - 2*r**4 + r**3 = 0 for r.
-2, 1
Factor 19*g**3 + 8*g - 20*g**2 + 3*g**4 - g**3 - 10*g**4 + g**5.
g*(g - 2)**3*(g - 1)
Let v(y) be the second derivative of -4*y + 0*y**3 - 1/20*y**6 - 3/40*y**5 - 1/84*y**7 - 1/24*y**4 + 0*y**2 + 0. Factor v(w).
-w**2*(w + 1)**3/2
Let y(i) = 10*i**5 - 2*i**4 - 12*i**3 - 26*i**2 - 8*i + 6. Let q(t) = 9*t**5 - t**4 - 12*t**3 - 25*t**2 - 8*t + 5. Let g(b) = -6*q(b) + 5*y(b). Factor g(c).
-4*c*(c - 2)*(c + 1)**3
Let q(l) = 6*l - 3. Let c(y) = y**2 + 8*y - 4. Let h(u) = 3*c(u) - 4*q(u). Determine a so that h(a) = 0.
0
Suppose -5*a - 5*z + 6 = -6*z, 0 = 2*a + z - 8. Factor 0*i**2 + i**2 + a*i**2 - 2*i**2.
i**2
Suppose -4*f = -2*x + 5*x + 6, 3 = 3*x + f. Factor x*z**2 - 3*z**2 + 3*z**3 - 4*z**3 - z**2.
-z**2*(z + 2)
Suppose 2*m = d - 42, 0 = -5*m - 3*d - 91 - 14. Let t be 10/(-24) + m/(-28). Find l, given that t*l**4 + 0 + 0*l**3 + 0*l + 0*l**2 = 0.
0
Let g(a) = -15*a**4 + 90*a**2 + 141*a + 24. Let q(n) = 3*n**4 - 18*n**2 - 28*n - 5. Let w(i) = -4*g(i) - 21*q(i). Factor w(f).
-3*(f - 3)*(f + 1)**3
Let d be ((-4)/2)/(2*(-2)/4). Find v such that 3/4*v + 3/4*v**d + 1/4*v**3 + 1/4 = 0.
-1
Let i = 6 - 2. Let h = -3 + i. Let b(t) = 4*t**2. Let v(g) = -g**2 - g. Let j(m) = h*b(m) + 2*v(m). Factor j(r).
2*r*(r - 1)
Suppose 2*j + 3*y - 27 = -3*j, y - 13 = -3*j. Suppose q + 0*q - j = 0. Factor 5*v**2 + 0*v**2 - q*v**2.
2*v**2
Let z(c) be the second derivative of -c**4/72 - c**3/12 + c**2/3 + 6*c. Suppose z(o) = 0. Calculate o.
-4, 1
Let q(n) = -n**2 + 23*n + 27. Let m be q(24). Determine l, given that 0*l**2 - 2/5*l**m - 4/5*l**4 + 0*l + 0 - 2/5*l**5 = 0.
-1, 0
Let k(u) be the third derivative of 0 - 1/75*u**6 + 0*u**4 + 7*u**2 + 1/75*u**5 + 2/525*u**7 + 0*u + 0*u**3. Find z such that k(z) = 0.
0, 1
Let i(k) be the second derivative of k**4/48 + k**3/12 + 4*k. Suppose i(s) = 0. What is s?
-2, 0
Let r(h) be the first derivative of h**4/12 - 2*h**3/9 + h**2/6 - 22. Let r(k) = 0. Calculate k.
0, 1
Let r(t) be the third derivative of -t**9/120960 + t**7/2520 + t**5/60 + 2*t**2. Let n(j) be the third derivative of r(j). Factor n(x).
-x*(x - 2)*(x + 2)/2
Let b(l) be the first derivative of -l**7/168 + l**5/80 - 6*l + 6. Let d(t) be the first derivative of b(t). Factor d(m).
-m**3*(m - 1)*(m + 1)/4
Solve 0 + 3*a + 21/2*a**2 = 0.
-2/7, 0
Let v = -107 + 536/5. Find c such that 0*c - v*c**2 + 0 = 0.
0
Let 33/2*l**3 - 6*l**4 + 0 - 39/4*l**2 + 3/2*l = 0. Calculate l.
0, 1/4, 1/2, 2
Find y such that 0 - 2/5*y**3 - 8/5*y**2 - 8/5*y = 0.
-2, 0
Let z = -38074/3 + 12878. Let x = -184 + z. Find h, given that x*h - 2*h**2 - 40/3*h**3 - 25/3*h**4 - 1/3 = 0.
-1, 1/5
Find j such that 5/4*j**3 + 1/4*j**2 - 1/4*j**4 - 1/4*j**5 - 2*j + 1 = 0.
-2, 1
Let s(l) be the first derivative of -2*l**5/5 - l**4/2 + 2*l**3/3 + l**2 + 9. Suppose s(o) = 0. What is o?
-1, 0, 1
Solve -1/6*r**2 - 1/2*r**3 + 1/6*r**4 + 1/3*r**5 + 1/6*r + 0 = 0 for r.
-1, 0, 1/2, 1
Let s(z) be the first derivative of z**4/10 - 14*z**3/15 + 11*z**2/5 - 2*z + 12. Solve s(y) = 0 for y.
1, 5
Suppose 0 = -2*s + 7*s - 40. Factor 11 - 12*i**2 - s - 4*i**3 - 12*i - 7.
-4*(i + 1)**3
Let s = -26 - -82/3. Factor -16/3*x + 25/3*x**2 + s - 19/3*x**3 + 7/3*x**4 - 1/3*x**5.
-(x - 2)**2*(x - 1)**3/3
Let i = -52 - -211/4. Find d, given that -3/2*d**2 + i*d**4 + 3/4*d + 3/4 - 3/2*d**3 + 3/4*d**5 = 0.
-1, 1
Let 2/11*u**3 + 0 + 2/11*u**5 - 4/11*u - 6/11*u**2 + 6/11*u**4 = 0. Calculate u.
-2, -1, 0, 1
Let i(v) be the first derivative of -28*v**3/3 + 102*v**2 - 56*v + 10. Factor i(h).
-4*(h - 7)*(7*h - 2)
Suppose -2*o + 2*r = o - 15402, -4*r = 2*o - 10284. Let c = o - 46168/9. Find q, given that 98/9*q**2 + c*q + 8/9 = 0.
-2/7
Let x(g) be the first derivative of 3 + 0*g - 1/5*g**2 - 2/15*g**3. Factor x(z).
-2*z*(z + 1)/5
Let a(w) = -w**3 - 4*w**2 + 3. Let o be a(-4). Let j(m) be the first derivative of 4/3*m**o + 2 + 0*m**4 + 0*m**2 - 2*m - 2/5*m**5. Factor j(r).
-2*(r - 1)**2*(r + 1)**2
Let l = 21 + -14. Suppose -n**5 + 9*n**3 - 2*n**5 + 3*n - 2*n**4 - l*n = 0. Calculate n.
-2, -2/3, 0, 1
Let w be 0 + 2/9 + (-4)/(-144). Let d(r) be the first derivative of -1/2*r**2 + 1 + 1/4*r - w*r**4 + 1/2*r**3 + 1/20*r**5. Find y such that d(y) = 0.
1
Let a(q) be the third derivative of 0 + 1/20*q**5 + 4*q**2 + 0*q - 1/20*q**6 + 1/4*q**4 - 1/70*q**7 + 0*q**3. Factor a(k).
-3*k*(k - 1)*(k + 1)*(k + 2)
Factor -32/3 + 16/3*r + 10*r**2 - 16/3*r**3 + 2/3*r**4.
2*(r - 4)**2*(r - 1)*(r + 1)/3
Suppose 0 = 4*f - 0*f - 60. Suppose -2*h - 3*h = -f. Suppose -2*d**h - 5*d**3 + 5*d**3 = 0. Calculate d.
0
Let r = 2 - -3. Suppose -r*m + m = 0. Factor -u**3 + m*u - 1/2*u**4 - 1/2*u**2 + 0.
-u**2*(u + 1)**2/2
Factor -2/9*l + 0 + 2/9*l**2.
2*l*(l - 1)/9
Let v be (-760)/14 - (-12)/42. Let x be (-39)/v + 2/12. Factor 2/9*k**4 - 2/3*k**2 + 8/9 - x*k + 4/9*k**3.
2*(k - 1)**2*(k + 2)**2/9
Suppose 4*j - 12 = -4*z, -4*z + 12 = 2*j - 2. Let d be 12/18 + (-10)/(-12). Factor 0 + 3/2*x**z - 3/2*x**2 + 3/2*x**3 - d*x**5 + 0*x.
-3*x**2*(x - 1)**2*(x + 1)/2
Let k(u) be the second derivative of -u**5/2 + 2*u**4/3 + 7*u**3/3 - 6*u**2 - 12*u. Factor k(n).
-2*(n - 1)**2*(5*n + 6)
Let v(c) be the second derivative of 0 + 4*c + 0*c**2 + 1/12*c**3 - 1/120*c**6 + 1/20*c**5 - 5/48*c**4. Determine g so that v(g) = 0.
0, 1, 2
Let l(u) = -u**2 - 7*u + 7. Let b be l(-7). Let c be 16/b + (-8)/28. Find k such that -k**c + 0*k + 2 + k + 0 = 0.
-1, 2
Determine a so that 0 - 3/2*a - 3/4*a**2 = 0.
-2, 0
Factor -4/3*l**2 + 0 + 2/3*l**3 + 2/3*l.
2*l*(l - 1)**2/3
Let l = 5 + 5. Factor n**3 - l - 3*n + 5*n**2 + 4 + n**2 + 2*n**3.
3*(n - 1)*(n + 1)*(n + 2)
Suppose 3*q = -2 - 1. Let p be q/1*6/(-30). Suppose -3/5*c - 1/5*c**3 - 3/5*c**2 - p = 0. What is c?
-1
Let i = -8 + -5. Let a = i - -15. Factor 4/5*r + 4/5 + 1/5*r**a.
(r + 2)**2/5
Let a(q) = 2*q**3 - 2*q**2 + 2*q - 2. Let w(k) = -3 + 2 + 5 - 5 + k**3. Let p(m) = a(m) - 4*w(m). Suppose p(g) = 0. What is g?
-1, 1
Let t(o) be the first derivative of -11*o**8/1680 + o**7/420 - 2*o**3 + 9. Let u(d) be the third derivative of t(d). Factor u(q).
-q**3*(11*q - 2)
Factor -24/7*w + 4/7 + 48/7*w**2 - 32/7*w**3.
-4*(2*w - 1)**3/7
Suppose -2/7*j**2 - 4/7*j - 2/7 = 0. Calculate j.
-1
Let p(y) = -y**3 - 6*y**2 - 5*y - 3. Let w be p(-5). Let n be ((-2)/w)/(6/18). Solve 41*k**2 + 38*k**4 - 16*k - 84*k**3 + 31*k**n - 7*k**5 + k**5 = 0 for k.
0, 1/3, 2
Let x(f) be the first derivative of -1/6*f**4 - 2 + 0*f + 0*f**2 + 0*f**3 + 2/15*f**5. Factor x(c).
2*c**3*(c - 1)/3
Let l(c) be the first derivative of c**4/60 - c**2/10 + 3*c - 1. Let m(s) be the first derivative of l(s). Find j, given that m(j) = 0.
-1, 1
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