1)**2*(w + 1)/4
Let p(s) be the first derivative of -1/12*s**4 + 0*s + 0*s**2 - 1/15*s**5 - 1 + 0*s**3. Find m, given that p(m) = 0.
-1, 0
Let l(f) be the second derivative of f**4/72 - 5*f**3/18 + 4*f**2/3 - 2*f - 9. Factor l(x).
(x - 8)*(x - 2)/6
Let m be 16/(5/(310/(-4))). Let w = 2234/9 + m. Factor 0 - w*r**2 - 2/9*r.
-2*r*(r + 1)/9
Let h(k) be the second derivative of k**5/180 + k**4/108 - k**3/54 - k**2/18 + 38*k. Solve h(b) = 0.
-1, 1
Let m(k) be the first derivative of 1/20*k**4 + 3 + 1/10*k**2 + 0*k + 2/15*k**3. Suppose m(i) = 0. Calculate i.
-1, 0
Suppose s - 18 = -5*x + 7, -2*x - 5*s - 13 = 0. Let w(i) be the second derivative of 0*i**2 - 1/50*i**5 + 0*i**3 - 1/75*i**x + 0 + 0*i**4 - i. Factor w(f).
-2*f**3*(f + 1)/5
Suppose 4*c + k = 2*k + 28, 5*c = -3*k + 52. Suppose -24 = -4*t - c. Determine o so that 7*o**4 + 5*o**4 - 4*o**t - 8*o**3 - 2*o**5 = 0.
0, 2
Suppose -28 - 2 = -2*a. Let h = a + -15. Find w, given that 2/9*w**3 + 2/3*w**4 + 0*w + 0*w**2 + 4/9*w**5 + h = 0.
-1, -1/2, 0
Let y(v) = 3*v**2 + v. Let r be y(-1). Determine j, given that 1/3*j**3 + 0 + 0*j**r + 0*j - 1/3*j**4 = 0.
0, 1
Let m(d) be the first derivative of d**5/45 - d**4/9 + 5*d**3/27 - d**2/9 + 15. Determine i, given that m(i) = 0.
0, 1, 2
Factor 75*d**4 + 80*d**3 - 125*d**5 + 144/5*d - 16/5 - 88*d**2.
-(d + 1)*(5*d - 2)**4/5
Let w(s) be the first derivative of s**6/60 + s**5/30 + 2*s**2 - 3. Let k(l) be the second derivative of w(l). Solve k(j) = 0 for j.
-1, 0
Suppose d - 5 + 1 = 0. Let v be -6*d/14 - -2. Factor 4/7*w**3 - v*w**4 - 4/7*w + 2/7 + 0*w**2.
-2*(w - 1)**3*(w + 1)/7
Let x(l) be the first derivative of -l**8/560 + l**6/40 - l**5/20 - l**3 + 4. Let u(o) be the third derivative of x(o). Suppose u(n) = 0. What is n?
-2, 0, 1
Factor 10*r + 6 + 14/3*r**2 + 2/3*r**3.
2*(r + 1)*(r + 3)**2/3
Let x(q) be the second derivative of -q**4/24 - q**3/4 - q**2/2 - 2*q. Factor x(c).
-(c + 1)*(c + 2)/2
Suppose -4*z = 3*r - 6, -3*z + 6 = 2*r + 2. Let g(h) be the second derivative of h - 2/15*h**3 + 0 + z*h**4 - 1/75*h**6 + 1/5*h**2 + 1/25*h**5. Factor g(a).
-2*(a - 1)**3*(a + 1)/5
Let x(t) be the first derivative of t**5/390 - t**4/39 + t**3/13 + 2*t**2 + 7. Let h(y) be the second derivative of x(y). Factor h(q).
2*(q - 3)*(q - 1)/13
Suppose 3*h + 2*m - 16 = -0*m, 0 = -h + m - 3. What is q in 18*q + 7/2*q**3 - 15*q**h - 4 = 0?
2/7, 2
Let l(w) be the second derivative of -w**4/72 + 5*w**3/36 - w**2/2 - 26*w. Factor l(h).
-(h - 3)*(h - 2)/6
Let w(l) be the first derivative of l**6/72 - l**5/60 - 5*l**4/48 - l**3/12 + 65. Factor w(t).
t**2*(t - 3)*(t + 1)**2/12
Factor 9*v**4 - 4*v**2 + v**2 + 433*v - 12*v**3 - 427*v.
3*v*(v - 1)**2*(3*v + 2)
Let j be (-4)/12 + 2/6. Suppose -2*r**3 + 2*r + 3 + r**4 + j*r**3 - 4 + 0*r = 0. Calculate r.
-1, 1
Factor -4 - 65 - 123 - 27*w - 21*w - 3*w**2.
-3*(w + 8)**2
Let m = 5 + -11. Let g = m + 6. Factor -1/2*j + g - 5/4*j**2.
-j*(5*j + 2)/4
Suppose 6*h - h + 25 = 0, 3*g = -2*h + 2. Let j(q) be the second derivative of 1/5*q**2 + 1/6*q**3 + 4*q + 1/100*q**5 + 0 + 1/15*q**g. Solve j(m) = 0 for m.
-2, -1
Let c(f) be the first derivative of -f**6/600 + f**5/100 + 7*f**3/3 + 5. Let q(v) be the third derivative of c(v). Solve q(k) = 0 for k.
0, 2
Let s(w) be the second derivative of w**7/4200 - w**5/600 + w**3/2 + 4*w. Let n(g) be the second derivative of s(g). Factor n(l).
l*(l - 1)*(l + 1)/5
Determine a so that a**5 - 3*a**3 + 13*a**2 - 12*a**2 + 3*a**4 - 2*a**5 = 0.
0, 1
Determine n, given that -13*n**3 - 12*n**5 + 37*n**3 + 4 - 6*n**4 + 10*n**4 - 12*n - 8*n**2 = 0.
-1, 1/3, 1
Suppose 3*k - 30 = -12*k. Factor 2/3 + 2/3*u**k - 4/3*u.
2*(u - 1)**2/3
Let i(t) be the second derivative of -8*t**7/21 + 34*t**6/15 - 4*t**5 + 4*t**4/3 - 6*t. Let i(d) = 0. Calculate d.
0, 1/4, 2
Suppose -5*v + 5*l = 15, -9 = -2*v - 0*l - 3*l. Factor 1/2*x**5 + 0*x - 5/4*x**4 + v*x**2 + 1/2*x**3 + 0.
x**3*(x - 2)*(2*x - 1)/4
Let f(z) = -4*z**4 - 8*z**3 - 6*z + 6. Let v(i) = 4*i**4 + 8*i**3 + 7*i - 7. Let x(l) = 7*f(l) + 6*v(l). Find n such that x(n) = 0.
-2, 0
Let c be 1/(-2) - 1/(-2). Let t(f) be the third derivative of 1/6*f**4 + f**2 + 0 - 1/30*f**5 + c*f - 4/9*f**3 + 1/360*f**6. Factor t(r).
(r - 2)**3/3
Suppose 0 = -2*v + 3*u + 6, 5*v + 2*u - 15 = -0. Let i(g) be the first derivative of 1/12*g**6 + 0*g**v + 3/10*g**5 + 0*g + 0*g**2 - 2 + 1/4*g**4. Factor i(d).
d**3*(d + 1)*(d + 2)/2
Let m = 35/12 + -9/4. Factor 5/3*c**2 + 0 - m*c.
c*(5*c - 2)/3
Let f(b) be the third derivative of -1/300*b**5 + 0*b + 4*b**2 + 0*b**3 + 0 + 1/60*b**4. Factor f(c).
-c*(c - 2)/5
Let k(q) = -7*q**3 + 12*q**2 + 11*q - 27. Let c(j) = -4*j**3 + 6*j**2 + 6*j - 14. Let m(r) = -11*c(r) + 6*k(r). Factor m(y).
2*(y - 1)*(y + 2)**2
Let o(b) be the third derivative of -1/200*b**6 + 0*b + 0*b**3 + 0 - 1/560*b**8 + 1/175*b**7 + 2*b**2 + 0*b**4 + 0*b**5. Find k such that o(k) = 0.
0, 1
Let d(z) be the third derivative of 0*z**3 - 3*z**2 + 1/72*z**4 + 0 - 1/360*z**6 + 0*z + 0*z**5. Find l such that d(l) = 0.
-1, 0, 1
Suppose 0 = d - 10 + 2. Factor -8*t**2 + 4*t**3 + d*t**2 - 2*t**5 - 2*t.
-2*t*(t - 1)**2*(t + 1)**2
Let n(o) be the first derivative of 2*o**3/33 + 8*o**2/11 + 32*o/11 - 7. Factor n(k).
2*(k + 4)**2/11
Let u(f) = 90*f**2 + 16*f - 6. Let h(t) = -1. Let k(q) = 2*h(q) + u(q). Factor k(b).
2*(5*b + 2)*(9*b - 2)
Suppose 0 - 8/3*s - 16/3*s**2 + 10/3*s**3 = 0. Calculate s.
-2/5, 0, 2
Let h(x) be the third derivative of -x**8/336 + x**7/35 - 7*x**6/60 + 4*x**5/15 - 3*x**4/8 + x**3/3 - 6*x**2. Suppose h(j) = 0. What is j?
1, 2
Let v(f) = -21*f**5 - 43*f**4 - 2*f**3 - f**2 + 7*f. Let l(z) = -21*z**5 - 42*z**4 - 3*z**3 + 6*z. Let i(b) = -7*l(b) + 6*v(b). Factor i(g).
3*g**2*(g + 1)**2*(7*g - 2)
Let -10/3*t**2 + 16/3*t + 2/3*t**3 - 8/3 = 0. Calculate t.
1, 2
Let q(v) = v**3 + 13*v**2 - v - 13. Let t be q(-13). Factor 3/2*o**3 - 1/2*o**4 + 0*o + t - o**2.
-o**2*(o - 2)*(o - 1)/2
Suppose 11 = y + 3*a, 0*a = -a + 2. Let u = y + -3. Factor p**3 + 0 - 5/3*p**u + 3*p**4 + 1/3*p.
p*(p + 1)*(3*p - 1)**2/3
Let j = -136/5 - -142/5. Factor 2/5 - 2/5*g**3 + j*g**2 - 6/5*g.
-2*(g - 1)**3/5
Let b(i) be the third derivative of -i**5/80 + i**4/2 - 8*i**3 + 29*i**2. Factor b(r).
-3*(r - 8)**2/4
Let n(u) be the first derivative of -u**4/6 + 4*u**3/3 - 4*u**2 + 16*u/3 - 6. Factor n(q).
-2*(q - 2)**3/3
Let b(o) be the first derivative of -2 - 1/48*o**5 + 1/2*o**2 - 1/6*o**3 + 0*o - 1/480*o**6 - 1/12*o**4. Let w(k) be the second derivative of b(k). Factor w(t).
-(t + 1)*(t + 2)**2/4
Let s(v) be the second derivative of 1/6*v**4 + 0 + 2/9*v**3 + 5*v + 0*v**2. Factor s(h).
2*h*(3*h + 2)/3
Let l(o) be the third derivative of -o**6/24 - 5*o**5/12 - 5*o**4/3 - 10*o**3/3 + 14*o**2. Factor l(h).
-5*(h + 1)*(h + 2)**2
Let x(s) be the second derivative of 7/48*s**4 - 2*s - 5/24*s**3 - 1/4*s**2 + 0. Factor x(y).
(y - 1)*(7*y + 2)/4
Suppose 0 = b - 1, -2*b = -f + 3*b - 3. Factor 4*p + p + 5*p + 2*p**f - 2*p + 6.
2*(p + 1)*(p + 3)
Let r = 4/89 + 73/356. Factor -3/4*f - 1/2 - r*f**2.
-(f + 1)*(f + 2)/4
Factor 0*b - 2/7*b**2 + 2/7.
-2*(b - 1)*(b + 1)/7
Suppose 48*n - 54*n = 0. Let d(m) be the third derivative of n - m**3 - 1/40*m**6 - 1/5*m**5 + 0*m - 5/8*m**4 - 2*m**2. Factor d(i).
-3*(i + 1)**2*(i + 2)
Suppose -90 - 16 = -53*f. Factor 0 + 1/2*l**2 + f*l.
l*(l + 4)/2
Factor 50/3*c**2 + 8/3 + 40/3*c.
2*(5*c + 2)**2/3
Let x(t) = -t**2 - 13*t + 142. Let f be x(7). Let -6/5*y**f + 0*y + 8/5 + 2/5*y**3 = 0. What is y?
-1, 2
Let x(v) be the second derivative of 21*v**5/20 - 3*v**4 - 2*v**3 - 5*v. Factor x(u).
3*u*(u - 2)*(7*u + 2)
Let c be (3 + -2 - 5) + 14/3. Factor 1/3 - c*a + 1/3*a**2.
(a - 1)**2/3
Let d(t) be the first derivative of 1/3*t**2 + 0*t**4 - 1/15*t**5 - 2 + 1/3*t**3 + 0*t. Factor d(h).
-h*(h - 2)*(h + 1)**2/3
Let t(k) = -k**2 - 6*k + 1. Let q(u) = u - 1. Let b(z) = -3*q(z) - t(z). Let s be b(-2). Solve 2*r + s*r - r - r**2 = 0.
0, 1
Let g(k) be the third derivative of 169*k**6/360 + 13*k**5/20 - 2*k**4/3 + 2*k**3/9 + 25*k**2. Factor g(y).
(y + 1)*(13*y - 2)**2/3
Suppose -5*x - 15 = -5*g, x = 4*g - g - 11. Let r(u) = 4*u**3 - u. Let w be r(x). Suppose 0 + 2/7*v + 4/7*v**2 + 2/7*v**w = 0. Calculate v.
-1, 0
Let b be (1/3)/((-2 + 1)*-3). Let n(u) be the first derivative of 0*u**2 + b*u**3 + 0*u + 3. Determine d so that n(