
Let h(w) be the second derivative of -w**6/20 - 21*w**5/40 - 15*w**4/8 - 13*w**3/4 - 3*w**2 - w. Factor h(d).
-3*(d + 1)**3*(d + 4)/2
Suppose 3*p + 6 = -4*x, -3*x + 20 = 2*p + 24. Factor -2*g**2 + x - 4/5*g - 8/5*g**3 - 2/5*g**4.
-2*g*(g + 1)**2*(g + 2)/5
Let m(u) be the second derivative of -u**6/60 + u**4/4 - 2*u**3/3 + 3*u**2/2 + 3*u. Let t(f) be the first derivative of m(f). Factor t(j).
-2*(j - 1)**2*(j + 2)
Factor 3*g**2 - g + g**3 - 3 - g**2 + 1.
(g - 1)*(g + 1)*(g + 2)
Suppose 5*f - 490 = 15. Suppose t - 5*j = 213, 3*t + j - f = 490. Factor -8*z**3 + 24 - 51*z**3 + t*z**2 + 21*z**4 - 17*z**3 - 132*z - 35*z**3.
3*(z - 2)**2*(z - 1)*(7*z - 2)
Let f(q) be the second derivative of q**6/120 - q**5/18 + q**4/8 - q**3/9 + q**2 - 3*q. Let m(z) be the first derivative of f(z). Determine o so that m(o) = 0.
1/3, 1, 2
Let o = 15/6573478 - -19260213995/33544458234. Let i = o + -2/729. Find f, given that 2/7*f**3 - i*f + 2/7*f**2 + 0 = 0.
-2, 0, 1
Factor -2/9*y**2 + 0 - 2/9*y.
-2*y*(y + 1)/9
Let v(m) = 25*m**4 + 20*m**3 - 15*m**2 + 5*m. Let b(i) = 13*i**4 + 10*i**3 - 7*i**2 + 2*i. Let f(l) = -5*b(l) + 2*v(l). Let f(c) = 0. Calculate c.
-1, 0, 1/3
Let a = 600 + -598. Solve -10/9*v + 2/9 + 8/9*v**a = 0 for v.
1/4, 1
Factor -147 + 2*f**2 - 5*f**2 - 39*f - 3*f.
-3*(f + 7)**2
Let d be ((-1664)/24)/(-13) - 5. Factor 2/3 - d*t**3 - 2/3*t**2 + 1/3*t.
-(t - 1)*(t + 1)*(t + 2)/3
Let q(r) be the first derivative of -r**5/20 - r**4/4 - r**3/2 + r**2 + 2. Let z(p) be the second derivative of q(p). Let z(d) = 0. What is d?
-1
Suppose j - 2*u - 13 = 0, -6*u = -5*j - 8*u + 5. Let b(t) be the second derivative of 1/30*t**4 + 0 + 0*t**2 + 1/15*t**3 + j*t. Factor b(z).
2*z*(z + 1)/5
Let g(s) be the third derivative of s**6/15 - 3*s**5/10 - 5*s**4/6 + s**3 + 7*s**2. Factor g(f).
2*(f - 3)*(f + 1)*(4*f - 1)
Let s(c) be the first derivative of -c**8/168 + 4*c**7/105 - c**6/10 + 2*c**5/15 - c**4/12 - c**2/2 + 2. Let k(n) be the second derivative of s(n). Factor k(g).
-2*g*(g - 1)**4
Suppose -f + 17 = -3*x, -3*x + 22 - 59 = -5*f. Suppose -3/5*z**3 - 9/5*z**f + 24/5*z**4 - 24/5*z**2 + 12/5*z + 0 = 0. Calculate z.
-1, 0, 2/3, 1, 2
Determine h, given that -12/7*h - 4/7*h**2 + 16/7 = 0.
-4, 1
Suppose -8 = -2*s - 0. Factor 2*k**3 - 1 - 2*k**5 + 1 - 4*k**3 + 4*k**s.
-2*k**3*(k - 1)**2
Let n(s) be the second derivative of 5*s**7/63 - 34*s**6/45 + 83*s**5/30 - 41*s**4/9 + 20*s**3/9 + 8*s**2/3 + 32*s. Determine a so that n(a) = 0.
-1/5, 1, 2
Let j(n) = -n**3 + 5*n**2 + 6*n + 6. Let i be j(6). Determine m so that -6 + m**3 + m - 2*m**2 + i = 0.
0, 1
Let v(k) = 20*k**2 - 40*k + 6. Let q(l) = 4*l**2 - 8*l + 1. Let a(w) = -14*q(w) + 3*v(w). Suppose a(i) = 0. Calculate i.
1
Let d(o) be the second derivative of -o**7/189 + 2*o**6/135 + o**5/30 - 28*o. Find g such that d(g) = 0.
-1, 0, 3
Let i(r) be the third derivative of -r**6/180 + r**4/12 + 2*r**3/9 - 3*r**2. Find z such that i(z) = 0.
-1, 2
Let o(n) = -3*n**3 + 8*n**2 - 5*n. Let d(q) = -3*q**3 + 9*q**2 - 6*q. Let g(v) = 4*d(v) - 3*o(v). Factor g(x).
-3*x*(x - 3)*(x - 1)
Suppose 0 = 12*g + 12*g - 48. Determine u so that 1/3 - 1/3*u**3 - u + u**g = 0.
1
Suppose -19*v + 15*v + 116 = 0. Factor -v*o**2 + 4 + 88*o - 12 - 213*o**2.
-2*(11*o - 2)**2
Let r = 16 + -4. Let l be ((1 - -3) + -2)/1. Suppose r*t - 10*t**l - 9*t**3 + t**2 - 3*t**4 - 3*t**3 + 12 = 0. Calculate t.
-2, -1, 1
Let a(y) be the third derivative of y**5/15 + 5*y**4/3 + 53*y**2. Solve a(f) = 0.
-10, 0
Let b(m) be the third derivative of m**5/90 + m**4/36 - 2*m**2. Find u such that b(u) = 0.
-1, 0
Let z be 11/22 + (-3618)/(-28). Let i = 130 - z. Factor -6/7*k**4 - 2/7*k**2 + 6/7*k**3 + 0 + 0*k + i*k**5.
2*k**2*(k - 1)**3/7
Let m = -4/59 + 71/177. Factor 0*x + 4/3 - x**2 - m*x**3.
-(x - 1)*(x + 2)**2/3
Let j(i) be the second derivative of 2*i + 0 - 1/120*i**5 + 1/18*i**3 + 0*i**2 + 1/72*i**4. Suppose j(r) = 0. Calculate r.
-1, 0, 2
Factor -4*q**4 + 15*q**4 + q**5 - 9*q**4 + q**3.
q**3*(q + 1)**2
Let j(m) be the first derivative of -11/2*m**4 - 1 + 0*m + 32/5*m**5 + 0*m**2 - 7/3*m**6 + 4/3*m**3. Factor j(q).
-2*q**2*(q - 1)**2*(7*q - 2)
Let v(f) be the first derivative of -f**5/70 + f**4/21 - 4*f + 5. Let a(b) be the first derivative of v(b). Suppose a(p) = 0. What is p?
0, 2
Let k(g) = g**2 - 10*g + 9. Suppose -y = 5*q - 46, -q - 8 = -2*q + y. Let b be k(q). Factor 1/4*a**2 + b*a + 1/4*a**5 + 0 + 3/4*a**3 + 3/4*a**4.
a**2*(a + 1)**3/4
Factor -4/5 + 8/5*q**2 + 2/5*q - 6/5*q**3.
-2*(q - 1)**2*(3*q + 2)/5
Let w(g) be the second derivative of -g**6/210 + g**5/140 + g**4/84 - g**3/42 + 3*g. Determine r, given that w(r) = 0.
-1, 0, 1
Let t = -1028/1857 + 3328574/102135. Let n = 162/5 - t. Find b such that 0*b**2 + 0 - n*b**3 + 0*b + 2/11*b**4 + 2/11*b**5 = 0.
-2, 0, 1
Let w be 7 + -8 + (-1)/(-2)*2. Factor 2/3*u**3 - 2/3*u**4 + 0 + 0*u**2 + w*u.
-2*u**3*(u - 1)/3
Let l(f) = f**2 + f + 5. Let x be l(0). Let o be (-21)/(-49) - x/(-21). Factor 2/3*s**3 - o*s - 2/3*s**2 + 2/3.
2*(s - 1)**2*(s + 1)/3
Let a(p) be the first derivative of -1/6*p**3 + 1/2*p**2 + 0*p - 2. Let a(u) = 0. What is u?
0, 2
Let h(a) be the first derivative of a**4/8 - 17*a**3/6 + 20*a**2 - 32*a + 40. Suppose h(s) = 0. What is s?
1, 8
Let l be 25/10 + 75/(-10). Let q be 3*l/((-45)/6). Suppose 2/5*o**q + 2/5 + 4/5*o = 0. Calculate o.
-1
Let z(m) = -16*m**3 + m**2 - 1. Let r be z(-1). Let 56*o**2 - r*o - 49*o**3 + 5*o**3 + 4 - 4 + 10*o**4 = 0. What is o?
0, 2/5, 2
Let z be (-5)/(-4200)*-106 - (-2)/14. Let u(t) be the third derivative of z*t**4 + 0*t + 2/15*t**3 - 1/150*t**5 - 4*t**2 + 0. Determine h so that u(h) = 0.
-1, 2
Let u(d) be the first derivative of 8*d**3/3 + 13*d**2 + 6*d + 17. Factor u(w).
2*(w + 3)*(4*w + 1)
Let k(q) be the first derivative of -q**3 - 6*q**2 - 12*q + 21. Let k(w) = 0. Calculate w.
-2
Let r = -5/221 + -25621/663. Let m = 39 + r. Solve 0 + 2/3*q**2 - 1/3*q**3 - m*q = 0 for q.
0, 1
Suppose -16 - 47 = -9*q. Let z(m) be the third derivative of 1/10*m**5 - m**2 + 1/315*m**q + 1/36*m**6 + 0*m + 7/36*m**4 + 0 + 2/9*m**3. Factor z(s).
2*(s + 1)**3*(s + 2)/3
Let k(i) be the second derivative of -3*i**5/110 + i**4/33 - 10*i. Factor k(f).
-2*f**2*(3*f - 2)/11
Let x(i) = 10*i**2 - 13*i + 4. Let n(r) = 29*r**2 - 40*r + 12. Let y(b) = -3*n(b) + 8*x(b). Find k, given that y(k) = 0.
2/7, 2
Let z(u) be the first derivative of -2*u**3/3 + u**2/2 + 3*u - 9. Factor z(p).
-(p + 1)*(2*p - 3)
Let a(m) be the first derivative of -2*m + 0*m**3 + 1/48*m**4 + 1/80*m**5 - 1 + 0*m**2. Let h(r) be the first derivative of a(r). Factor h(x).
x**2*(x + 1)/4
Suppose 6*d = 2*d + 56. Let c be 24/d - (-4)/14. Factor -2*p - 3*p**c + p**2 + 2*p**3 + 2 + 0*p.
2*(p - 1)**2*(p + 1)
Let q be 6*(1 + -1 + -3). Let a be (-4)/12*q/21. Factor 0*t**3 + 0*t**2 + 0 + a*t**4 + 0*t.
2*t**4/7
Let f be (-24)/(-9) + -3 - -7. Let u = 7 - f. Factor 0*h - 1/3*h**5 - h**4 - h**3 - u*h**2 + 0.
-h**2*(h + 1)**3/3
Let q = 1194377/2219 - 1/8876. Let f = 542 - q. Factor f*m**5 - 3/2*m**3 - 9/4*m**4 + 0*m**2 + 0*m + 0.
3*m**3*(m - 1)*(5*m + 2)/4
Let d(h) be the first derivative of -2*h**3/9 - 4*h**2/3 - 4. Factor d(x).
-2*x*(x + 4)/3
Let i(m) be the third derivative of -m**7/6300 + m**6/1800 + m**5/150 + m**4/6 + m**2. Let q(g) be the second derivative of i(g). Factor q(u).
-2*(u - 2)*(u + 1)/5
Suppose -3*v + 6*v = 9. Suppose -v*m - 12 = 4*o, 0*o - 2*o - 6 = 0. Factor 1/2*r**5 + 0*r + 0 + 0*r**3 + 1/2*r**4 + m*r**2.
r**4*(r + 1)/2
Let j(q) be the third derivative of q**6/900 - q**5/100 + q**4/30 - q**3/3 + q**2. Let d(h) be the first derivative of j(h). Let d(z) = 0. What is z?
1, 2
Let h be (-10)/45 - 161/(-36) - 3. Find o, given that 5/4*o + 1/4 + h*o**4 + 1/4*o**5 + 5/2*o**2 + 5/2*o**3 = 0.
-1
Let y(o) be the second derivative of o**6/240 + 3*o**5/80 + o**4/8 - 2*o**3/3 + o. Let d(b) be the second derivative of y(b). Suppose d(t) = 0. Calculate t.
-2, -1
Let u = 13 - 13. Suppose 4*j - 2*j = u. Factor j*c + 14/5*c**4 + 2/5*c**2 + 0 - 2*c**3 - 6/5*c**5.
-2*c**2*(c - 1)**2*(3*c - 1)/5
Let a(z) be the first derivative of -z - 2/5*z**5 + z**3 - 1/2*z**2 - 1 + 1/4*z**4. Factor a(d).
-(d - 1)**2*(d + 1)*(2*d + 1)
Find f, given that -10/13*f**3 + 2/13*f**4 - 8/13*f + 0 + 16/13*f**2 = 0.
0, 1, 2
Let o(l) = 5*l**5 - 13*l**3 + 3*l**2 + 2*l + 3. Let c(k) = 