ive of r**7/14 + r**6/24 + 6*r**2 - 5. Let w(q) be the second derivative of i(q). Factor w(o).
5*o**3*(3*o + 1)
Let h(i) be the second derivative of -i**6/15 - i**5/2 - 7*i**4/6 - i**3 + 84*i. Factor h(t).
-2*t*(t + 1)**2*(t + 3)
Let h be 4 - (30/(-36) + -3). Let j(c) be the second derivative of -4/3*c**2 - 35/9*c**6 - h*c**5 + 0 - 3*c - 40/9*c**3 - 145/18*c**4 - 7/9*c**7. Factor j(n).
-2*(n + 1)**3*(7*n + 2)**2/3
Let r(y) be the first derivative of 3*y**4/20 - 2*y**3/5 + 3*y**2/10 - 231. Solve r(c) = 0 for c.
0, 1
Let i = -41199/5 - -8240. Suppose 0 + 2/5*g**3 - 3/5*g**2 + 0*g + i*g**4 = 0. Calculate g.
-3, 0, 1
Factor -9*g**2 - g**2 - 648*g - 35 - 937 - 70*g**2 + 3*g**4 - g**2 + 18*g**3.
3*(g - 6)*(g + 3)**2*(g + 6)
Let h(f) = -11*f**4 - 32*f**3 + 15*f**2 + 7*f. Let q(r) = 5*r**4 + 16*r**3 - 8*r**2 - 4*r. Let c(g) = -4*h(g) - 7*q(g). Suppose c(i) = 0. What is i?
-2, 0, 2/9
Let w(v) be the first derivative of v**5/10 + 5*v**4/6 - 2*v**3 + 11*v + 21. Let z(s) be the first derivative of w(s). Solve z(r) = 0.
-6, 0, 1
Let b(p) be the third derivative of -p**6/480 + p**5/20 - 152*p**2. What is z in b(z) = 0?
0, 12
Let x(z) be the second derivative of z**8/84 + 2*z**7/105 - z**6/30 - z**5/15 + 7*z**2/2 - 5*z. Let i(b) be the first derivative of x(b). Factor i(c).
4*c**2*(c - 1)*(c + 1)**2
Factor 16 - 3*z**3 + 8*z**2 + 5*z**3 - 16.
2*z**2*(z + 4)
Let p(s) be the third derivative of -11*s**4/24 - 5*s**3/6 - s**2. Let h be p(-2). Factor -5*l**2 - 48*l + h*l**3 - 29*l**3 - 85*l**2 - 8 - 38*l**3.
-2*(l + 1)*(5*l + 2)**2
Suppose 49*u + 13245 = 13392. Determine g, given that 1/10*g**u + 3/10 - 1/10*g - 3/10*g**2 = 0.
-1, 1, 3
Let u(r) = -3*r**3 + r**2. Let z(s) = 7*s**3 - 64*s**2 - 55*s. Let q(g) = -4*u(g) - z(g). Factor q(b).
5*b*(b + 1)*(b + 11)
Suppose 315 = 14*k + 49*k. Let g = 2 + 1. Factor x**3 + 0*x**3 - g*x**4 + 0*x**5 + x**k - x**2 + 2*x**3.
x**2*(x - 1)**3
Let r(w) = -w**2 - 33*w + 36. Let b(q) = -3*q**2 - 132*q + 144. Let h(d) = 2*b(d) - 9*r(d). Factor h(f).
3*(f - 1)*(f + 12)
Let v(j) be the second derivative of j**5/90 + j**4/9 - 5*j**2/2 - 4*j. Let c(l) be the first derivative of v(l). Factor c(m).
2*m*(m + 4)/3
Let u be (10/(-4))/((-20)/16). Suppose -20*s**3 - 5*s**3 + 12*s**2 + 26*s**2 + 20*s + u*s**2 = 0. Calculate s.
-2/5, 0, 2
Factor -8/7*q**2 + 0 - 8/7*q - 2/7*q**3.
-2*q*(q + 2)**2/7
Suppose 2*b - 5*d = -2, b = d + 2*d. Let r be 2/2 + 7 + b. Solve -6*v**r + v**3 - 4*v**3 + 6 + 3*v - 2*v + 2*v = 0 for v.
-2, -1, 1
Let h(z) = 20*z**2 + 79*z - 2. Let u be h(-4). Find j, given that 0*j + 1/3 - 1/3*j**u = 0.
-1, 1
Factor -11163*k**4 - 4/3*k + 0 - 10919*k**3 + 728/3*k**2.
-k*(k + 1)*(183*k - 2)**2/3
Let h(k) be the first derivative of -k**4/20 - k**3/5 - 62. Factor h(q).
-q**2*(q + 3)/5
Let b(p) be the second derivative of 22*p + 1/6*p**4 + 0 + p**2 - 2/3*p**3. Factor b(y).
2*(y - 1)**2
Let v be 8 + -11 - (2 + -7). Factor -35*b**v + 258*b - 83*b - 150 + 413*b - 53*b.
-5*(b - 15)*(7*b - 2)
Let p(o) be the third derivative of 0*o**3 + 0 - 2*o**2 + 0*o**5 - 1/200*o**6 + 1/40*o**4 + 0*o. Factor p(x).
-3*x*(x - 1)*(x + 1)/5
Let p(w) be the first derivative of -w**5/25 - w**4/20 + w**3/3 - 3*w**2/10 + 17. Factor p(n).
-n*(n - 1)**2*(n + 3)/5
Let h(i) be the second derivative of -i**5/150 + i**4/30 + i**3/5 + 27*i**2/2 + 3*i. Let a(p) be the first derivative of h(p). Find d, given that a(d) = 0.
-1, 3
Let q = 950/2859 + 1/953. Factor z**2 - 1 - q*z + 1/3*z**3.
(z - 1)*(z + 1)*(z + 3)/3
Let l(c) = -c**2 - 6*c - 2. Let x be l(-4). Let i = 12 - 7. Solve -2*y**i + 6*y**4 + x*y - 3*y - 6*y**2 - y**5 = 0.
-1, 0, 1
Factor -2*g + 108*g**3 - 106*g**3 + 1 + 133*g**2 - 133*g**2 - g**4.
-(g - 1)**3*(g + 1)
Determine q, given that -10 - 52/5*q**2 + 2/15*q**5 - 62/3*q + 4/3*q**3 + 6/5*q**4 = 0.
-5, -1, 3
Factor -2*j**4 + 4*j**3 + 21*j**2 - 30*j**2 + 43*j**2 + 30*j - 2*j**3.
-2*j*(j - 5)*(j + 1)*(j + 3)
Let a(d) be the first derivative of 5*d**5 - 135*d**4/4 + 75*d**3 - 145*d**2/2 + 30*d - 71. Factor a(k).
5*(k - 3)*(k - 1)**2*(5*k - 2)
Let k = -12507 - -74419/6. Let b = k + 104. Factor -1/3*s**2 + 1/6*s - 1/3*s**3 + 1/6*s**5 + 1/6*s**4 + b.
(s - 1)**2*(s + 1)**3/6
Let r(c) be the third derivative of c**8/1008 - c**7/504 - c**6/216 + c**5/72 + 9*c**3/2 + 41*c**2. Let j(d) be the first derivative of r(d). Factor j(f).
5*f*(f - 1)**2*(f + 1)/3
Let f = -4/4733 - 1150103/18932. Let s = 61 + f. Factor -1/4*a**2 + s*a - 1/4*a**3 + 1/4.
-(a - 1)*(a + 1)**2/4
Let d be (72/45)/(3*6/45). Factor 0*v + 4/9*v**d + 0*v**2 + 0 - 4/9*v**3.
4*v**3*(v - 1)/9
Suppose 3*q + 41 = 8. Let m = -11 - q. Factor m - k**2 - 5 + 6.
-(k - 1)*(k + 1)
Let y(k) be the second derivative of -k**6/720 + k**5/120 - k**4/48 + 5*k**3/3 + 5*k. Let t(a) be the second derivative of y(a). Factor t(x).
-(x - 1)**2/2
Let a(u) be the third derivative of 0*u**4 + 0*u + 0 + 1/280*u**6 - 30*u**2 + 0*u**3 - 1/140*u**5. Solve a(h) = 0 for h.
0, 1
Let i(h) = 5*h**2 + 9*h - 8. Let t(d) = 6*d**2 + 9*d - 7. Let j(m) = -4*i(m) + 3*t(m). Let c(v) = -6*v**2 - 28*v + 34. Let k(o) = 3*c(o) - 10*j(o). Factor k(f).
2*(f - 1)*(f + 4)
Let i(b) = b - 1. Let g(x) = x**2 + 11*x - 30. Let m(r) = -3*g(r) - 12*i(r). Factor m(k).
-3*(k - 2)*(k + 17)
Factor 1/8*c**5 + 0 + 0*c**2 + 3/4*c**3 + 0*c + 5/8*c**4.
c**3*(c + 2)*(c + 3)/8
Suppose -1/8*p**4 - 9/8*p**3 - 27/8*p**2 + 0 - 27/8*p = 0. Calculate p.
-3, 0
Let w(n) be the third derivative of -n**6/1440 - n**5/60 - n**4/6 - 4*n**3/3 + 10*n**2. Let p(g) be the first derivative of w(g). Solve p(f) = 0 for f.
-4
Let t(w) be the second derivative of 0*w**3 + 0*w**2 + 1/210*w**7 + 15*w - 1/100*w**5 - 1/60*w**4 + 1/150*w**6 + 0. Factor t(o).
o**2*(o - 1)*(o + 1)**2/5
Let h be 3/(-1 + -2) + 5. Let r(s) = 0*s**2 + 2*s**2 + h*s + 2*s**2. Let y(x) = -x**2 + 1. Let m(w) = r(w) + 2*y(w). Determine l, given that m(l) = 0.
-1
Let g = 166 + -163. Let y(i) be the first derivative of 1/3*i**g - 1/5*i**5 - 1/2*i**2 - 4 + 1/4*i**4 + 0*i. Find c such that y(c) = 0.
-1, 0, 1
Factor 12 + 3/8*a**3 + 45/4*a**2 - 189/8*a.
3*(a - 1)**2*(a + 32)/8
Let y(m) be the third derivative of m**6/320 + m**5/40 + m**4/64 - 3*m**3/8 - 16*m**2. Factor y(k).
3*(k - 1)*(k + 2)*(k + 3)/8
Let u(n) be the third derivative of 22*n**2 + 0*n**4 + 0*n**5 + 0 - 1/315*n**7 + 0*n**3 + 0*n - 1/180*n**6. Factor u(x).
-2*x**3*(x + 1)/3
Let s(g) be the first derivative of 3*g**4/4 + 59*g**3 + 345*g**2/2 + 171*g - 237. Factor s(p).
3*(p + 1)**2*(p + 57)
Let m(y) be the second derivative of 3*y**5/20 + 5*y**4/2 + 23*y**3/2 + 21*y**2 - 106*y. Factor m(c).
3*(c + 1)*(c + 2)*(c + 7)
Let d = 13/187 - -205/2431. Let -6/13*a - 2/13*a**3 - d - 6/13*a**2 = 0. What is a?
-1
Let p(r) = -r + 22. Let x be p(17). Suppose x*f = -3 + 13. Factor 0 - 2*a**f + 0 + 3*a**2.
a**2
Let v = -42/661 + 23327/65439. Let o = v - 1/9. What is l in -2/11*l**3 + o*l - 2/11*l**2 + 2/11 = 0?
-1, 1
Let l(x) be the second derivative of x**8/3360 + x**7/420 + 2*x**4 + 19*x. Let f(b) be the third derivative of l(b). Factor f(h).
2*h**2*(h + 3)
Let w(g) be the third derivative of -g**8/70560 + g**7/5880 - 4*g**5/15 + 17*g**2. Let p(c) be the third derivative of w(c). Factor p(s).
-2*s*(s - 3)/7
Let i(b) be the second derivative of 1/4*b**5 + 0 + 15*b - 5/2*b**4 - 10*b**2 + 15/2*b**3. Find v such that i(v) = 0.
1, 4
Let m(j) be the first derivative of j**4/36 - 16*j**3/27 - 293. Factor m(u).
u**2*(u - 16)/9
Factor 23 + 68*v - 17*v - 3*v**5 - 23 + 18 - 12*v**4 + 22*v**2 + 20*v**2.
-3*(v - 2)*(v + 1)**3*(v + 3)
Suppose -3*y = 4*f + 2*y - 6, 0 = -4*f + 3*y + 22. Factor 10*p**4 - 17*p**4 + 3*p**f + 8*p**3.
-4*p**3*(p - 2)
Let d(x) be the second derivative of 0 + 15*x + 23/18*x**3 - 5/36*x**4 + 5/3*x**2. Factor d(r).
-(r - 5)*(5*r + 2)/3
Let g(q) = -q**3 + 4*q**2 - 4*q - 10. Suppose 6*d + 13 + 17 = 0. Let i(t) = -t**2 - t - 1. Let h(f) = d*g(f) + 5*i(f). Factor h(m).
5*(m - 3)**2*(m + 1)
Factor 115*u**2 - 6*u + 5577/4*u**4 + 0 + 2197/4*u**5 - 1443/2*u**3.
u*(u + 3)*(13*u - 2)**3/4
Let b(m) be the third derivative of 1/336*m**8 + 0*m + 0*m**3 - 1/210*m**7 - 1/120*m**6 + 0 + 1/60*m**5 + 0*m**4 + 2*m**2. Suppose b(p) = 0. Calculate p.
-1, 0, 1
Let q(i) be the second derivative of -i**7/70 + 17*i**6/50 - 141*i**5/50 + 111*i**4/10 - 45*i**3/2 + 243*i**2/10 - 3*i + 1. Solve q(d) = 0 