f.
-1, 0, 1
Let f(s) be the second derivative of -s**6/210 - s**5/70 + s**4/21 + 4*s**3/21 - 33*s. Factor f(x).
-x*(x - 2)*(x + 2)**2/7
Let z(s) be the second derivative of -s**8/840 - 17*s**7/1260 - s**6/18 - s**5/15 - 5*s**4/12 - 3*s. Let g(p) be the third derivative of z(p). Factor g(b).
-2*(b + 2)**2*(4*b + 1)
Let a(r) be the third derivative of 1/120*r**5 + 0*r**3 - 3*r**2 + 0 + 0*r**4 + 0*r. Factor a(k).
k**2/2
Suppose -29 + 4 = -5*p. Factor 4 - 6*f - 4*f**p + 4*f**3 - 4*f**2 + 2*f**5 + 4*f**3.
-2*(f - 1)**3*(f + 1)*(f + 2)
Let k(b) = -46*b**5 + 129*b**4 - 109*b**3 + 39*b**2 - b. Let h(y) = 47*y**5 - 128*y**4 + 109*y**3 - 38*y**2 + 2*y. Let i(a) = -3*h(a) - 2*k(a). Factor i(c).
-c*(c - 1)**2*(7*c - 2)**2
Let o be (-4)/10 - 24/(-10). Find j, given that 2*j + 1 + 3*j**o - j**2 + 1 - 6 = 0.
-2, 1
Let h(g) be the third derivative of 0*g**5 + 0*g**3 + 0 + 0*g + 0*g**4 + 1/70*g**7 - 1/160*g**6 + 6*g**2. Solve h(b) = 0.
0, 1/4
Factor 2/7*d + 2/7*d**2 + 0.
2*d*(d + 1)/7
Let a be 3/(-4) + 75/20. Find k, given that -6*k**3 + 2*k**3 + k**3 + 12*k + 8 - k**a = 0.
-1, 2
Suppose -3*v + 6 = 5*y, -5*y = -4*v + 7 + 1. Factor 1/2*m**2 + 0*m + y.
m**2/2
Let r(f) be the third derivative of f**8/70560 - f**6/2520 - f**5/20 + f**2. Let u(q) be the third derivative of r(q). Factor u(i).
2*(i - 1)*(i + 1)/7
Let v(j) be the third derivative of -j**6/720 - j**5/180 - j**4/144 + 9*j**2. Factor v(f).
-f*(f + 1)**2/6
Let y(p) = p**2 + 22*p + 24. Let f(q) = q**2. Let d(a) = 3*f(a) - y(a). Suppose d(k) = 0. Calculate k.
-1, 12
Let m(x) be the second derivative of x**7/420 - x**5/20 - x**4/6 - x**3/6 + 4*x. Let a(w) be the second derivative of m(w). Factor a(r).
2*(r - 2)*(r + 1)**2
Let j(y) be the third derivative of 0*y**4 + 0*y + 1/20*y**6 + 1/20*y**5 + 1/70*y**7 - 7*y**2 + 0*y**3 + 0. Factor j(m).
3*m**2*(m + 1)**2
Let q(o) = o**3 - o**2 + o. Let a(t) = -2*t**4 + 36*t**3 - 196*t**2 + 516*t - 512. Let v(r) = -a(r) + 4*q(r). Solve v(f) = 0 for f.
4
Find i, given that 0 + 1/8*i**3 - 1/8*i + 1/8*i**2 - 1/8*i**4 = 0.
-1, 0, 1
Let j(r) be the third derivative of r**5/105 + 5*r**4/42 + 12*r**2. Factor j(x).
4*x*(x + 5)/7
Let d(k) be the second derivative of -1/25*k**5 + 0 - k + 1/30*k**4 + 0*k**2 + 0*k**3 + 1/75*k**6. Factor d(p).
2*p**2*(p - 1)**2/5
Let b(x) be the third derivative of -x**5/20 + 3*x**4/8 - x**3 - 15*x**2. Factor b(p).
-3*(p - 2)*(p - 1)
Suppose d - 5*d = 0. Suppose d = -m + 6*m. Find f such that 0*f + 0*f**3 + m - 2/5*f**4 + 0*f**2 + 2/5*f**5 = 0.
0, 1
Let y(g) = -g + 7. Let i be y(3). Find w, given that -1/4*w**i + 0*w**2 + 0*w + 0*w**3 + 0 = 0.
0
Let m(k) = 4*k**4 + 6*k**3 - 5*k**2 - 5. Let t(g) = -3*g**4 - 5*g**3 + 4*g**2 + 4. Let r = 4 + 1. Let y(d) = r*t(d) + 4*m(d). Solve y(o) = 0 for o.
0, 1
Let m(h) = h - 6. Let x = -4 + 10. Let s be m(x). Suppose 1/6*y**2 + 1/6*y**3 + 0*y + s = 0. Calculate y.
-1, 0
Let t(p) be the second derivative of -p**4/3 - 80*p**3/9 - 26*p**2/3 + p + 20. Determine a, given that t(a) = 0.
-13, -1/3
Let h be (-30)/4*12/(-18). Let p(u) be the third derivative of 0*u - 2/15*u**3 - 49/300*u**h + 7/30*u**4 + 0 - u**2. Factor p(b).
-(7*b - 2)**2/5
Let u(x) be the second derivative of x**4/66 + x**3/33 - 2*x**2/11 + 6*x. Suppose u(f) = 0. Calculate f.
-2, 1
Let m(h) be the first derivative of 1/5*h + 1/5*h**2 - 3 + 0*h**3 - 1/10*h**4 - 1/25*h**5. Solve m(x) = 0 for x.
-1, 1
Let h(p) be the second derivative of -p**8/10080 - p**7/3780 - p**4/4 - p. Let q(t) be the third derivative of h(t). Factor q(b).
-2*b**2*(b + 1)/3
Let l(a) be the first derivative of 25*a**3/2 + 45*a**2/2 + 27*a/2 + 21. Factor l(z).
3*(5*z + 3)**2/2
Let a(s) be the first derivative of s**3 - 3*s**2/2 - 1. Solve a(o) = 0 for o.
0, 1
What is u in -4/5*u + 0 + 14/5*u**2 - 18/5*u**3 + 2*u**4 - 2/5*u**5 = 0?
0, 1, 2
Let u(f) be the second derivative of -1/3*f**3 + 0 - f - 1/24*f**4 - f**2. Let u(x) = 0. Calculate x.
-2
Let m(u) be the second derivative of u**7/21 - u**6/15 - u**5/5 + u**4/3 + u**3/3 - u**2 - 9*u. Factor m(v).
2*(v - 1)**3*(v + 1)**2
Let y(k) be the first derivative of 1 + 98/5*k**5 - 14*k**4 + 0*k**2 + 8/3*k**3 + 0*k. Factor y(p).
2*p**2*(7*p - 2)**2
Suppose -z = -2*z + 2. Let l be (-2)/(-2 + -1 + z). Factor -l*f - 4 - f - f**2 - f.
-(f + 2)**2
Factor 2/3*t**3 + 4/9*t + 0 - 14/9*t**2.
2*t*(t - 2)*(3*t - 1)/9
Suppose f + 6 = 4*f. Let n be f + 1 + 14/(-6). Determine g, given that 0 + n*g + 1/3*g**2 = 0.
-2, 0
Let a(z) be the first derivative of 1/90*z**5 - 1/180*z**6 + 1/36*z**4 - 1/9*z**3 + z**2 + 0*z + 2. Let v(y) be the second derivative of a(y). Factor v(s).
-2*(s - 1)**2*(s + 1)/3
Let a(t) = 40*t**4 - 30*t**3 - 61*t**2 + 19*t + 10. Let r(u) = 8*u**4 - 6*u**3 - 12*u**2 + 4*u + 2. Let d(z) = 2*a(z) - 11*r(z). Suppose d(s) = 0. What is s?
-1, -1/4, 1
Suppose -248 = 3*w - 2*p, 0 = -0*p - p + 4. Let c = w - -562/7. Factor c*n + 4/7 - 2/7*n**2.
-2*(n - 2)*(n + 1)/7
Solve -3*x**2 + 0 - 4/5*x + 2/5*x**5 - 3/5*x**4 - 16/5*x**3 = 0.
-1, -1/2, 0, 4
Let k = 718 - 43079/60. Let n(m) be the third derivative of 0*m**3 + 0*m - 1/24*m**4 + 0 + m**2 - k*m**5. Factor n(x).
-x*(x + 1)
Determine p, given that -3/2 - 1/2*p**3 - 5/2*p**2 - 7/2*p = 0.
-3, -1
Suppose -23*x = -27*x. Factor -3/2*o**2 - 3/2*o + x.
-3*o*(o + 1)/2
Let l(i) be the second derivative of 3*i + 0*i**2 + 1/6*i**3 + 0 - 9/20*i**5 + 0*i**4. Factor l(h).
-h*(3*h - 1)*(3*h + 1)
Let -4/17*s**3 + 0*s**2 + 2/17 + 4/17*s - 2/17*s**4 = 0. Calculate s.
-1, 1
Let q(f) be the third derivative of f**7/70 - f**5/10 + f**3/2 + 14*f**2. What is g in q(g) = 0?
-1, 1
Factor 0*w + 2/13*w**2 + 2/13*w**3 + 0.
2*w**2*(w + 1)/13
Suppose 2*v + 4*v**4 - 8*v**2 + 4*v**2 + 2*v**5 - 4*v**5 = 0. What is v?
-1, 0, 1
Suppose -3*i + 6*i - 4*m = -1, -i + 3*m - 2 = 0. Suppose 26 = 3*s - z, -2*s + z - 46 = -7*s. Factor -4*b**3 - 12*b + 3*b**3 - i + s + 6*b**2.
-(b - 2)**3
Let v = 16 - 12. Factor 3*l**4 - l**4 + v*l**4 - 3*l**4 - 3*l**5.
-3*l**4*(l - 1)
Factor 2/9 + 2/9*z**2 - 4/9*z.
2*(z - 1)**2/9
Let j(f) = 3*f**2 - f. Let d be j(1). Let -3 + 6*y - y**2 + d*y**2 - 4*y**2 = 0. What is y?
1
Let m(f) = -f**3 - 7*f**2 - 9*f. Let t be m(-6). Factor p**4 + 7*p - 16*p**2 + t - 3*p**4 + 0*p + 5*p - 12*p**3.
-2*(p - 1)*(p + 1)*(p + 3)**2
Let f(q) be the third derivative of q**5/42 + q**4/28 - 16*q**2. Determine d, given that f(d) = 0.
-3/5, 0
Factor -2*h**3 + 0*h + 35/2*h**5 + 0*h**2 + 0 - 2*h**4.
h**3*(5*h - 2)*(7*h + 2)/2
Let u(r) be the third derivative of r**7/210 + r**6/120 - r**5/60 - r**4/24 - 16*r**2. Factor u(g).
g*(g - 1)*(g + 1)**2
Let a be 2/((-4)/3 + 2). Suppose 0*r = a*r - 9. Find j such that 12/7*j**2 + 8/7*j**r - 16/7*j**4 + 6/7*j**5 + 4/7 - 2*j = 0.
-1, 2/3, 1
Let o(k) be the first derivative of 1/3*k**3 + 1 + k**2 - 1/6*k**4 + 0*k - 1/240*k**6 + 1/24*k**5. Let w(n) be the second derivative of o(n). Factor w(r).
-(r - 2)**2*(r - 1)/2
Let h(i) be the first derivative of -i**8/1344 + i**7/840 + i**6/480 - i**5/240 - 2*i**2 + 3. Let f(x) be the second derivative of h(x). Factor f(u).
-u**2*(u - 1)**2*(u + 1)/4
Let u(c) be the second derivative of -1/20*c**5 - 1/6*c**4 + 0 - 3*c + 1/6*c**3 + c**2. Factor u(w).
-(w - 1)*(w + 1)*(w + 2)
Let r(a) be the third derivative of a**6/840 - a**5/105 - 11*a**4/168 - a**3/7 + 14*a**2. Factor r(l).
(l - 6)*(l + 1)**2/7
Let i(k) be the third derivative of k**5/36 + k**4/6 + 2*k**3/9 + 36*k**2. Let i(w) = 0. Calculate w.
-2, -2/5
Suppose 0 = n - 0*n - 3. Suppose n*z = 6*z - 15. Factor -2*k + 2*k**5 - 5*k**2 + k**2 + 0*k**z + 4*k**4.
2*k*(k - 1)*(k + 1)**3
Let i be -3 - (18/(-24))/((-3)/(-12)). Factor 2/3*s**2 + i*s**3 - 2/3*s**4 + 0 + 0*s.
-2*s**2*(s - 1)*(s + 1)/3
Let q(v) be the second derivative of -49*v**4/6 + 28*v**3/3 - 4*v**2 + 3*v. Factor q(b).
-2*(7*b - 2)**2
Factor 0 + 0*z**2 - 7/6*z**4 + 1/3*z**3 + 0*z.
-z**3*(7*z - 2)/6
Let d(k) be the third derivative of -k**8/840 + k**6/150 - k**4/60 + 6*k**2. What is o in d(o) = 0?
-1, 0, 1
Let z(k) be the second derivative of k**5/90 + 3*k**2/2 + 9*k. Let j(o) be the first derivative of z(o). Find d such that j(d) = 0.
0
Factor -3*o**2 + 3 - 4 + 3 - 4 + 7*o.
-(o - 2)*(3*o - 1)
Let v(g) be the third derivative of 0 - 2/3*g**3 + 0*g - 1/10*g**5 - 5/12*g**4 + 1/105*g**7 - 2*g**2 + 1/60*g**6. Factor v(x).
2*(x - 2)*(x + 1)**3
Let w(d) be the