of k(w). Factor f(g).
3*g*(g - 1)*(g + 1)
Let u(v) be the third derivative of v**7/735 + v**6/140 + v**5/210 - v**4/28 - 2*v**3/21 + 19*v**2. Factor u(s).
2*(s - 1)*(s + 1)**2*(s + 2)/7
Let g(h) be the second derivative of h**5/180 - h**4/24 - 5*h**2/2 - 8*h. Let a(n) be the first derivative of g(n). Factor a(p).
p*(p - 3)/3
Let s(y) be the third derivative of 5*y**5/4 - 15*y**4/4 + 9*y**3/2 + 5*y**2. Find u such that s(u) = 0.
3/5
Let c(r) be the third derivative of -r**6/40 - r**5/8 - r**4/8 + 11*r**2. Factor c(w).
-3*w*(w + 2)*(2*w + 1)/2
Factor 0 + 285/11*v**3 - 64/11*v**2 - 225/11*v**4 + 4/11*v.
-v*(v - 1)*(15*v - 2)**2/11
Let h(f) be the second derivative of 2*f**7/7 - f**6/3 + f**5/10 - f. Factor h(w).
2*w**3*(2*w - 1)*(3*w - 1)
Let p be 2/7 + 80/14. Factor 3*o - 10*o**2 - 6 + p*o + 7*o**2.
-3*(o - 2)*(o - 1)
Let m(f) be the second derivative of 2*f**5/5 + 17*f**4/6 + 20*f**3/3 + 4*f**2 - 6*f. Factor m(v).
2*(v + 2)**2*(4*v + 1)
Let a(q) be the second derivative of q**5/30 + q**4/12 + 2*q**2 + 4*q. Let i(o) be the first derivative of a(o). Factor i(p).
2*p*(p + 1)
Let g(y) be the first derivative of y**6/6 - 2*y**5/5 + y**4/4 + 6. Suppose g(k) = 0. What is k?
0, 1
Let y(a) be the first derivative of -1 - 2*a - a**2 - 1/6*a**3. Solve y(b) = 0 for b.
-2
Let p be (-7)/1*(-4)/14. Factor 2*u**3 + 2*u - p*u**2 + 2 - 1 - 4*u + 1.
2*(u - 1)**2*(u + 1)
Suppose 10 = 3*f + a, 8 = 2*f + 4*a - 12. Find v, given that -8/3 - 8/3*v - 2/3*v**f = 0.
-2
Factor -7/6*n - 1/3 - 4/3*n**2 - 1/2*n**3.
-(n + 1)**2*(3*n + 2)/6
Let u(p) be the third derivative of -p**5/300 - p**4/4 - 15*p**3/2 - 47*p**2. Solve u(f) = 0 for f.
-15
Let v(m) = m**3 - 13*m**2 + 5. Let w be v(13). Let h(s) be the first derivative of 1/15*s**w + 0*s**4 + 0*s + 0*s**2 + 1 - 1/9*s**3. Let h(i) = 0. Calculate i.
-1, 0, 1
Suppose -4/5*v + 2/5*v**4 + 4/5*v**3 + 0*v**2 - 2/5 = 0. What is v?
-1, 1
Let d(b) = -b**2 + 1. Let h(w) = -w**2 + 1. Let f(n) = 2*d(n) + h(n). Factor f(k).
-3*(k - 1)*(k + 1)
Let q = -880/9 - -98. Find m such that 2/9*m**2 + 0 - q*m = 0.
0, 1
Let w be 98/8 + (-5)/20. Suppose 25*v + 2*v**3 - 7*v + w*v**2 + 16 + 6*v = 0. Calculate v.
-2
Factor 2/7*s - 2/7*s**3 - 4/7 + 4/7*s**2.
-2*(s - 2)*(s - 1)*(s + 1)/7
Let p be (-4)/24 - (203/(-12))/7. Suppose 15/2*n**4 - p*n**5 + 3*n - 9/4*n**3 - 9*n**2 + 0 = 0. What is n?
-1, 0, 1/3, 2
Let b be 9/(-54)*(-3 + 1). Let q(a) be the first derivative of -4/3*a - b*a**2 - 1 + 2/9*a**3. Solve q(h) = 0 for h.
-1, 2
Suppose 13 = v - 2*t, 4*v + v - 2*t - 25 = 0. Suppose -1/3*f**2 - 2/3*f**v + 1/3 + 2/3*f = 0. Calculate f.
-1, -1/2, 1
Let t(k) be the third derivative of -k**5/12 - 5*k**4/8 + 9*k**2. Let t(v) = 0. Calculate v.
-3, 0
Solve 8*v**3 - 7*v**4 - 3*v**3 - v**4 + 3*v**4 = 0.
0, 1
What is v in 0*v - 1/3*v**2 + 1/3 = 0?
-1, 1
Factor 9*k - 10*k**3 + 6*k**2 + 111*k**5 - 108*k**5 - 6 - 2*k**3.
3*(k - 1)**3*(k + 1)*(k + 2)
Let o(r) be the third derivative of r**6/1440 + r**5/240 - r**3/2 + 3*r**2. Let z(m) be the first derivative of o(m). Solve z(b) = 0.
-2, 0
Let u(t) be the first derivative of -t**7/126 - t**6/90 + t**5/20 + 5*t**4/36 + t**3/9 - 3*t + 7. Let v(l) be the first derivative of u(l). Solve v(q) = 0.
-1, 0, 2
Let w(d) be the third derivative of -1/1260*d**7 + 0*d**6 + 1/360*d**5 + 0*d + 2*d**2 + 0 + 0*d**3 + 0*d**4. Factor w(f).
-f**2*(f - 1)*(f + 1)/6
Suppose 2*v + 0*v = 0. Suppose -4*p + p + 15 = 0. Find q, given that -1/3*q**2 + v - q**3 + 0*q - q**4 - 1/3*q**p = 0.
-1, 0
Let g(k) be the third derivative of -k**7/1680 - k**6/360 - k**5/240 + k**3/6 - k**2. Let i(w) be the first derivative of g(w). Solve i(c) = 0.
-1, 0
Let j(h) be the third derivative of -h**6/360 + h**5/30 - 3*h**2. Factor j(t).
-t**2*(t - 6)/3
Let u(w) be the second derivative of -w**6/60 + w**5/10 + w**4/12 - w**3 - 9*w**2/4 - 4*w. Suppose u(j) = 0. What is j?
-1, 3
Suppose 3*j = 100 - 19. Factor 10 - 6*q - 10 + j*q**2.
3*q*(9*q - 2)
Let h(f) be the third derivative of -f**6/900 + f**5/300 - f**3/3 - f**2. Let y(x) be the first derivative of h(x). Factor y(u).
-2*u*(u - 1)/5
Let s be (32/24)/((-2)/6). Let t(o) = o**2 - o + 1. Let i(u) = 6*u**2 - 6*u + 4. Let c(y) = s*t(y) + i(y). Factor c(v).
2*v*(v - 1)
Suppose 0 = 3*y - a + 5, 0*a + 2*a = y + 10. Let g be 1/(-6)*-4 - y. Factor -2/3 - 4*q**2 - 8/3*q - g*q**4 - 8/3*q**3.
-2*(q + 1)**4/3
Determine a so that -6*a + 4*a**2 - 6*a**2 + 2*a = 0.
-2, 0
Let b(a) be the third derivative of -a**7/210 + a**6/90 + a**5/90 - a**4/18 + a**3/18 + 28*a**2. Determine o, given that b(o) = 0.
-1, 1/3, 1
Let u(h) be the first derivative of -h**3/6 + h**2 - 3*h/2 - 9. Suppose u(m) = 0. Calculate m.
1, 3
Let n(c) be the second derivative of c**4/21 + 8*c**3/21 + 6*c**2/7 + 6*c. Let n(k) = 0. Calculate k.
-3, -1
Let t(x) be the third derivative of -x**5/60 + x**4/24 - 6*x**2. Factor t(h).
-h*(h - 1)
Factor 8*u**4 + 3*u**2 + 2*u**4 + 0*u**2 + 6*u**3 - 7*u**4.
3*u**2*(u + 1)**2
Let i(u) be the first derivative of -5*u**6/144 + u**5/12 - u**4/12 + u**3/3 - 6. Let k(b) be the third derivative of i(b). Factor k(r).
-(5*r - 2)**2/2
Let m(d) be the third derivative of -1/840*d**8 + 1/105*d**7 + 0 + 1/15*d**3 + 3*d**2 - 1/30*d**6 + 1/15*d**5 + 0*d - 1/12*d**4. Factor m(t).
-2*(t - 1)**5/5
Let d(s) = -s**2 + 8*s - 9. Let h be d(7). Let t be (h/1)/((-1)/12). Factor 20*o**2 + 16/3 + 50/3*o**3 - t*o.
2*(o + 2)*(5*o - 2)**2/3
Let i(r) = 600*r**4 + 673*r**3 + 256*r**2 + 39*r. Let g(b) = -300*b**4 - 336*b**3 - 128*b**2 - 20*b. Let k(s) = -7*g(s) - 4*i(s). Factor k(d).
-4*d*(3*d + 1)*(5*d + 2)**2
Let s(g) = -5*g - 20. Let k be s(-4). Factor 1/6*z**4 + 1/6*z**3 - 1/6*z - 1/6*z**2 + k.
z*(z - 1)*(z + 1)**2/6
Solve -2/11*q**3 + 2/11*q + 2/11*q**2 + 0 - 2/11*q**4 = 0.
-1, 0, 1
Let x(g) = g - 7. Let u be x(11). Suppose u*a = a + 6. Factor -5*s + 0*s**2 + 2 + 0 + a*s**2.
(s - 2)*(2*s - 1)
Let y(b) be the first derivative of 0*b + 2 - 1/16*b**4 + 1/6*b**3 + 0*b**2. Suppose y(a) = 0. What is a?
0, 2
Suppose 2*n - 3*v - 14 = 8, 0 = -5*n - 2*v + 17. Suppose -i**3 + n*i**3 - 2*i**3 - 2*i = 0. Calculate i.
-1, 0, 1
Let a(j) be the second derivative of -8*j - 4*j**2 + j**4 + 0 - 10/3*j**3. Factor a(k).
4*(k - 2)*(3*k + 1)
Let j(x) = -1 + 1 + 0 - 1. Let v(r) = r**2 + 3*r - 1. Let m(w) = 6*j(w) - 2*v(w). Factor m(u).
-2*(u + 1)*(u + 2)
Let q(c) = 3*c**2 + 13*c + 1. Let k(n) = -n**2 + n + 1. Let g(w) = k(w) - q(w). Factor g(v).
-4*v*(v + 3)
Let u = 4 - -2. Factor -3 + 6*s + u + 29*s**2 - 26*s**2.
3*(s + 1)**2
Let r(c) be the second derivative of -c**5/60 + 5*c**4/36 - 7*c**3/18 + c**2/2 + 41*c. Factor r(m).
-(m - 3)*(m - 1)**2/3
Let f(s) be the second derivative of s**6/1440 + s**5/120 + s**4/24 - s**3/6 + 4*s. Let a(y) be the second derivative of f(y). Factor a(h).
(h + 2)**2/4
Let f = 78/5 + -151/10. Let l = 3 + -1. Find i, given that 1/2*i + f*i**l + 0 = 0.
-1, 0
Let w = 523 - 521. Suppose -32/5*k + 14/5*k**w + 8/5 = 0. Calculate k.
2/7, 2
Let a(o) = 4*o**2 + 4*o - 7. Suppose 3*c - 5*c + 2 = 0. Let k(n) = 0 + c - 3*n - 3*n**2 + 4. Let l(m) = -5*a(m) - 7*k(m). Factor l(j).
j*(j + 1)
Let k(n) be the second derivative of n**4/12 - n**3 + 3*n**2/2 - 2*n. Let m be k(6). Find d, given that -3*d + d + 3*d - d**m = 0.
-1, 0, 1
Let s(y) be the second derivative of y**6/360 - y**5/30 + y**4/6 - 4*y**3/9 - y**2 - 3*y. Let b(k) be the first derivative of s(k). Suppose b(o) = 0. What is o?
2
Let l(j) = -j**2 + 6*j. Let n(t) = -t**3 + 2*t**2 + 2*t + 1. Let q be n(2). Let w be l(q). Factor -3*u**3 + 6*u**3 - u**w - u**4 - 2*u**3 + u**2.
-u**2*(u - 1)*(u + 1)**2
Let q be 24/18*6/4. Solve 2 - 24*j**q + 2 - 6*j + 0 - 14*j**3 = 0.
-1, 2/7
Determine u so that -12/5*u + 3 - 3/5*u**2 = 0.
-5, 1
Let y(r) be the second derivative of -r**6/180 - 2*r**3/3 + r. Let l(f) be the second derivative of y(f). Factor l(h).
-2*h**2
Let p(z) = 4*z**2 - 1. Let m be p(1). Suppose -m*v = -v. Factor a**2 + v*a**3 - 2*a**3 + a**2.
-2*a**2*(a - 1)
Let k be 0*(-1 - 9/(-6)). Let d**2 + k*d + d**3 + d**2 + d = 0. What is d?
-1, 0
Let o(n) be the first derivative of 3*n**4/32 - n**3/2 + 3*n**2/4 + 30. Factor o(l).
3*l*(l - 2)**2/8
Let y(o) be the first derivative of -o**6/15 + o**4/2 - 2*o**3/3 - 4*o + 1. Let t(p) be the first derivative of y(p). Factor t(g).
-2*g*(g - 1)**2*(g + 2)
Let o(y) = -y - 2