12 - k**2. Let n(p) be the second derivative of y(p). Factor n(z).
z*(4*z - 1)**2/2
Let b(a) be the second derivative of -a**4/4 - a**3 - 3*a**2/2 - 3*a. Suppose b(j) = 0. Calculate j.
-1
Let r(z) be the second derivative of -1/10*z**4 + 0*z**3 + 0*z**2 - z - 3/100*z**5 + 0. Factor r(g).
-3*g**2*(g + 2)/5
Let v(x) = -x**5 - x**3 + x**2 - 1. Let c(f) = -4*f**5 + f**3 + 5*f**2 - f**2 - 3 + 0*f**4 - f**4 - 3*f**3. Let h(p) = -2*c(p) + 6*v(p). Factor h(o).
2*o**2*(o - 1)*(o + 1)**2
Let y(f) be the first derivative of -2*f**5/5 + f**4 - 2*f**3/3 + 4. Determine a, given that y(a) = 0.
0, 1
Determine w so that 0 - 2/13*w**2 - 22/13*w**4 - 6/13*w**5 - 22/13*w**3 + 4/13*w = 0.
-2, -1, 0, 1/3
Let u(y) be the first derivative of 1/8*y**6 + 1/8*y**2 + 1/6*y**3 - 1/4*y**4 + 0*y - 1/10*y**5 - 6. Find l such that u(l) = 0.
-1, -1/3, 0, 1
Let o be 6/12 - 25/(-70). Factor -o*n + 4/7 + 2/7*n**2.
2*(n - 2)*(n - 1)/7
Let g(b) be the third derivative of 4*b**5/15 - 13*b**4/6 + 2*b**3 - 16*b**2. Suppose g(o) = 0. What is o?
1/4, 3
Let t(l) be the third derivative of l**7/1575 - l**5/75 + 2*l**4/45 - l**3/15 + 33*l**2 + 2. Factor t(h).
2*(h - 1)**3*(h + 3)/15
Let i(v) be the third derivative of -v**6/360 + v**5/120 + v**4/12 + v**3 + 2*v**2. Let t(z) be the first derivative of i(z). Determine s, given that t(s) = 0.
-1, 2
Let g(r) = r**2 + 3*r - 2. Let v(t) = -t. Let f(l) = -g(l) - 4*v(l). Factor f(z).
-(z - 2)*(z + 1)
Let j(h) be the second derivative of -h**7/1260 + h**5/60 + h**4/4 - 3*h. Let i(o) be the third derivative of j(o). What is t in i(t) = 0?
-1, 1
Let r(z) be the second derivative of -z**7/273 + z**6/195 + 3*z**5/130 - 5*z**4/78 + 2*z**3/39 - 7*z. Determine o, given that r(o) = 0.
-2, 0, 1
Factor -2*a**4 - 8/5*a**2 + 0 + 0*a + 10*a**5 - 32/5*a**3.
2*a**2*(a - 1)*(5*a + 2)**2/5
Let s be 0 + 4/(-1680)*-4. Let v(z) be the third derivative of 0 + 1/3*z**4 - s*z**7 - 1/30*z**6 + z**2 - 4/3*z**3 + 1/10*z**5 + 0*z. Factor v(f).
-2*(f - 1)**2*(f + 2)**2
Let g(a) = -9*a**2 + 15*a + 20. Let k(y) = -4*y**2 + 8*y + 10. Let f(u) = 3*g(u) - 7*k(u). Let c be f(12). Factor p**2 - 2 + c*p - 4*p + 3*p.
(p - 1)*(p + 2)
Factor 1/3*s + s**3 - s**2 - 1/3*s**4 + 0.
-s*(s - 1)**3/3
Factor -2/3 + 8/9*l - 8/9*l**3 + 2/9*l**4 + 4/9*l**2.
2*(l - 3)*(l - 1)**2*(l + 1)/9
Let j = -156 - -93. Let s = j + 445/7. Find r such that -2/7 + s*r - 2/7*r**2 = 0.
1
Let w = -1 - -3. Let c be (10/8)/((125/(-5))/(-5)). Determine d so that -c - 1/4*d**w + 1/2*d = 0.
1
Let f(n) = -10*n**4 + 6*n**3 + 4*n**2 - 7*n + 7. Let a(t) = -7*t**4 + 4*t**3 + 3*t**2 - 5*t + 5. Let l = 8 + -15. Let o(z) = l*a(z) + 5*f(z). Factor o(c).
-c**2*(c - 1)**2
Let o be 12/7 + (-4)/(-14). Let a(u) be the third derivative of 0*u + 0*u**3 + 3*u**o - 1/24*u**4 + 1/60*u**5 + 0. Solve a(y) = 0 for y.
0, 1
Let a(d) be the third derivative of d**6/10 + d**5/15 - 4*d**4/3 + 8*d**3/3 + 11*d**2. Suppose a(q) = 0. Calculate q.
-2, 2/3, 1
Let n(l) = -l**2 + 5*l - 4. Let y be n(4). Let 0 + y*m**2 + 1/3*m**5 - 1/3*m**4 + 0*m + 0*m**3 = 0. What is m?
0, 1
Let v(u) be the first derivative of -u**6/45 + 2*u**5/75 + u**4/30 - 2*u**3/45 + 1. Factor v(h).
-2*h**2*(h - 1)**2*(h + 1)/15
Let d(o) = o + 8. Let y be d(-5). Suppose y*g - 6 = -0. Factor 0 - 1/6*x**3 - 2/3*x - 2/3*x**g.
-x*(x + 2)**2/6
Suppose -4*p + 18 = -26. Suppose 5*g - p = 4*r, 2*r - 1 + 11 = 4*g. Determine h so that 3*h**4 + 0*h**4 - 5*h**4 - 2*h**2 - 4*h**g = 0.
-1, 0
Factor -2/3*a**2 - 32/9*a + 4/3*a**3 + 2/9*a**4 + 8/3.
2*(a - 1)**2*(a + 2)*(a + 6)/9
Let k(c) be the second derivative of -c**6/180 + c**5/60 - c**3/6 + c. Let l(p) be the second derivative of k(p). Factor l(o).
-2*o*(o - 1)
Let p(g) = 3*g**4 + 43*g**3 + 112*g**2 + 2*g - 160. Let t(u) = -u**4 - u**3 + u**2 + u. Let n(r) = -p(r) + 2*t(r). Factor n(q).
-5*(q - 1)*(q + 2)*(q + 4)**2
Let r = -2 + 2. Suppose 5*f = r, -p + 3*p + f = 0. Determine c so that p + 0*c - 2/5*c**2 = 0.
0
Let t(w) be the first derivative of 0*w**2 + 0*w + 1/6*w**3 - 2. Factor t(v).
v**2/2
Let i(z) be the third derivative of -1/300*z**5 - 1/60*z**4 + 0 - 2*z**2 + 0*z**3 + 0*z. Solve i(t) = 0 for t.
-2, 0
Let m(c) be the second derivative of -c**5/60 - c**4/12 - c**3/9 - 5*c. Factor m(a).
-a*(a + 1)*(a + 2)/3
Let w(n) be the third derivative of -n**8/112 - n**7/35 + 75*n**2. Factor w(t).
-3*t**4*(t + 2)
Suppose j + 12 = -5*l + l, 0 = 2*j - 2*l - 6. Factor -2/7*x**4 + 2/7*x**3 + j + 0*x**2 + 0*x.
-2*x**3*(x - 1)/7
Let k(n) = -2*n**2 - 6*n - 7. Let o(v) = -4*v**2 - 12*v - 13. Let b = 11 + -8. Let q(a) = b*o(a) - 5*k(a). Find h such that q(h) = 0.
-2, -1
Let b = 14 - 9. Let x(r) = 3*r**3 + 9*r**2 - 1 + 0*r + 4*r - 2*r + b*r**3. Let o(k) = k**3 - 1. Let i(j) = -o(j) + x(j). Factor i(a).
a*(a + 1)*(7*a + 2)
Let y(l) be the third derivative of l**8/168 - l**7/35 + l**6/60 + l**5/10 - l**4/6 - 6*l**2. Factor y(h).
2*h*(h - 2)*(h - 1)**2*(h + 1)
Let p(k) = 25*k**5 + 40*k**4 + 8*k**3 - 7*k**2 - 7*k + 7. Let m(l) = -13*l**5 - 20*l**4 - 4*l**3 + 3*l**2 + 3*l - 3. Let r(d) = -7*m(d) - 3*p(d). Factor r(q).
4*q**3*(q + 1)*(4*q + 1)
Let m(l) = -7*l**2 - 48*l + 9. Let t(w) = -2*w**2 - 12*w + 2. Let g(f) = -2*m(f) + 9*t(f). Factor g(a).
-4*a*(a + 3)
Let o(t) = -t**2 - 20*t - 27. Let z = 4 - 6. Let k(l) = 21*l + 27. Let r(x) = z*k(x) - 3*o(x). Determine h so that r(h) = 0.
-3
Let h(n) be the first derivative of -n**8/840 - n**7/420 + n**6/180 + n**5/60 - 4*n**3/3 + 2. Let p(o) be the third derivative of h(o). Factor p(s).
-2*s*(s - 1)*(s + 1)**2
Let i = 6 - 1. Suppose u + i*u**2 - u**2 - 5*u**2 = 0. What is u?
0, 1
Let r(h) = -h**3 + 4*h**2 - 3*h - 3. Let p be r(4). Let a be ((-36)/p - 2) + 0. Solve 0 - a*l**2 - 2/5*l = 0 for l.
-1, 0
Let m(d) be the second derivative of -3/25*d**5 - 1/210*d**7 - 2/15*d**4 - 1/25*d**6 + 0*d**2 - 9*d + 0 + 0*d**3. Factor m(n).
-n**2*(n + 2)**3/5
Let f be (1260/8)/(-15)*(-4)/24. Factor 5/4*m**3 + 1/4*m**4 + 0 + f*m**2 + 3/4*m.
m*(m + 1)**2*(m + 3)/4
Suppose 2*g = 2*a - 2, -12 = -3*g - a - 3. Find s, given that -4/11*s**g + 2/11*s**5 + 0*s**3 - 2/11*s + 4/11*s**4 + 0 = 0.
-1, 0, 1
Let k(c) be the first derivative of 8*c**4/11 + 16*c**3/33 + c**2/11 - 21. Find p, given that k(p) = 0.
-1/4, 0
Let w(y) = -3*y**5 - 4*y**4 - 5*y**3 + 9*y**2 - 2*y. Let k(c) = 2*c**5 + 4*c**4 + 4*c**3 - 8*c**2 + 2*c. Let g(b) = 5*k(b) + 4*w(b). Factor g(q).
-2*q*(q - 1)**3*(q + 1)
Let l(r) be the second derivative of 0 - 3*r - 1/10*r**5 - 9*r**2 - r**3 + 5/6*r**4. Factor l(z).
-2*(z - 3)**2*(z + 1)
Let f(o) = o**3 + 6*o**2 + 2. Let i = 8 + -14. Let l be f(i). Determine a, given that 0*a**4 + l*a**2 - 3*a**4 + a**4 = 0.
-1, 0, 1
Let x(y) be the third derivative of 0*y - 3*y**2 + 0 + 0*y**3 - 1/330*y**5 - 1/132*y**4. Let x(k) = 0. Calculate k.
-1, 0
Let x = -1 + 5. Suppose -10 = -x*a - a. Factor a*h - h**5 - 5*h**3 + 3*h**5 + h**3.
2*h*(h - 1)**2*(h + 1)**2
Let y = 6/35 - -2/5. Factor -2/7*k + 4/7*k**3 + y*k**2 - 2/7*k**5 - 2/7*k**4 - 2/7.
-2*(k - 1)**2*(k + 1)**3/7
Factor 3*k**2 + 0 - 9/2*k**4 - 3/2*k**3 + 0*k.
-3*k**2*(k + 1)*(3*k - 2)/2
Let 31*y**4 + 8*y**3 - 25*y**4 + 14*y**4 = 0. What is y?
-2/5, 0
Let a(r) be the first derivative of -4*r**5/5 + 6*r**4 - 44*r**3/3 + 12*r**2 - 31. Determine t, given that a(t) = 0.
0, 1, 2, 3
Determine r, given that 0 + 3/4*r**4 + 0*r**3 - 3/4*r**2 + 0*r = 0.
-1, 0, 1
Factor -19*b**2 - 20 + 20*b + 20*b**2 - 6*b**2.
-5*(b - 2)**2
Let w = 3665594 + -4618649443/1260. Let j = 1/252 - w. Suppose -2/5*p**4 + 0*p**2 + 2/5 - 4/5*p**3 + j*p = 0. Calculate p.
-1, 1
Suppose -16 = n + 8. Let p be 2/(-10)*40/n. Determine o so that -1/3*o**2 + p + 0*o = 0.
-1, 1
Let m(v) be the second derivative of v**5/10 - 7*v**4/6 + 5*v**3 - 9*v**2 + 23*v. What is f in m(f) = 0?
1, 3
Let b(f) be the third derivative of 0*f - 1/3*f**3 - 5*f**2 + 0 - 1/60*f**6 - 1/4*f**4 - 1/10*f**5. Factor b(y).
-2*(y + 1)**3
Suppose 4*a + 4 = 16. Factor 6*j - 27 - 32*j + a*j - 3*j**2 + 5*j.
-3*(j + 3)**2
Let t(i) be the third derivative of -i**6/24 - 5*i**5/12 - 5*i**4/4 + 38*i**2. Let t(j) = 0. Calculate j.
-3, -2, 0
Factor -1/3*p**5 + 0*p**3 + 0*p + 0*p**4 + 0*p**2 + 0.
-p**5/3
Let j(n) be the third derivative of -1/672*n**8 + 0*n**3 + 0*n**7 - 1/48*n**4 + 0*n**5 - n**2 + 1/120*n**6 + 0 + 0*n. Solve j(l) = 0.
-1, 0, 1
Let a(r) be the first derivative of -r