*4 - 8 - 4*h**3 + 7*h**4 - 14*h**2 + 7*h.
4*(h - 1)**3*(h + 2)
Suppose -14 = -3*w - 2. Factor -2 + 4 - 3*f**w + 2*f**3 - 3*f + f**5 + 6*f**4 - 3 - 2*f**2.
(f - 1)*(f + 1)**4
Let z(r) be the second derivative of 0 + 1/18*r**4 - 3/10*r**5 + 2/9*r**3 - 5/63*r**7 - 13/45*r**6 + 0*r**2 - 3*r. Factor z(o).
-2*o*(o + 1)**3*(5*o - 2)/3
Let m = -3 + 8. Factor -4*a**4 + 2*a**3 + 5*a**5 + 0*a**4 - 3*a**m.
2*a**3*(a - 1)**2
Let l(h) be the third derivative of -1/1344*h**8 + 0*h + 0*h**7 + 0*h**3 - 3*h**2 + 0*h**5 + 0*h**4 + 0 + 1/480*h**6. What is n in l(n) = 0?
-1, 0, 1
Factor 2*x**3 + 8*x**2 - 11*x**2 + x**3.
3*x**2*(x - 1)
Let g(z) be the third derivative of -z**9/20160 - z**8/6720 + z**7/840 - z**5/20 - 7*z**2. Let r(o) be the third derivative of g(o). Factor r(s).
-3*s*(s - 1)*(s + 2)
Let b(k) = -1. Let n(c) = -c**3 + c**2 - 1. Suppose -4*f - 1 - 3 = 0. Let r(a) = f*b(a) + n(a). Factor r(l).
-l**2*(l - 1)
Let w(y) = 2*y**2 + 98*y - 204. Let d be w(-51). Factor -2/3*t**3 - 2/3*t**4 + d + 2/3*t**2 + 2/3*t.
-2*t*(t - 1)*(t + 1)**2/3
Let w(b) be the first derivative of b**4/12 - b**3/9 - 2*b**2/3 + 4*b/3 - 5. Factor w(r).
(r - 2)*(r - 1)*(r + 2)/3
Factor -324/5*j**3 + 72*j**2 + 32/5 + 108/5*j**4 - 176/5*j.
4*(j - 1)*(3*j - 2)**3/5
Let n(v) be the third derivative of -v**7/735 + v**5/105 - v**3/21 + 3*v**2 - 1. What is z in n(z) = 0?
-1, 1
Let m(r) be the third derivative of r**8/26880 - r**7/5040 + r**6/2880 - r**4/6 + 4*r**2. Let a(j) be the second derivative of m(j). Let a(v) = 0. Calculate v.
0, 1
Suppose 0 = -7*s + 3*s + 16. Let -3*t**5 + 6*t**3 + 6*t**5 + 2*t**3 + t**3 - 3*t**2 - 9*t**s = 0. Calculate t.
0, 1
Let w(u) be the third derivative of -1/75*u**5 + 4*u**2 - 1/150*u**6 - 1/840*u**8 + 1/20*u**4 + 0*u + 0 - 1/15*u**3 + 1/175*u**7. Factor w(z).
-2*(z - 1)**4*(z + 1)/5
Let m(k) = -5*k**3 - k**2 + k. Let u be m(1). Let r = u - -7. Find t such that 2/5*t**3 - 4/5*t**r + 0 + 2/5*t = 0.
0, 1
Let x(o) be the third derivative of -3*o**2 + 1/240*o**6 + 0 - 1/60*o**5 + 1/48*o**4 + 0*o + 0*o**3. Let x(a) = 0. Calculate a.
0, 1
Let d = 3/106 - -191/742. Let x(m) be the second derivative of 0*m**4 + 3*m + 1/70*m**5 - 1/7*m**3 + d*m**2 + 0. Factor x(n).
2*(n - 1)**2*(n + 2)/7
Let a(m) be the first derivative of -4*m**2 - 8*m**2 + m**3 + 0*m**3 + 3*m**2 + 27*m - 2. Factor a(h).
3*(h - 3)**2
Suppose a + 11 = 4*i, 5*a + 5 + 16 = 3*i. Suppose r = -j - 4*r - 13, 2*j = i*r + 10. Solve 0*w + 0 + 0*w**j - 1/2*w**4 + 1/2*w**3 = 0.
0, 1
Let f(h) be the second derivative of -7*h**4/6 + 2*h**3/3 - 11*h. Determine r so that f(r) = 0.
0, 2/7
Let p(f) be the first derivative of -f**6/3 + 2*f**5 - 5*f**4 + 20*f**3/3 - 5*f**2 + 2*f + 15. Determine u so that p(u) = 0.
1
Let m be (-6)/(-4)*(-12)/(-6). Factor -3*g**3 - g**2 + 24*g**3 + 0*g**m - 5*g**2.
3*g**2*(7*g - 2)
Let p = -2566/15 - -171. Let b = p + 2/5. Solve -1/3*r**2 + 0*r - r**4 - b*r**5 - r**3 + 0 = 0.
-1, 0
Let o(k) be the first derivative of 21*k**4/20 + 37*k**3/5 + 3*k**2 + 41. Suppose o(l) = 0. Calculate l.
-5, -2/7, 0
Let k(x) be the first derivative of 27*x**4/4 + 24*x**3 - 66*x**2 + 48*x - 32. Factor k(n).
3*(n + 4)*(3*n - 2)**2
Let d(m) be the second derivative of -1/4*m**2 + 1/60*m**6 - 1/8*m**4 + 0 - 1/80*m**5 - 6*m + 7/24*m**3. Factor d(j).
(j - 1)**2*(j + 2)*(2*j - 1)/4
Suppose 2*f - 4 = -0. Factor 0*k**f - 1/2*k + 0 + 1/2*k**3.
k*(k - 1)*(k + 1)/2
Let i(g) be the second derivative of 0 - 1/6*g**4 - g**2 - 2*g + 2/3*g**3. Factor i(y).
-2*(y - 1)**2
Let z be -6*(2 + -3)*(-15)/(-60). Factor -z - 2*y - 1/2*y**2.
-(y + 1)*(y + 3)/2
Let b(r) be the first derivative of r**6/1260 + r**5/105 + r**4/28 + 3*r**3 + 3. Let n(u) be the third derivative of b(u). Factor n(f).
2*(f + 1)*(f + 3)/7
Let s(y) be the third derivative of y**10/15120 - y**8/3360 - y**4/24 + 3*y**2. Let d(b) be the second derivative of s(b). Determine c so that d(c) = 0.
-1, 0, 1
Factor -7*x**2 - 5*x**2 - 8*x**3 + 12*x**4 + 2*x**2 + 8*x - 2*x**2.
4*x*(x - 1)*(x + 1)*(3*x - 2)
Let x(s) = -s**2 + 3*s + 10. Let t(i) = -i + 14. Let r be t(9). Let m be x(r). Factor 0 + 0*l + m*l**2 - l**4 + 1/2*l**3 + 1/2*l**5.
l**3*(l - 1)**2/2
Suppose 0 = 4*g + 3*v - v - 12, 2*g - 2*v = 6. Let j(w) be the first derivative of -1/3*w**g - 2 + 0*w - 1/2*w**2. Factor j(a).
-a*(a + 1)
Let g(d) be the second derivative of 0*d**4 + 0 - 5*d + 0*d**3 + 1/135*d**6 + 0*d**2 + 1/90*d**5. Suppose g(s) = 0. What is s?
-1, 0
Let q(d) = -3*d - d + d**2 + 4*d. Let b(c) = -2*c**3 + c**2 + 2*c. Suppose -4*r - 1 = -l, 3*l + 2*r - 3 = 3*r. Let w(k) = l*b(k) - q(k). Factor w(h).
-2*h*(h - 1)*(h + 1)
Factor -16/5*j**2 + 0 - 2/5*j**4 - 8/5*j - 2*j**3.
-2*j*(j + 1)*(j + 2)**2/5
Let g(f) be the third derivative of -f**6/10 - f**5/6 + f**4/12 + 21*f**2. Find d, given that g(d) = 0.
-1, 0, 1/6
Let b(j) be the first derivative of -j**5/270 + j**3/27 - j**2 - 4. Let v(h) be the second derivative of b(h). Factor v(n).
-2*(n - 1)*(n + 1)/9
Let p be 8/2*(-70)/(-736). Let k = p + -3/23. What is v in 0 + 0*v**2 + 0*v**3 + 0*v - 1/4*v**5 + k*v**4 = 0?
0, 1
Let d(j) = 7*j**2 + 3*j. Let i(b) = 15*b**2 + 3*b + 3. Let w(q) = -30*q**2 - 7*q - 5. Let k(f) = -5*i(f) - 3*w(f). Let x(y) = -9*d(y) + 4*k(y). Factor x(s).
-3*s*(s + 1)
Let j(m) be the first derivative of 5*m**3/3 + 5*m**2/2 - 10*m + 23. Solve j(o) = 0 for o.
-2, 1
Let j = -1 + 4. Suppose -k - 6 = -4*k + j*r, 0 = 5*k + 5*r + 10. Factor -2/5*y**3 + 0*y + k - 4/5*y**2.
-2*y**2*(y + 2)/5
Suppose -3*b + 11*b - 4*b**4 + 4 - 39*b**3 + 31*b**3 = 0. Calculate b.
-1, 1
Determine m, given that 3*m + 0*m**3 + 15*m**2 + 19*m - 12*m + 5*m**3 = 0.
-2, -1, 0
Let o(a) = -2*a - 19. Let y be o(-11). Let s(k) be the first derivative of -1/25*k**5 - 1/15*k**y + 0*k - 1/10*k**4 + 0*k**2 - 3. Determine g so that s(g) = 0.
-1, 0
Let d(z) = -3*z**4 - 9*z**3 + 5. Suppose -3*a - 3*s + 18 = 0, -2*a + 18 = a + 5*s. Let y(v) = 4*v**4 + 10*v**3 - 6. Let o(g) = a*d(g) + 5*y(g). Factor o(q).
2*q**3*(q - 2)
Factor -2/5 - 27/5*c**2 - 23/5*c**3 - 7/5*c**4 - 13/5*c.
-(c + 1)**3*(7*c + 2)/5
Let g = -3 + 3. Let l = -11 - -13. Suppose 0*k**3 + g*k + 0*k**l + 2/7*k**4 + 0 = 0. What is k?
0
Let t(d) = d**2 + 21*d - 20. Let w be t(-22). Factor 1 + 1/2*l**3 - l**w - 1/2*l.
(l - 2)*(l - 1)*(l + 1)/2
Let w(p) be the second derivative of -p**4/84 - p**3/42 + 23*p. Find q such that w(q) = 0.
-1, 0
Factor 1/8*b**4 + 1/2*b**3 + 5/8*b**2 + 1/4*b + 0.
b*(b + 1)**2*(b + 2)/8
Let k = 60 - 58. Let 2/3*a**3 - 2/9*a**k + 4/9 - 2/9*a**4 - 2/3*a = 0. Calculate a.
-1, 1, 2
Let o(a) be the second derivative of a + 3/40*a**5 - 1/8*a**4 + 0*a**2 + 0 + 0*a**3. Let o(c) = 0. Calculate c.
0, 1
Factor -28/3*x + 14/3*x**2 + 2 + 8/3*x**3.
2*(x - 1)*(x + 3)*(4*x - 1)/3
Let a(f) = 3*f**3 - f**2 - 9*f - 7. Let s = 4 + -4. Suppose -o - 2*o - 3 = s. Let y(d) = d**2 + 1. Let x(j) = o*y(j) - a(j). Let x(n) = 0. Calculate n.
-1, 2
Let y(b) be the third derivative of b**8/5040 + b**7/945 + b**6/540 + 5*b**4/24 + 3*b**2. Let d(r) be the second derivative of y(r). Factor d(h).
4*h*(h + 1)**2/3
Suppose 5*b - 10*b = 3*m - 22, 3*b - 14 = -m. Let s(x) be the first derivative of -1 + 0*x**2 - 3/2*x**4 + 0*x - 2/5*x**b - 4/3*x**3. Solve s(a) = 0 for a.
-2, -1, 0
Let p(o) be the first derivative of 1/4*o**2 + 0*o - 3 + 0*o**4 - 1/5*o**5 + 1/3*o**3 - 1/12*o**6. Determine f, given that p(f) = 0.
-1, 0, 1
Let j(l) = -l**2 - 31*l + 316. Let s be j(8). Solve -4/7*p**s + 8/7*p**3 - 4/7*p**2 + 0*p + 0 = 0.
0, 1
Factor -486/5 - 6*i**4 + 2/5*i**5 - 108*i**2 + 36*i**3 + 162*i.
2*(i - 3)**5/5
Let g(x) be the first derivative of 1/2*x**2 + 0*x**3 + 1 + 3*x - 1/12*x**4. Let n(r) be the first derivative of g(r). Let n(z) = 0. What is z?
-1, 1
Let p(u) = -4*u**4 - 4*u**3 + 4*u**2 + 4*u. Let r(z) = 12*z**4 + 11*z**3 - 13*z**2 - 11*z + 1. Let k(j) = -11*p(j) - 4*r(j). Factor k(w).
-4*(w - 1)**2*(w + 1)**2
Factor 0*d**2 + 0*d + 1/3*d**4 + 0 - 1/3*d**3.
d**3*(d - 1)/3
Let g(a) be the second derivative of a**8/30240 - a**6/1080 - a**5/270 - 5*a**4/12 - 4*a. Let t(j) be the third derivative of g(j). Suppose t(o) = 0. What is o?
-1, 2
Let d(y) be the third derivative of y**5/80 + y**4/32 + 9*y**2. Solve d(a) = 0 for a.
-1, 0
Let w be (3 + (-2)/1)*-1. Let d = 1 + w. Factor d*q**3 - 4*q**5 + q**2 + 9*q**4 - q**3 - 5*q**3.
-q**2*(q - 1)**2*(4*q - 1)
