 that h(c) = 0.
1
Let w(c) be the third derivative of c**8/10080 + c**7/1890 - c**6/1080 - c**5/90 + c**4/12 + c**2. Let y(h) be the second derivative of w(h). Factor y(a).
2*(a - 1)*(a + 1)*(a + 2)/3
Determine t so that 1/3*t**5 + 1/3*t**4 + 0 - 4/3*t**2 + 0*t - 4/3*t**3 = 0.
-2, -1, 0, 2
Let k(m) be the third derivative of -m**2 + 1/30*m**5 - 1/2*m**3 - 1/216*m**6 + 0 + 0*m - 1/18*m**4. Let z(i) be the first derivative of k(i). Factor z(y).
-(y - 2)*(5*y - 2)/3
Let p(h) be the first derivative of -2*h**5/65 - h**4/26 + 12. Factor p(q).
-2*q**3*(q + 1)/13
Let c be (-4)/5 - (-545)/25. Let p be (3 - 51/c)*7. Factor 5/3*x**3 - x**2 + 1/3 - 2/3*x**p - 1/3*x.
-(x - 1)**3*(2*x + 1)/3
Let b(s) be the third derivative of s**7/1680 - s**6/720 - s**5/240 + s**4/48 - s**3 + 3*s**2. Let w(m) be the first derivative of b(m). Factor w(f).
(f - 1)**2*(f + 1)/2
Find k, given that -3/2*k**2 + 0*k + 0*k**3 + 0 + 3/2*k**4 = 0.
-1, 0, 1
Find o, given that 2*o**4 + 10*o**2 - 30 - 12*o**3 + 30 = 0.
0, 1, 5
Solve 1 + 13*a**3 + 1 - 21*a**4 + 19*a**2 - a - 8*a - 4*a = 0 for a.
-1, 2/7, 1/3, 1
Suppose -73*v - 3*v**2 + 73*v - 1 + 5*v**2 - v**4 = 0. Calculate v.
-1, 1
Let o(r) = -r**2 + 3. Let f = 2 + 0. Let l(i) = i + 4*i**2 - 5*i - 4 + 3*i - 2*i**f. Let c(w) = 2*l(w) + 3*o(w). Factor c(a).
(a - 1)**2
Let v be -1 - (50/(-15) + 5 - 3). Factor 2/3*s**3 - 1/3*s - 1/3*s**4 + 2/3*s**2 - 1/3*s**5 - v.
-(s - 1)**2*(s + 1)**3/3
Let n(j) = j**4 + 2*j**3 + 3. Let m(i) = -1. Let u(z) = 3*m(z) + n(z). Find d such that u(d) = 0.
-2, 0
Suppose 0*c = c - 7. Suppose c*p = 3*p. Determine b, given that 2/11*b**2 - 2/11*b + p = 0.
0, 1
Suppose 103*c - 60*c - 3*c**2 - 55*c = 0. Calculate c.
-4, 0
Let s(f) be the second derivative of -f**7/42 - f**6/30 + f**5/20 + f**4/12 + 12*f. What is l in s(l) = 0?
-1, 0, 1
Let b(o) be the third derivative of -o**11/110880 + o**9/10080 - o**7/1680 + 7*o**5/60 + 2*o**2. Let g(u) be the third derivative of b(u). Factor g(h).
-3*h*(h - 1)**2*(h + 1)**2
Let j(v) be the third derivative of v**5/20 + v**4/4 - 9*v**2. Suppose j(s) = 0. Calculate s.
-2, 0
Let n(a) = -5*a**2 + 2*a + 3. Let v(k) = 4*k**2 - 2*k - 2. Suppose 4*l + l = -10. Let t(r) = l*n(r) - 3*v(r). Solve t(h) = 0.
0, 1
Let q(x) be the third derivative of x**6/300 + x**5/75 + x**4/60 - 7*x**2. Factor q(d).
2*d*(d + 1)**2/5
Factor -2/9*l**4 - 8/3*l - 26/9*l**2 - 4/3*l**3 - 8/9.
-2*(l + 1)**2*(l + 2)**2/9
Let r = -98 - -100. Factor 1/4 + 1/4*o**r - 1/2*o.
(o - 1)**2/4
Let -9 - m - 3*m**2 + 5*m + m + 7*m = 0. Calculate m.
1, 3
Suppose 0 = -5*o + t + 19, 3*o + 11 = 4*t + 36. Let x = 487/3 + -158. Factor 8*i**2 + o*i**3 + x*i + 2/3.
(i + 2)*(3*i + 1)**2/3
Let i(r) be the third derivative of -r**8/224 + r**7/84 + r**6/360 - 7*r**5/180 + 7*r**4/144 - r**3/36 + 10*r**2. What is x in i(x) = 0?
-1, 1/3, 1
Suppose 3*o - 17 = -8. Suppose -2*c + u + o = 6, 2*u - 6 = -5*c. Factor 1/3*k**5 + 0 + 2/3*k**4 + 0*k + 1/3*k**3 + c*k**2.
k**3*(k + 1)**2/3
Suppose 5*i - 2*a - 53 = 0, 0 = i - 2*i - 2*a + 1. Factor 8*b**4 + 11*b**4 + 6*b**3 - i*b**4 - 4*b**2.
2*b**2*(b + 1)*(5*b - 2)
Suppose t + 3*t + 300 = 0. Let k be t/(-21) - 12/(-28). Determine x so that 0*x**2 - 1/3*x**k + 0*x**3 - 1/3*x**5 + 0 + 0*x = 0.
-1, 0
Let v(l) be the first derivative of 9*l**4/4 - l**3 - 5*l**2/2 - l + 7. Find a, given that v(a) = 0.
-1/3, 1
Let d(j) be the second derivative of 1/21*j**4 - 4/21*j**3 + 2/7*j**2 - 5*j + 0. Suppose d(u) = 0. Calculate u.
1
Let r(g) be the second derivative of 4*g + 0 - 3/4*g**5 + 0*g**3 - 7/10*g**6 + 0*g**2 + 1/2*g**4. Determine b, given that r(b) = 0.
-1, 0, 2/7
Let y be (0 - -1)*(-5)/(-5). Suppose -7 = -2*t + y. Solve -4*l + 2*l**2 + 4*l + 7*l**t - 9*l**3 = 0 for l.
0, 2/7, 1
Factor 2*t**2 + 0*t**2 + 41*t - 13*t + 10*t**2 + 8.
4*(t + 2)*(3*t + 1)
Let y(x) = x**3 + x**2 + x + 1. Suppose -4*i - 12 = -0. Let f(m) = -m**3 + 5*m**2 + 13*m + 7. Let g(a) = i*f(a) - 6*y(a). Find s, given that g(s) = 0.
-3, -1
Find j such that 6/5*j**2 - 2/5*j**3 + 0 - 4/5*j = 0.
0, 1, 2
Let l = 3503/1152 + 9/128. Factor 2/9*w**5 + 32/9*w**2 + 4/9 + 4/3*w**4 + l*w**3 + 2*w.
2*(w + 1)**4*(w + 2)/9
Let y(b) = 8*b**2 + b - 1. Suppose -3*f + 0 + 3 = 0. Let a be y(f). Factor -a*w**5 - 11*w**4 + 3 + w**4 - 3 - 2*w**3.
-2*w**3*(w + 1)*(4*w + 1)
Let g(h) be the first derivative of h**5/80 - h**4/24 + h**3/24 + 4*h - 2. Let s(f) be the first derivative of g(f). Determine m, given that s(m) = 0.
0, 1
Let b = -13 - -19. Let r be b/(-4) - (-21)/6. Suppose 3*h**r + 1/2*h**3 + 6*h + 4 = 0. Calculate h.
-2
Let p(y) be the third derivative of -y**6/1260 + y**4/84 + y**3/3 + 3*y**2. Let q(w) be the first derivative of p(w). Factor q(c).
-2*(c - 1)*(c + 1)/7
Let f(x) = x**2 - 1. Let c be (-2)/7 + 18/14. Let o be f(c). Factor o*s - 2/3*s**2 + 0.
-2*s**2/3
Let z(i) = -4*i**4 + 12*i**3 - 17*i**2 - i + 5. Let x(s) = 6*s**4 - 18*s**3 + 25*s**2 + s - 7. Let g(w) = 5*x(w) + 7*z(w). Factor g(l).
2*l*(l - 1)**3
Let b be -2 + 11/3 - -1. Let j be 20/(-15)*(-9)/6. Factor -2/3 - b*f**j + f**3 + 7/3*f.
(f - 1)**2*(3*f - 2)/3
Suppose 0 = -3*r + r - 12. Let b(p) = 3*p**4 + 14*p**3 + 17*p**2 - 17. Let j(o) = o**4 + 5*o**3 + 6*o**2 - 6. Let m(i) = r*b(i) + 17*j(i). Solve m(h) = 0.
0, 1
Let p(w) be the first derivative of 4*w**3/7 - 2*w**2/7 + 9. Find b such that p(b) = 0.
0, 1/3
Let a(d) = 2*d**3 - 50*d**2 - 90*d - 46. Let z(b) = b**3 - 17*b**2 - 30*b - 15. Let p(g) = -3*a(g) + 8*z(g). What is w in p(w) = 0?
-3, -1
Let h = -4 - -6. Factor 0*v**h + 3*v**2 - v - 2*v**2.
v*(v - 1)
Let n(z) = -z**2 + 7*z - 2. Let q be n(6). Let u = -2 + q. Determine j so that -2/5 - 2/5*j**u + 4/5*j = 0.
1
Factor 0 + 1/2*n + 0*n**2 - n**3 + 0*n**4 + 1/2*n**5.
n*(n - 1)**2*(n + 1)**2/2
Let y(f) be the third derivative of f**5/300 - 3*f**4/10 + 54*f**3/5 - 11*f**2. Factor y(m).
(m - 18)**2/5
Let k = 5 + -3. Determine o, given that -k*o**2 - 17*o + 21*o - 2*o**2 = 0.
0, 1
Suppose 19 = 3*j + s, 0*s + s = 2*j - 6. Suppose -c - 5 = j*w - 0*c, -w - 10 = 2*c. Let -f**3 + f + 0*f**3 + w*f = 0. What is f?
-1, 0, 1
Let o(k) = -k**2. Let x(m) = 2*m**2 + 4*m. Let f(l) = 4*o(l) + x(l). Factor f(v).
-2*v*(v - 2)
Let m(s) = 4*s**4 - s**2. Let n(v) = -2*v - 3. Let a be n(-2). Let y(i) = 2*i**3 - 2*i**3 - i**4. Let c(r) = a*m(r) + 3*y(r). Let c(z) = 0. Calculate z.
-1, 0, 1
Let r(v) be the second derivative of v**3/3 - 3*v**2 + v. Let i be r(6). Factor -2*g - g**2 + i*g - 5*g.
-g*(g + 1)
Let l(n) be the third derivative of n**6/6 - 22*n**5/15 + 14*n**4/3 - 16*n**3/3 + 6*n**2. Factor l(j).
4*(j - 2)**2*(5*j - 2)
Let i(r) be the first derivative of r**8/1008 - r**7/315 + r**5/90 - r**4/72 + r**2/2 + 3. Let c(q) be the second derivative of i(q). Find o such that c(o) = 0.
-1, 0, 1
Let o(u) be the third derivative of u**8/112 - u**7/35 + u**6/40 + 13*u**2. Determine t so that o(t) = 0.
0, 1
Suppose 3*p - 5*c + 22 = 0, -5*p - 15 = 4*c + 34. Let w(k) = k + 14. Let q be w(p). Factor 3*f**4 - 8*f**q + 3 - 5*f**4 - 3.
-2*f**4*(4*f + 1)
Factor 0*o**2 + 0 - 1/4*o + 1/4*o**3.
o*(o - 1)*(o + 1)/4
Let l(z) be the second derivative of 8*z - 1/9*z**2 - 1/27*z**3 + 1/6*z**4 + 4/135*z**6 + 0 - 11/90*z**5. Factor l(t).
2*(t - 1)**3*(4*t + 1)/9
Let n(w) be the first derivative of 0*w - 1/8*w**2 - 5/12*w**3 + 6 - 1/4*w**4. Find t such that n(t) = 0.
-1, -1/4, 0
Let n = 124 + -122. Let i(g) be the second derivative of -1/7*g**3 - 1/14*g**4 - 3*g + 0 - 1/70*g**5 - 1/7*g**n. Suppose i(a) = 0. Calculate a.
-1
Suppose 3*q - 3 - 3 = 0. Suppose -3 + m - q - m**2 + 7 = 0. Calculate m.
-1, 2
Let v = -4 + 7. Let z = v + 1. Factor 0*i**2 + 2/7*i**z - 4/7*i - 2/7 + 4/7*i**3.
2*(i - 1)*(i + 1)**3/7
Factor 3/4*y + 0 + 3/4*y**2.
3*y*(y + 1)/4
Let a = 24 + -20. Let z(g) be the first derivative of -4*g + 7*g**2 - 1 - 7/2*g**a + 4/3*g**3. Determine c, given that z(c) = 0.
-1, 2/7, 1
Suppose 0 = -p - 3 + 5. Let h(m) be the second derivative of 1/3*m**4 + 2*m + 0 - m**3 - 2*m**p. Factor h(f).
2*(f - 2)*(2*f + 1)
Let r = -18 - -22. Suppose -r*u = 3 - 11. Factor -1/2 - 3/2*g - g**u.
-(g + 1)*(2*g + 1)/2
Suppose 9*i = 43 + 11. Let y(u) be the third derivative of -1/72*u**4 + 0 + 0*u - 1/180*u**5 - 2*u**2 + 1/18*u**3 + 1/360*u**i. Factor y(d).
(d - 1)**2*(d + 1)/3
Let v(o) = -o**3 - o**2 + 1. Let f(x) = x**4 - 4*x**3 - 7*x**2 + 2*x + 4. Let y(m)