et q(z) be the first derivative of p(z). Factor q(r).
-(r + 1)**2/4
Let u(x) be the third derivative of x**5/270 - x**4/27 + 4*x**3/27 - 3*x**2. Factor u(m).
2*(m - 2)**2/9
Let p(q) be the third derivative of 2*q**7/735 - q**6/105 - 11*q**5/105 + 2*q**4/7 - 14*q**2 + q. Factor p(c).
4*c*(c - 4)*(c - 1)*(c + 3)/7
Suppose 7*a - 4 = 5*a. Let v(f) = -a*f**4 + 4 + 11*f**2 + f**3 - 2 - 2 + 8*f - 3. Let d(z) = -z**3 - z**2 - 1. Let u(q) = 5*d(q) + v(q). Factor u(t).
-2*(t - 1)**2*(t + 2)**2
Let t be (0 - (2 + -2))/(-2). Suppose 3*x = 4*p - 21, t*x = -3*p + 5*x + 24. Solve 6/5*r**4 - 4/5*r**2 - 6/5*r - 2/5 + 4/5*r**p + 2/5*r**5 = 0.
-1, 1
Let o(p) be the second derivative of 0*p**2 + 0 - 1/20*p**5 + 0*p**3 + 1/30*p**6 - 2*p - 1/12*p**4 + 1/42*p**7. Suppose o(k) = 0. What is k?
-1, 0, 1
Let y(z) = z**3 + 41*z**2 - 39*z + 126. Let s be y(-42). Factor 0*a + s*a**2 + 0 + 0*a**3 - 1/2*a**5 - 1/2*a**4.
-a**4*(a + 1)/2
Let b(u) be the third derivative of u**5/180 + u**4/24 - 2*u**3/9 + 7*u**2. Factor b(l).
(l - 1)*(l + 4)/3
Let c = 516/5 - 102. What is t in -4/5 + c*t - 2/5*t**2 = 0?
1, 2
Let v(u) be the first derivative of -u**4/4 + u**3 + 3. Let d be v(3). Let -4*o**4 - 2*o**5 + d*o**5 + 4*o**5 + 2*o**3 + 0*o**4 = 0. What is o?
0, 1
Factor 8*x**3 - 9*x**3 - 35*x - 4*x**3 + 25*x**2 + 15.
-5*(x - 3)*(x - 1)**2
Let o(m) be the first derivative of 20*m**3/3 - 25*m**2/2 + 5*m - 22. Factor o(t).
5*(t - 1)*(4*t - 1)
Let v(d) be the first derivative of d**4/32 + d**3/2 + 3*d**2 + 8*d + 46. Factor v(i).
(i + 4)**3/8
Let f(m) = m + 1. Let t(i) = -2*i**2 + 10*i. Let p(w) = -4*f(w) + t(w). Suppose p(o) = 0. Calculate o.
1, 2
Let i(h) be the second derivative of h**7/420 - h**5/60 + h**3/2 - 8*h. Let j(a) be the second derivative of i(a). Factor j(f).
2*f*(f - 1)*(f + 1)
Let u(c) = -c + 7. Let j be u(5). Factor 4/5*m + 2/5*m**j - 6/5.
2*(m - 1)*(m + 3)/5
Factor -36*l + 41*l + 3*l**2 + 6 - 2*l**2.
(l + 2)*(l + 3)
Let i(w) be the third derivative of w**7/945 - w**6/270 + w**5/270 + 3*w**2. Determine o, given that i(o) = 0.
0, 1
Let i(l) be the second derivative of l**7/126 + 19*l**6/90 + 13*l**5/6 + 175*l**4/18 + 125*l**3/18 - 625*l**2/6 + 18*l. Factor i(s).
(s - 1)*(s + 5)**4/3
Factor 4*z - z**4 - z**3 - 4*z + z + 17*z**2 - 16*z**2.
-z*(z - 1)*(z + 1)**2
Suppose f = 5*b - 3, -f - 3 = 2*b - b. Let d(n) be the second derivative of b + 1/24*n**3 - 1/48*n**4 + 0*n**2 - 3*n. Suppose d(w) = 0. What is w?
0, 1
Solve 0 - 4/3*v**3 + 4/3*v + 0*v**2 = 0.
-1, 0, 1
Factor 5*l - 1 - 2*l**3 + 2*l**5 + 5*l**4 - 2*l - 2*l**4 - 2*l**2 - 3*l**5.
-(l - 1)**4*(l + 1)
Suppose -12*y**2 + 4 + 8*y - 12*y**2 + 28*y**2 = 0. What is y?
-1
Suppose -2*t + 10 = -0*t. Suppose 2*d**4 + 2*d**5 + d - t*d - 10*d**2 + 0*d**5 - 6*d**3 = 0. Calculate d.
-1, 0, 2
Let r be 6/(-1 - 29)*(3 - 4). Suppose 1/5 - 1/5*j**2 + r*j - 1/5*j**3 = 0. What is j?
-1, 1
Let j(g) = -g**4 - 3*g**3 + 4*g**2 + 6*g - 6. Let l(q) = q**4 + 2*q**3 - 3*q**2 - 5*q + 5. Let m(r) = -5*j(r) - 6*l(r). Find s such that m(s) = 0.
0, 1, 2
Let g(d) be the first derivative of -1/24*d**4 - 1/2*d**2 + 0*d**3 + 2 + 0*d - 1/120*d**5. Let h(t) be the second derivative of g(t). Factor h(n).
-n*(n + 2)/2
Let a(p) be the first derivative of 0*p**2 + 0*p - 1/2*p**4 - 4/15*p**5 - 2/9*p**3 + 1. Factor a(s).
-2*s**2*(s + 1)*(2*s + 1)/3
Let t(x) be the second derivative of x**5/80 + x**4/48 + 18*x. Let t(f) = 0. What is f?
-1, 0
Let m(k) be the first derivative of k**4/16 + 3*k**3/4 + 3*k**2 + 5*k + 17. Let m(p) = 0. What is p?
-5, -2
Let h(m) be the third derivative of m**8/112 - 2*m**7/35 + m**6/10 + m**5/10 - 5*m**4/8 + m**3 - 6*m**2. Factor h(k).
3*(k - 2)*(k - 1)**3*(k + 1)
Factor 3*u**3 - 73 + 73.
3*u**3
Let k(g) = 2 + 2*g - 3 - 7*g**2 + 6. Let l be (0 - -1)/(-1)*6. Let q(c) = -8*c**2 + 2*c + 6. Let h(y) = l*k(y) + 5*q(y). Determine a, given that h(a) = 0.
0, 1
Determine r, given that 0*r - 2/9*r**2 + 8/9 = 0.
-2, 2
Let n(q) be the first derivative of -q**4/16 + q**3/6 - q**2/8 + 18. Let n(h) = 0. Calculate h.
0, 1
Let l(n) be the second derivative of -n**6/30 - 3*n**5/100 + n**4/30 + 2*n + 1. Factor l(i).
-i**2*(i + 1)*(5*i - 2)/5
Let n(r) = 2*r - 2. Let z be n(4). Let h = -4 + z. Factor -8/3*x + 4/3 - 5/3*x**h.
-(x + 2)*(5*x - 2)/3
Let q be (-1)/2*4 - -3. Suppose n + 0 = q. Solve -4*g**2 + 3*g**2 + 1 - n = 0 for g.
0
Factor -1/4*c**2 + 0 - 3/4*c.
-c*(c + 3)/4
Suppose -5*s + 35 = -4*j - 0*s, 3*s - 9 = 0. Let n be 1*4/(-30)*j. Factor -1/3*q + 0 - 1/3*q**3 - n*q**2.
-q*(q + 1)**2/3
Factor 3/4*z**2 + 0 + 3/4*z**3 - 3/2*z.
3*z*(z - 1)*(z + 2)/4
Let n = 0 - -7. Let u(h) be the second derivative of 1/6*h**4 - 1/10*h**5 + 1/21*h**n - 2*h + 0*h**2 - 1/15*h**6 + 0*h**3 + 0. Find i, given that u(i) = 0.
-1, 0, 1
Let c(a) be the third derivative of -a**6/240 + a**5/30 + a**4/48 - a**3/3 - a**2. Factor c(o).
-(o - 4)*(o - 1)*(o + 1)/2
Let s(a) be the first derivative of 0*a**2 + 1/900*a**6 + 0*a - 1/150*a**5 - 1 + 1/3*a**3 + 1/60*a**4. Let r(y) be the third derivative of s(y). Factor r(p).
2*(p - 1)**2/5
Let p(h) be the first derivative of h**4 - 4*h**3/3 - 10*h**2 - 12*h + 49. Factor p(v).
4*(v - 3)*(v + 1)**2
Let z(p) be the third derivative of 1/105*p**6 - 1/42*p**4 - 1/588*p**8 + 4/735*p**7 + 4/21*p**3 + 0 + 4*p**2 + 0*p - 4/105*p**5. Suppose z(g) = 0. What is g?
-1, 1, 2
Let n be ((-2193)/(-170) - 13)/((-6)/20). Find b such that n*b**2 + b - 1/3*b**4 - b**3 + 0 = 0.
-3, -1, 0, 1
Let f = -107 + 110. Factor 2/3*n**f - 5/3*n**2 - 1/3 + 4/3*n.
(n - 1)**2*(2*n - 1)/3
Let t(y) be the first derivative of -y**3/21 + 2*y**2/7 - 4*y/7 - 7. Factor t(r).
-(r - 2)**2/7
Let i = 319/5 + -63. Suppose 5*l + 7 + 3 = 0, -4*z + l = -10. Factor -4/5*q**3 - 2/5*q**5 - i*q**z + 6/5*q - 2/5 + 6/5*q**4.
-2*(q - 1)**4*(q + 1)/5
Let c(f) = -2*f**4 + 6*f**3 - 4*f. Let q(l) = l**4 - 5*l**3 + 3*l. Let h(k) = 3*c(k) + 4*q(k). Suppose h(b) = 0. What is b?
-1, 0
Factor -1/6*y**2 + 1/6*y**3 - 2/3*y + 2/3.
(y - 2)*(y - 1)*(y + 2)/6
Let f = 27 + -24. Let q = -4 + 7. Let -5*g**4 + g**5 + g**f + 5*g - 10*g**2 + 13*g**3 - 1 - 4*g**q = 0. What is g?
1
Let j(o) be the second derivative of -o**7/28 - o**6/12 - o**5/40 + o**4/24 + 26*o. Factor j(u).
-u**2*(u + 1)**2*(3*u - 1)/2
Let x(t) be the second derivative of 3*t + 0*t**4 + 7/720*t**6 - 1/3*t**3 + 0*t**2 - 1/120*t**5 + 0. Let l(f) be the second derivative of x(f). Factor l(m).
m*(7*m - 2)/2
Let d(v) be the third derivative of -1/135*v**5 + 0*v + 4*v**2 - 1/108*v**4 + 0 + 0*v**3 - 1/540*v**6. Solve d(g) = 0.
-1, 0
Let t(z) = 5*z**4 + 29*z**3 - 11*z**2 - 24*z. Let o(d) = -2*d**2 - 2*d**2 + 2*d**4 + 14*d**3 - 8*d - 3*d**3 - d**3. Let k(a) = -11*o(a) + 4*t(a). Factor k(p).
-2*p*(p - 2)**2*(p + 1)
Let i(r) be the third derivative of -r**6/80 + r**5/20 + 3*r**2. Suppose i(h) = 0. Calculate h.
0, 2
Factor -7/4*x**3 - 3/2 - 17/4*x - 17/4*x**2 - 1/4*x**4.
-(x + 1)**2*(x + 2)*(x + 3)/4
Let r be (-4)/(-16) + 91/(-44). Let d = r + 91/44. Factor -1/2 + d*a**3 + 5/4*a - a**2.
(a - 2)*(a - 1)**2/4
Suppose 0 = -v - 0*v - 2*j + 8, 0 = -5*v + 2*j + 4. Factor -9/4*h**5 - 1/2*h**v + 0 - 5*h**4 + 0*h - 13/4*h**3.
-h**2*(h + 1)**2*(9*h + 2)/4
Let g be (-132)/(-10)*(-220)/(-176). Find f such that 1 + g*f**2 + 9/2*f**4 - 15/2*f - 29/2*f**3 = 0.
2/9, 1
Suppose 6*i = 2*i + 16. Suppose i*n + 4 - 28 = 0. Factor -4*m + 2 - 7*m**3 + 7*m + n*m**3.
-(m - 2)*(m + 1)**2
Let i be (5 - -1)*(-1)/(-3). Factor 2*s**2 - 3*s - 1 - i*s**2 + 3*s**2 + 3*s**3 - 2.
3*(s - 1)*(s + 1)**2
Let d(x) be the first derivative of -8*x**6/21 - 12*x**5/35 + 5*x**4/7 + 4*x**3/7 - 2*x**2/7 + 27. Suppose d(l) = 0. What is l?
-1, 0, 1/4, 1
Let k = -166 - -166. Let a(l) be the first derivative of 1/8*l**4 + k*l**3 - 1/6*l**6 + 0*l - 4 + 1/10*l**5 + 0*l**2. Suppose a(f) = 0. Calculate f.
-1/2, 0, 1
Let j(i) be the third derivative of 0*i**3 + 0*i + 0*i**4 - i**2 + 1/120*i**5 + 0 - 2/105*i**7 - 1/120*i**6. Factor j(r).
-r**2*(2*r + 1)*(4*r - 1)/2
Let c(u) be the third derivative of -u**5/12 + 35*u**4/24 - 5*u**3 - 16*u**2. Factor c(v).
-5*(v - 6)*(v - 1)
Find n, given that 4*n**3 + 0*n**3 - 13*n**5 + 17*n**5 - 8*n**4 = 0.
0, 1
Suppose w = -5*b - 2 - 2, 0 = 4*b - w - 4. Suppose -r + b = -2. Factor -3*x**3 - r*x**3 + 3*x**3.
-2*x**3
Let p(s) be the first derivative of 5*s**3/3 - 5*s**2 - 10. Factor p(v).