). Find h, given that r(h) = 0.
-2, -1, 0
Let p(o) = -o**3 + 3*o + 1. Let j be p(-2). Let m be j/(-6)*(-45)/10. Factor -m*k - 3/4*k**2 - 3/2.
-3*(k + 1)*(k + 2)/4
Let m = 85 + -82. Factor 0 - 4/3*q**2 - 2/3*q - 2/3*q**m.
-2*q*(q + 1)**2/3
Let h = -9 - -11. Let y(x) be the third derivative of 0*x**4 - x**h - 1/40*x**5 + 0 + 0*x**3 + 1/80*x**6 + 0*x. Let y(a) = 0. Calculate a.
0, 1
Let n = -69/7 - -359/35. Factor 2/5 - n*u**2 + 2/5*u**3 - 2/5*u.
2*(u - 1)**2*(u + 1)/5
Let q(a) be the third derivative of 0*a + 1/40*a**4 - 7*a**2 + 0 + 0*a**3 - 3/100*a**5. Find h, given that q(h) = 0.
0, 1/3
Let k(l) be the first derivative of -10*l**3/3 - 3*l**2 + 4*l + 2. Solve k(z) = 0.
-1, 2/5
Let g(i) be the second derivative of -i**6/50 + 6*i**5/25 - 3*i**4/4 - 4*i**3/5 + 24*i**2/5 + 4*i - 4. What is x in g(x) = 0?
-1, 1, 4
Let u(x) be the first derivative of -2/9*x**3 + 1/6*x**2 - 1/18*x**6 + 0*x**4 + 3 + 0*x + 2/15*x**5. Factor u(a).
-a*(a - 1)**3*(a + 1)/3
Let i be (3 - 2)/(-1)*5. Let l = 8 + i. Determine c so that 3*c**4 + 0*c + 1/2*c**2 + 9/4*c**l + 0 + 5/4*c**5 = 0.
-1, -2/5, 0
Suppose -l - 2*q = -4*l - 2, -4*l - 3*q + 20 = 0. Let c be (4 - l)*6/4. Determine w so that 9*w - c*w**3 + 2*w**3 - 3*w**2 - 11*w = 0.
-2, -1, 0
Let r = -2 + 20. Suppose 11*n - r = 5*n. Suppose 1/2*a**4 + 0*a**2 + 0*a + 0 + 1/2*a**n = 0. Calculate a.
-1, 0
Let q(b) = b**5 + b**4 + b**3 + b**2 - b - 1. Let z(n) = 6*n**5 + 2*n**4 + 2*n**3 + 6*n**2 - 4*n - 4. Let c(d) = 4*q(d) - z(d). Determine a so that c(a) = 0.
-1, 0, 1
Let q = 114/11 - 548/55. Let z = -11 - -11. Factor z*n**3 + q*n**4 + 0 + 0*n - 2/5*n**2.
2*n**2*(n - 1)*(n + 1)/5
Factor -4 + 2*r**4 + 7 - 6*r**2 + r**4.
3*(r - 1)**2*(r + 1)**2
Let g = 26 + -22. Let w(z) be the second derivative of -3*z - 1/24*z**3 + 0 + 0*z**2 - 1/48*z**g. Factor w(c).
-c*(c + 1)/4
Suppose 34*i = 30*i + 16. Determine p so that -1/2*p + 7/4*p**2 + 0 - 7/4*p**i + 1/2*p**3 = 0.
-1, 0, 2/7, 1
Let q be (10/(-12))/((-21)/28). Factor -8/9*x**2 - 2/9 + q*x.
-2*(x - 1)*(4*x - 1)/9
Suppose 16 - 8 = 2*r. Let h(u) be the first derivative of 1/3*u**2 - 1 + 7/9*u**3 + 1/3*u**r + 0*u - 4/15*u**5. Determine d, given that h(d) = 0.
-1/2, 0, 2
Let o(d) be the first derivative of d**6/4 - 6*d**5/5 + 9*d**4/4 - 2*d**3 + 3*d**2/4 + 10. Find v such that o(v) = 0.
0, 1
Let t = 149 + -146. Factor 1/2*d**2 - 1/6*d + 1/6*d**4 + 0 - 1/2*d**t.
d*(d - 1)**3/6
Suppose 4*d = d. Let v(z) be the first derivative of d*z + 2 + 0*z**2 - 1/6*z**6 + 1/5*z**5 + 0*z**3 + 0*z**4. Factor v(x).
-x**4*(x - 1)
Let h(k) = k**2 + 6*k + 2. Let f be h(-8). Let p = f + -16. Factor 1/4*s**p + 1/4 + 1/2*s.
(s + 1)**2/4
Let w(z) be the third derivative of 0 + 0*z + 4*z**2 - 3/80*z**5 - 1/12*z**3 - 11/96*z**4. Factor w(d).
-(d + 1)*(9*d + 2)/4
Suppose -3*l = -2*l + 1. Let v be (l - -1)/(2 + 0). Factor v*m**2 - 2/3*m**3 + 0 + 0*m - 2/3*m**4.
-2*m**3*(m + 1)/3
Let l(d) be the third derivative of 0*d**4 + 1/180*d**5 + 0*d + 2*d**2 - 1/18*d**3 + 0. Factor l(a).
(a - 1)*(a + 1)/3
Let c(t) be the third derivative of -t**6/240 + t**5/10 - t**4 + 16*t**3/3 - 26*t**2. Determine g so that c(g) = 0.
4
Let v(s) be the third derivative of 0*s**3 + 0 + 3*s**2 + 0*s**4 + 1/160*s**6 + 0*s - 1/80*s**5. Find z, given that v(z) = 0.
0, 1
Let q be (-84)/(-825) + 6/75. Let 2/11*p**3 + q*p + 4/11*p**2 + 0 = 0. What is p?
-1, 0
Let p = 27 - 132/5. Factor 0 - 1/5*q - 3/5*q**4 + 1/5*q**3 + p*q**2.
-q*(q - 1)*(q + 1)*(3*q - 1)/5
Let 0*w + 0 + 4/5*w**3 + 6/5*w**4 + 0*w**2 = 0. Calculate w.
-2/3, 0
Let x be ((-1)/2)/(5/(-50)). Factor r**2 + 36*r**4 + 2*r**2 - 3*r**2 + 15*r**x + 12*r**3.
3*r**3*(r + 2)*(5*r + 2)
Let i be (-10)/15*12/2. Let y = i + 10. What is k in -y*k**4 + 68/5*k**3 + 8/5 - 8/5*k - 38/5*k**2 = 0?
-2/5, 2/3, 1
Let i = 620/2219 - -2/317. Factor -26/7*s + 120/7*s**2 + i + 128/7*s**4 - 32*s**3.
2*(s - 1)*(4*s - 1)**3/7
Let v be (-6 - 1505/(-252))*(0 - 1). Let n(r) be the second derivative of 1/6*r**2 + 0*r**3 + 0 - v*r**4 + 2*r. Factor n(u).
-(u - 1)*(u + 1)/3
Let o(z) be the third derivative of -z**6/120 - 3*z**5/40 - z**4/4 - 7*z**3/6 - 9*z**2. Let b(w) be the first derivative of o(w). Factor b(v).
-3*(v + 1)*(v + 2)
Let j(k) be the third derivative of k**9/60480 + k**8/4032 + k**7/630 + k**6/180 - k**5/30 - 4*k**2. Let r(f) be the third derivative of j(f). Factor r(a).
(a + 1)*(a + 2)**2
Let f(t) = -t**2 + 12*t + 4. Suppose 0 = y - 2, -8 + 46 = 3*b + y. Let d be f(b). Factor a**4 - 2*a**3 + a**2 - a**d + a**4.
a**2*(a - 1)**2
Let a be ((-3)/2 - 0)*-2. Factor 2/5*k**2 - 1/5*k + 0 - 1/5*k**a.
-k*(k - 1)**2/5
Let o(s) = -s**3 + 5*s**2 + 8*s - 3. Let v be o(6). Let y = v + -7. Find i such that -i + 0*i**2 - 6 - 14*i - 6*i**y = 0.
-2, -1/2
Find g, given that 1/3*g**3 + g**2 - 1/3*g**4 - 1/3*g - 2/3 = 0.
-1, 1, 2
Suppose 10 = -5*u - 2*d, 4*d - 8 = 2*u - 28. Let m(i) be the second derivative of 0*i**2 + u*i**3 - 1/15*i**6 - i + 0*i**5 + 0 + 1/6*i**4. Factor m(j).
-2*j**2*(j - 1)*(j + 1)
Let w(g) = 3*g**3 + 2*g - 1. Let n be w(1). Find m such that -4*m**n + 6*m**3 + 0*m**4 - 3*m**2 + m**4 = 0.
0, 1
Let v = -6 - -12. Suppose -3*z + 3*g + 0*g = -24, g = -z + v. Factor 3*d - 4 - 2*d - z*d - 2*d**2.
-2*(d + 1)*(d + 2)
Factor -t**2 + 27*t - t**4 + 0*t**4 + t**3 - 28*t + 2*t**2.
-t*(t - 1)**2*(t + 1)
Let m = -1410 + 4240/3. Factor -2/3*h**3 + 4/3 + 2*h**2 + m*h - 2/3*h**4.
-2*(h - 2)*(h + 1)**3/3
Let o = 1/6 - 0. Let c(x) be the first derivative of -2 + 1/4*x**2 - o*x**3 + 0*x. What is w in c(w) = 0?
0, 1
Let d(p) be the third derivative of p**7/1155 + p**6/110 + 3*p**5/110 + p**4/33 - 21*p**2. Determine u so that d(u) = 0.
-4, -1, 0
Let a = 48 - 45. Let p be 2*1 + (-15)/9. Factor 0 + 0*y**a - p*y**4 + y**2 - 2/3*y.
-y*(y - 1)**2*(y + 2)/3
Suppose -2 = -7*m + 6*m. Suppose x - 2*k = 2*x - 2, -x + m*k + 2 = 0. Suppose -3/2*n**5 - 9/4*n**4 + 9/4*n**x + 3/4*n + 0 + 3/4*n**3 = 0. Calculate n.
-1, -1/2, 0, 1
Suppose -15 = -3*h + 2*f, h + 3*f - 6*f - 12 = 0. Suppose 1 = 4*x + c - 2, 3*x + h*c + 9 = 0. Suppose 2/5*w + 0 - 2/5*w**x = 0. Calculate w.
0, 1
Let y(x) be the third derivative of 0 + 0*x - x**2 - 1/540*x**6 - 1/54*x**4 + 0*x**3 - 1/90*x**5. Find o such that y(o) = 0.
-2, -1, 0
Suppose -5*u = 5*i, 5*u = 2*i - 0*i - 21. Factor -1/3*f**i + 0*f + 0*f**2 + 1/3*f**4 + 0.
f**3*(f - 1)/3
Suppose 0 = 3*k - 4*k + 2, 78 = 5*d - k. Factor -3*l**2 - 6*l**4 - 2*l**2 - d*l**3 + 2 - 7*l**2.
-2*(l + 1)**3*(3*l - 1)
Factor -40*y - 48/11 - 162/11*y**3 - 1044/11*y**2.
-2*(y + 6)*(9*y + 2)**2/11
Let w be ((-8)/(-28))/((-2)/(-14)). Factor w*o**2 + 4*o**2 - 5*o**2 - 2 + o.
(o - 1)*(o + 2)
Let m(c) be the third derivative of -c**7/60 + c**6/90 + 7*c**5/60 - c**4/6 + c**3/3 - 2*c**2. Let o(b) be the first derivative of m(b). Factor o(y).
-2*(y - 1)*(y + 1)*(7*y - 2)
Find r such that 1/2*r**4 - 1/2*r**2 - 1/2*r**3 + 0 + 1/2*r = 0.
-1, 0, 1
Let p(v) = 15*v**3 - 2*v**2 + v. Let f be p(1). Let z be (-12)/28 + 62/f. Factor 3*l**3 + 3*l + 2 - 6*l**2 + z - 6.
3*l*(l - 1)**2
Let s(a) = 4*a + 3*a - 3*a + 5*a**3 - a**2. Let y(c) = -6*c**3 + c**2 - 5*c. Let k(o) = 5*s(o) + 4*y(o). Let k(x) = 0. What is x?
0, 1
Let m(l) be the first derivative of -l**8/672 + l**7/420 - l**2/2 + 3. Let d(c) be the second derivative of m(c). Factor d(t).
-t**4*(t - 1)/2
Let c(d) be the second derivative of 1/231*d**7 + 1/22*d**5 + 0 - 1/33*d**4 + 3*d + 0*d**3 - 4/165*d**6 + 0*d**2. Let c(l) = 0. What is l?
0, 1, 2
Let w(t) be the first derivative of -5 - 5/9*t**3 - 2/3*t - 7/6*t**2. Factor w(o).
-(o + 1)*(5*o + 2)/3
Suppose 33 = 5*n - 2*b, 2*n - 3*n - b = -1. Let d(r) be the first derivative of -4/21*r**3 + 0*r**2 - 1 + 2/35*r**n + 1/14*r**4 + 0*r. Let d(p) = 0. What is p?
-2, 0, 1
Let m be 2*(-11)/126 + (-4)/(-14). Let l(n) be the first derivative of -1 + 0*n**2 - 1/15*n**5 - 1/6*n**4 + 0*n - m*n**3. Suppose l(k) = 0. Calculate k.
-1, 0
Let a(v) be the second derivative of v**4/4 - 9*v**3 + 243*v**2/2 + 13*v. Factor a(w).
3*(w - 9)**2
Let s = 24 - 719/30. Let z(u) be the third derivative of 0 - 2/3*u**3 + 1/12*u**4 + s*u**5 - u**2 + 0*u. Factor z(v).
2*(v - 1)*(v + 2)
Let p(y) be the third derivative of -y**7/42 + 7*y**6/24 - 5*y**5/4 + 15*y**4/8 - 38*y**2. Solve p(s) = 0 for s.
0, 1, 3
Let x(a) = -1 + 4 - 10*a + 9*a - 2 - a**2. Let g(l) = 2*l**5 + 6*l**4 + 4*l**3 + 2*l*