Factor 0 - 1/4*h**g - 1/4*h**2 + 0*h.
-h**2*(h + 1)/4
Let m(f) be the first derivative of f**3/12 + f**2/2 - 15*f + 114. Determine o, given that m(o) = 0.
-10, 6
Factor 0*u**3 + 0*u + 0 + 1/2*u**5 - 3/2*u**4 + 0*u**2.
u**4*(u - 3)/2
Suppose 2*k + 2050*q - 2045*q = -40, 4*k - 3*q - 24 = 0. Find h such that -8/9*h**4 + 0*h**2 - 4/9*h**5 - 4/9*h**3 + 0 + k*h = 0.
-1, 0
Let t = 30020 + -30018. Let y = -62 + 188/3. Factor 2/5 + y*s**t - 14/15*s - 2/15*s**3.
-2*(s - 3)*(s - 1)**2/15
Let p(l) = 9*l**4 + 4*l**3 - 14*l**2 + 7*l + 3. Let a(o) = -8*o**4 - 4*o**3 + 14*o**2 - 6*o - 2. Let x(y) = 6*a(y) + 4*p(y). Factor x(f).
-4*f*(f - 1)*(f + 2)*(3*f - 1)
Let b(l) be the third derivative of -l**8/5040 - l**7/630 - l**6/270 + l**3/6 + 14*l**2. Let u(r) be the first derivative of b(r). Factor u(c).
-c**2*(c + 2)**2/3
Suppose -2*o = -5*b + 578, 2*b + 4*o + 460 = 6*b. Let u = -116 + b. Factor u*y**4 + 4/3*y**3 - 2/3*y + 0 + 0*y**2 - 2/3*y**5.
-2*y*(y - 1)**2*(y + 1)**2/3
Let k = -1/23 - -28/115. Let w(d) be the second derivative of 0*d**4 + 4/15*d**6 + 0*d**2 + k*d**5 + 2/21*d**7 - 4*d + 0 + 0*d**3. Factor w(m).
4*m**3*(m + 1)**2
Let d(r) = -r**2 + 3*r - 10. Let j be d(4). Let a = 16 + j. Determine b so that -8 - 2 + 12*b + a - 4*b**2 = 0.
1, 2
Let q(r) = -35*r**2 + 1695*r - 35250. Let s(h) = -9*h**2 + 424*h - 8812. Let b(g) = 4*q(g) - 15*s(g). Factor b(u).
-5*(u - 42)**2
Find b, given that -6*b**2 + 14/3*b**3 - 2/3 + 10/3*b - 4/3*b**4 = 0.
1/2, 1
Let x(z) be the second derivative of -27*z**4/4 - 29*z**3/2 - 3*z**2 - 3*z + 11. Factor x(p).
-3*(p + 1)*(27*p + 2)
Let v(i) = -2*i**3 - 3*i**2 - i - 1. Let f be v(-2). Suppose o - f*p - 37 = -12, 5*p + 25 = 2*o. Factor o + 0*s - 1/2*s**5 - s**4 + 0*s**3 + 0*s**2.
-s**4*(s + 2)/2
Factor -4*o + 0*o - 155*o**2 + 4*o**3 + 134*o**4 + 21*o**2.
2*o*(o - 1)*(o + 1)*(67*o + 2)
Solve 180*s**2 - 8*s**3 - 252 + 744*s + 0*s**3 + 29*s**3 + 297*s**2 = 0.
-21, -2, 2/7
Let v be (-96)/(-45) - 2 - (21 - 9244/420). Factor 2/7 + 2/7*u**4 + 12/7*u**2 + v*u + 8/7*u**3.
2*(u + 1)**4/7
Let g(s) = -2*s**3 + 11*s + 9. Let u(o) = o**2 + 12*o + 17. Let a be u(-11). Let q(m) = 2*m**3 - 12*m - 10. Let n(w) = a*g(w) + 5*q(w). What is f in n(f) = 0?
-1, 2
Let n(t) be the third derivative of -t**7/70 + 11*t**5/20 - 9*t**4/4 + 4*t**3 + 11*t**2 + 4*t. Factor n(b).
-3*(b - 2)*(b - 1)**2*(b + 4)
Let p(q) be the first derivative of 3*q**5/40 - q**4/8 - q**3/4 + 3*q**2/4 + 12*q + 3. Let m(j) be the first derivative of p(j). Let m(x) = 0. What is x?
-1, 1
Let c(w) be the third derivative of w**9/2016 - w**8/672 + w**7/1680 + w**6/720 + 3*w**3/2 - 5*w**2. Let y(z) be the first derivative of c(z). Factor y(b).
b**2*(b - 1)**2*(3*b + 1)/2
Let r(j) be the second derivative of 2 - 1/90*j**6 - 16/9*j**3 - 8/3*j**2 - 2/15*j**5 + 7*j - 2/3*j**4. Suppose r(v) = 0. Calculate v.
-2
Determine w so that 124*w - 392 + 5*w**3 - w**3 + 21*w + 48*w**2 - 61*w = 0.
-7, 2
Let t(m) be the third derivative of 0*m + 1/510*m**5 - 3/68*m**4 + 0*m**3 - 59*m**2 + 0. Solve t(q) = 0 for q.
0, 9
Let n(m) be the second derivative of -3/10*m**4 - 9/50*m**5 + 0 - 6*m - 1/5*m**3 - 1/25*m**6 + 0*m**2. Factor n(g).
-6*g*(g + 1)**3/5
Let t be (-82)/943 - (-381)/552*20/15. Find n such that t*n - 2/3 - 1/6*n**2 = 0.
1, 4
Find p, given that 4 + 28*p**3 + 37*p**2 + 20*p**4 - 4 - 25*p**2 + 4*p**5 = 0.
-3, -1, 0
Let m(i) be the third derivative of i**8/168 - i**7/21 - 7*i**6/20 - 23*i**5/30 - 2*i**4/3 - 9*i**2 - 2. Solve m(z) = 0 for z.
-1, 0, 8
Determine j, given that 16/13 + 20/13*j**2 - 2/13*j**3 - 34/13*j = 0.
1, 8
Let d(m) be the first derivative of -4/5*m**3 + 0*m + 3/10*m**4 - 14 - 1/25*m**5 + 4/5*m**2. Determine h, given that d(h) = 0.
0, 2
Let p(q) be the second derivative of 1/6*q**4 - 8/3*q**3 + 0 + 16*q**2 - 12*q. Suppose p(t) = 0. What is t?
4
Let n(m) be the first derivative of m**6/2 - 3*m**4/4 - 142. Let n(j) = 0. What is j?
-1, 0, 1
Let r(h) be the third derivative of -69*h**5/4 + 515*h**4/6 + 10*h**3/3 - 317*h**2. Factor r(p).
-5*(p - 2)*(207*p + 2)
Let o(x) be the second derivative of -x**7/42 - 7*x**6/30 + 9*x**5/20 + 7*x**4/12 - 4*x**3/3 - 7*x - 2. Let o(z) = 0. What is z?
-8, -1, 0, 1
Let x(z) = -z**3 - z - 1. Let t(c) = 63*c**3 - 112*c**2 + 59*c - 10. Let j(v) = 2*t(v) - 2*x(v). Factor j(y).
2*(4*y - 3)**2*(4*y - 1)
Suppose 4*c**2 - 9*c**2 + 54*c + 243 + c**2 + 7*c**2 = 0. What is c?
-9
Let j(w) be the second derivative of 1/25*w**5 + 2/15*w**4 + 0 + 0*w**2 + 19*w - 8/15*w**3 - 1/75*w**6. Factor j(m).
-2*m*(m - 2)**2*(m + 2)/5
Let l(t) = t**2 - 9*t - 8. Let s be l(10). Factor -25*z**4 + s*z + 427*z**2 + 35*z**3 - 437*z**2 - 2*z.
-5*z**2*(z - 1)*(5*z - 2)
Let x(r) be the third derivative of 1/300*r**6 + 1/75*r**5 + 0 + 0*r**3 + 0*r**4 - 6*r**2 + 0*r. Determine a so that x(a) = 0.
-2, 0
Let a(f) be the third derivative of -f**6/360 + f**5/90 + f**4/72 - f**3/9 + 74*f**2. Suppose a(d) = 0. Calculate d.
-1, 1, 2
Let x(q) = 5*q**2 - 2*q**2 - 75*q - 4 + 73*q. Let a(f) = 3*f**2 - f - 5. Suppose -p + 1 = 3*w, -3*p - 2*w = w + 9. Let t(i) = p*x(i) + 4*a(i). Factor t(r).
-3*r*(r - 2)
Let c(t) = 23*t**2 - 4*t + 1. Let q be c(1). Let j be (-8)/q*10/(-18). Factor -2/3 - j*p**2 - 8/9*p.
-2*(p + 1)*(p + 3)/9
Let -1/4 + 5/8*o - 1/2*o**2 + 1/8*o**3 = 0. What is o?
1, 2
Let h(i) be the third derivative of i**6/90 + 8*i**5/15 + 32*i**4/3 + 2*i**3 + 23*i**2. Let p(y) be the first derivative of h(y). Let p(g) = 0. What is g?
-8
Suppose -c - 5*o + 17 = 6, 3*o = 3*c + 57. Let n = -10 - c. Let n*g + 2*g**4 - 2*g**3 + 2*g - 6*g**2 - 4*g + 7 - 3 = 0. What is g?
-1, 1, 2
Let g be (-8 - (-132)/18)/((-22)/99). Factor 1/2*d**4 - 7/2*d + 9/2*d**2 + 1 - 5/2*d**g.
(d - 2)*(d - 1)**3/2
Let k(d) = -2*d**2 + 16*d - 3. Let o(t) = -2*t**2 + 16*t - 4. Suppose -5*a + 53 = 73. Let b(w) = a*k(w) + 3*o(w). Factor b(p).
2*p*(p - 8)
Let q = -1388/5 + 278. Let b(n) be the first derivative of -q*n**5 + n**2 + 2/3*n**3 + 0*n + 1 - 1/2*n**4. Determine y so that b(y) = 0.
-1, 0, 1
Suppose -6*q + 186 - 54 = 0. Let b(a) = 5 + 23*a**2 + 12*a**3 - 15 + 53*a**2 - q. Let i(p) = -p**3 - 7*p**2 + 3. Let r(v) = -3*b(v) - 32*i(v). Factor r(z).
-4*z**2*(z + 1)
Let p(d) be the third derivative of d**8/840 + d**7/84 + 2*d**6/45 + d**5/15 - 5*d**3/6 + 4*d**2. Let o(u) be the first derivative of p(u). Factor o(z).
2*z*(z + 1)*(z + 2)**2
Let b(s) be the first derivative of -s**7/84 + s**6/15 + s**5/20 - s**4/2 - 3*s**3/4 - 11*s - 13. Let c(r) be the first derivative of b(r). Factor c(m).
-m*(m - 3)**2*(m + 1)**2/2
Suppose -11*a = -6*a - 635. Let x = a + -124. Factor -26*s - 2*s**x - 12 - 40/3*s**2.
-2*(s + 3)**2*(3*s + 2)/3
Let a(q) = -4*q - 4. Let x be a(-1). Let c be x/(7 + -3)*(-2)/4. Solve -2/5*m**2 + 0 + 1/5*m**3 + c*m = 0 for m.
0, 2
Let a(t) be the first derivative of 0*t**4 - 4/15*t**5 - 19 + 4/3*t**3 - 4/3*t**2 + 0*t. Let a(l) = 0. Calculate l.
-2, 0, 1
Let v(i) be the third derivative of -i**8/3360 + i**7/630 - i**6/360 + 3*i**4/8 + 8*i**2. Let d(p) be the second derivative of v(p). Factor d(w).
-2*w*(w - 1)**2
Let a(b) be the third derivative of -b**6/24 - b**5/4 + 10*b**3/3 + 82*b**2. Determine j so that a(j) = 0.
-2, 1
Let l = 89/28 - 17/7. Let d(a) be the first derivative of -4 + 0*a + 3/8*a**2 + 9/16*a**4 - l*a**3 - 3/20*a**5. Suppose d(b) = 0. What is b?
0, 1
Let w(h) = 5*h**5 + 3*h**4 - 11*h**3 - 7*h**2 + 12*h + 2. Let d(g) = g**4 - 2*g**3 + g**2 - g - 1. Let i(f) = -2*d(f) - w(f). Determine s, given that i(s) = 0.
-2, -1, 0, 1
Let b = -410 - -416. Let r(j) be the first derivative of 3/20*j**4 - 1/5*j**2 + 1/25*j**5 - 13 - 1/15*j**3 - 1/30*j**b + 0*j. Determine l, given that r(l) = 0.
-1, 0, 1, 2
Let h = -2164/5 + 434. Let a(p) be the first derivative of -3*p**2 + 4/3*p**3 - h*p**5 + 2*p - 1 + p**4 + 1/3*p**6. Determine l so that a(l) = 0.
-1, 1
Suppose -2*m + 4 = 4*o + 2*m, m - 1 = 3*o. Suppose 4*h + 5*v - 48 = 0, v = -o*v. Factor 27*c**3 + 4*c**3 - h*c**3 + 4*c + 11*c**3 - 22*c**2.
2*c*(3*c - 1)*(5*c - 2)
Let w(m) be the first derivative of -27/10*m**2 + 1/5*m**3 + 19 + 24/5*m. Solve w(j) = 0 for j.
1, 8
Let c be (-30)/(-25)*(-10)/3. Let o(l) = -10*l**2 + 35*l - 40. Let n(m) = 9*m**2 - 34*m + 41. Let k(w) = c*o(w) - 5*n(w). Factor k(b).
-5*(b - 3)**2
Factor -2159*v**3 - 95*v + 25 + 130*v**2 + 6*v**4 + 2089*v**3 - v**