i**6. Factor r(h).
(h + 1)**3*(9*h - 2)
Let d = 5 - 1. Suppose 5*q - 4 = -p + d*p, -2*p + 8 = 2*q. Find y, given that -4/3*y**5 + p*y**2 + 2/3*y**3 - 2*y**4 + 2/3*y + 0 = 0.
-1, -1/2, 0, 1
Let z = -1725/2 + 864. Determine t, given that z*t**4 + 0 - 1/2*t**2 + 0*t + 0*t**3 - t**5 = 0.
-1/2, 0, 1
Let q(i) be the first derivative of i**3 + 33*i**2/2 - 8. Determine g so that q(g) = 0.
-11, 0
Let x = 254/3 + -84. What is a in 2/3 + x*a**2 - 2*a**3 + 2*a - 4/3*a**4 = 0?
-1, -1/2, 1
Let a(j) be the third derivative of -j**6/200 - j**5/25 - j**4/8 - j**3/5 - 3*j**2. Solve a(k) = 0 for k.
-2, -1
Let d be 41/8 + -5 + 123/24. Factor -12*o**3 + d*o**4 - 3/2*o + 33/4*o**2 + 0.
3*o*(o - 1)**2*(7*o - 2)/4
Let r(u) be the second derivative of u**5/40 - u**4/24 - u**3/12 + u**2/4 - 5*u. Factor r(i).
(i - 1)**2*(i + 1)/2
Suppose 4*f + f = 5. Let u = 5 - 0. Factor u + 3*w**2 - w**2 + 6*w - f.
2*(w + 1)*(w + 2)
Find v such that 1/3*v + 1/3*v**2 - 2/3 = 0.
-2, 1
Let u(i) = 4*i - 8*i - 19*i**2 + 21*i**2. Suppose 4*r - 2*j = -14, 2*r = 3*j + 4 - 1. Let x(p) = -6*p**2 + 11*p. Let w(t) = r*x(t) - 17*u(t). Factor w(n).
2*n*(n + 1)
Let h(v) be the second derivative of 0*v**2 + 1/27*v**4 + 0 + 7/90*v**5 + 0*v**3 - 7*v. Factor h(u).
2*u**2*(7*u + 2)/9
Let s(a) = 4*a + 1. Let v(b) = -2*b. Let c(u) = 2*s(u) + 5*v(u). Let f be c(1). Factor 2/7*m + f + 2/7*m**2.
2*m*(m + 1)/7
Let k(x) be the third derivative of -6*x**2 - 1/120*x**6 - 1/15*x**3 - 7/120*x**4 + 0 - 1/1050*x**7 - 3/100*x**5 + 0*x. Find v, given that k(v) = 0.
-2, -1
Let s(f) be the third derivative of -f**7/210 - f**6/40 + f**4/6 + 11*f**2. Determine g so that s(g) = 0.
-2, 0, 1
Let z = 163/3230 + -2/95. Let b = 71/102 - z. Factor 0*c + 0 + b*c**2 + c**4 - 5/3*c**3.
c**2*(c - 1)*(3*c - 2)/3
Let i = -12 - -17. Let w(t) be the third derivative of -1/30*t**i + 1/12*t**4 - 1/30*t**6 + 0 + 0*t**3 + 2*t**2 + 0*t. Determine k, given that w(k) = 0.
-1, 0, 1/2
Suppose -3*g = 4*p - 22, 3*p + 5*g - 26 = -p. Let u(k) be the first derivative of 1/2*k**3 - 1/4*k**2 - 3/8*k**p + 1/10*k**5 + 0*k - 3. Factor u(h).
h*(h - 1)**3/2
Let y(r) be the second derivative of -r**8/210 + 8*r**7/525 - r**6/60 + r**5/150 - 2*r**2 - 4*r. Let a(k) be the first derivative of y(k). Factor a(z).
-2*z**2*(z - 1)*(2*z - 1)**2/5
Let k be ((-3)/5)/(3/(-15)). Suppose -5*m + 20 = 4*s, 4*s - 10 = -k*m + 2*s. Factor m*x**3 + 7*x**3 + x**3 - 2*x**2.
2*x**2*(4*x - 1)
Let w = 17 - 15. Determine v, given that -3 - 5*v**2 + 6*v**2 + 2*v**w = 0.
-1, 1
Let p(t) be the third derivative of t**5/12 + 5*t**4/24 - 5*t**3/3 - 6*t**2. Suppose p(h) = 0. What is h?
-2, 1
Let y(m) be the first derivative of 3*m**4/20 + 4*m**3/5 + 3*m**2/2 + 6*m/5 + 35. Solve y(n) = 0 for n.
-2, -1
Let 4*p**2 + 16*p**5 + p - 2*p**3 - 4*p**2 - 15*p**5 = 0. Calculate p.
-1, 0, 1
Let l(a) be the first derivative of -a**4/8 - a**3/3 - a**2/4 + 11. Factor l(b).
-b*(b + 1)**2/2
Let q be 6/(-21) + (-240)/42. Let f(i) = i**2 + 4*i - 7. Let b be f(q). Factor 2/7*w**b + 2/7*w**2 + 0 + 0*w - 2/7*w**4 - 2/7*w**3.
2*w**2*(w - 1)**2*(w + 1)/7
Let g(x) be the third derivative of x**6/8 + x**5/10 - 3*x**2. What is o in g(o) = 0?
-2/5, 0
Let u(f) be the first derivative of f**5 - 25*f**4/4 + 5*f**3 + 25*f**2/2 - 20*f + 9. Factor u(j).
5*(j - 4)*(j - 1)**2*(j + 1)
Suppose 5*k + 6*z + 75 = z, -3*k - 53 = -5*z. Let h be (-6)/(-8)*k/(-18). Let 4/3 + h*b**2 + 2*b = 0. Calculate b.
-2, -1
Factor 3*b**2 - b**2 + 42 + 6 + 24*b + b**2.
3*(b + 4)**2
Let y be (305/40 - 7)*2/5. What is h in 1/4*h**2 + 0 - y*h = 0?
0, 1
Solve 5*i**3 - 6*i + 2 - 3*i**4 + 1 + i**3 + 0*i**3 = 0.
-1, 1
Let v(l) be the third derivative of -4*l**7/35 - l**6/10 + 9*l**5/40 + l**4/32 - l**3/8 + 8*l**2. Find q such that v(q) = 0.
-1, -1/4, 1/4, 1/2
Suppose -6*q = -3*q. Factor 9*c**4 + 0*c**2 + q - 9*c**3 + 4/3*c.
c*(3*c - 2)**2*(3*c + 1)/3
Let r(o) be the third derivative of 0*o + 1/66*o**4 - 1/33*o**3 + 0 - o**2 - 1/330*o**5. Factor r(s).
-2*(s - 1)**2/11
Let k(d) be the first derivative of 0*d - 3/2*d**4 + 3 - 7/15*d**6 + 38/25*d**5 + 2/15*d**3 + 2/5*d**2. Factor k(w).
-2*w*(w - 1)**3*(7*w + 2)/5
Let a(v) = v**2 - v + 1. Let q(i) = 3*i**2 - 33*i + 6. Let t(d) = -6*a(d) + q(d). Factor t(b).
-3*b*(b + 9)
Let f(h) = h**5 + 7*h**4 - 33*h**3 + 41*h**2 - 16*h. Let r(l) = 8*l**4 - 32*l**3 + 40*l**2 - 16*l. Let d(v) = -4*f(v) + 3*r(v). Solve d(a) = 0 for a.
-4, 0, 1
Let d(n) be the second derivative of -n**6/40 + 3*n**5/40 - n**4/16 + 10*n. Suppose d(h) = 0. What is h?
0, 1
Let x(p) be the third derivative of -5/24*p**4 + 0 + 1/20*p**5 + 0*p - 1/210*p**7 + 1/3*p**3 - 2*p**2 + 1/120*p**6. Factor x(m).
-(m - 1)**3*(m + 2)
Let c(w) be the second derivative of w**7/42 + 7*w**6/60 + 9*w**5/40 + 5*w**4/24 + w**3/12 + 29*w. Factor c(h).
h*(h + 1)**3*(2*h + 1)/2
Let h = 4 + -6. Let y be (h/(-3))/(2/27). Factor y*u**2 - 4*u + 3*u**3 + 13*u + 3 + 0*u**3.
3*(u + 1)**3
Factor -4*l**2 + 6*l**2 + 16*l**2 - 33*l - 2 + 17.
3*(l - 1)*(6*l - 5)
Let c = -1888/15 - -380/3. Let -2/5*o**5 - 6/5*o**4 + 0*o + 0 + 0*o**2 - c*o**3 = 0. What is o?
-2, -1, 0
Determine c so that 4/7*c**4 + 36/7*c + 0 + 60/7*c**2 + 4*c**3 = 0.
-3, -1, 0
Suppose 2*y + y = 0. Suppose -6 = -f + 2*a, y = -5*f - 3*a + 2*a + 8. Factor -2*j**2 - j + 0*j**2 + 3*j**f.
j*(j - 1)
Let t(d) be the third derivative of -d**7/14 + 41*d**6/120 + 4*d**5/15 - d**4/2 - 8*d**2. Determine y so that t(y) = 0.
-2/3, 0, 2/5, 3
Let r(i) be the third derivative of i**8/336 - i**6/30 - i**5/30 + i**4/8 + i**3/3 + 3*i**2. Factor r(m).
(m - 2)*(m - 1)*(m + 1)**3
Let j = 51 + -29. Let w = j - 64/3. Factor 0 - 4/3*a**4 + w*a + 10/3*a**3 - 8/3*a**2.
-2*a*(a - 1)**2*(2*a - 1)/3
Suppose 10 = -4*i - i. Let f(y) = -2*y - 2. Let m be f(i). Determine j, given that 8/7 - 8/7*j + 2/7*j**m = 0.
2
Let n = -2509/7 + 359. Solve -4/7*w**3 - 8/7*w**2 - n*w**5 + 10/7*w**4 - 2/7 + 8/7*w = 0 for w.
-1, 1/2, 1
Suppose -4*j = 3*t - 1, -4*j + 26 = t - 3*t. Let x = 4 - j. Determine k so that 0*k - 1/4*k**4 + 0 + 1/4*k**5 + 0*k**2 + x*k**3 = 0.
0, 1
Let f(s) be the third derivative of s**5/360 + s**4/36 + 6*s**2. Factor f(n).
n*(n + 4)/6
Let f(o) = -o**2 - 2*o + 28. Let b be f(-6). Let p(h) be the first derivative of -h - 1/2*h**b + 1 + 0*h**3 + 1/5*h**5 + h**2. Suppose p(i) = 0. Calculate i.
-1, 1
Determine b, given that -8 - 290*b**2 - 270*b**4 + 6*b**5 - 85*b + 5*b - 60*b**5 - 450*b**3 = 0.
-2, -1/3
Suppose 4*a = 7*a. Let b(i) be the third derivative of 0 + 0*i**3 - 2*i**2 + a*i**4 - 1/735*i**7 - 1/210*i**5 + 0*i + 1/210*i**6. Factor b(u).
-2*u**2*(u - 1)**2/7
Let g(p) be the third derivative of p**5/4 - 17*p**4/24 + 13*p**3/6 - 2*p**2. Let a(q) = -7*q**2 + 8*q - 6. Let f(u) = -13*a(u) - 6*g(u). Solve f(d) = 0 for d.
0, 2
Let u(g) be the first derivative of -1/16*g**4 - 4*g - 27/8*g**2 - 4 - 3/4*g**3. Let p(n) be the first derivative of u(n). Suppose p(r) = 0. Calculate r.
-3
Let q(w) = -11*w**2 + 8*w + 3. Let t(c) = 4*c**2 - 3*c - 1. Let s(z) = -4*z. Let r be s(2). Let v(n) = r*t(n) - 3*q(n). Factor v(f).
(f - 1)*(f + 1)
Let r be (1*(-2 - -2))/(-2). Factor 4*o**3 - 3*o + 12*o**4 + 2 + 6*o - 14*o**2 + r*o - 7*o**5.
-(o - 1)**3*(o + 1)*(7*o + 2)
Let r be (-38)/(-9) + -4 - 10/45. Factor 22/5*i**2 - 4/5*i + r.
2*i*(11*i - 2)/5
Factor -2/5*g**3 + 0 + 4/5*g**2 + 0*g.
-2*g**2*(g - 2)/5
Let j = 19/6 - 5/2. Let r = -9 + 13. Let 0 + 0*y - 8*y**3 - j*y**5 + r*y**4 + 16/3*y**2 = 0. Calculate y.
0, 2
Suppose -32/3*o - 38/3*o**3 - 2/3*o**5 - 50/3*o**2 - 14/3*o**4 - 8/3 = 0. Calculate o.
-2, -1
Suppose 8*t**3 + 2 - 4*t**4 + 8*t + 3*t**4 - 114*t**2 + 3*t**4 + 126*t**2 = 0. Calculate t.
-1
Let i(s) be the third derivative of s**8/6720 + s**7/1680 + s**5/15 + 2*s**2. Let t(c) be the third derivative of i(c). Factor t(a).
3*a*(a + 1)
Let s(h) be the second derivative of -h**5/190 + h**3/57 + 7*h. Factor s(n).
-2*n*(n - 1)*(n + 1)/19
Determine k so that 37*k**2 - 5*k**3 - 35*k - 11 - 7*k**2 + 51 - 25*k = 0.
2
Let s(m) = -m**2 + 1. Let b(q) = 5*q**2 - q - 6. Let f(p) = b(p) + 6*s(p). Factor f(u).
-u*(u + 1)
Let o(d) be the first derivative of d**3/12 + 5*d**2/4 + 9*d/4 + 35. Determine s, given that o(s) = 0.
-9, -1
Let d(y) be the first derivative of 32*y**6/51 - 192*y**5/85 + 53*y**4/17 - 106*y**3/51 + 12*y**2/17 - 2*y/17 - 15. Find r, given that d(r) = 0.
1/4,