r p(w).
-3*(w - 2)**2
Suppose 24*a = 9*a + 45. Let g be (-2)/(-7) - (-6)/28. Find p, given that -5/2*p**3 + 4 + 2*p - g*p**4 - a*p**2 = 0.
-2, 1
Let m(l) be the first derivative of -2*l**3/21 - 9*l**2/7 - 16*l/7 - 38. Factor m(c).
-2*(c + 1)*(c + 8)/7
Let u(p) be the third derivative of -2*p**7/105 - p**6/6 + 7*p**5/15 + 29*p**4/6 - 20*p**3 - 29*p**2 - 7*p. Determine j, given that u(j) = 0.
-5, -3, 1, 2
Factor -54/5*c**3 - 24*c**2 + 0*c + 0 + 3/5*c**4.
3*c**2*(c - 20)*(c + 2)/5
Suppose w = -33*w + 102. Let i(p) be the second derivative of 0*p**2 + 1/30*p**6 + 1/12*p**4 + 6*p + 1/24*p**w + 0 + 1/168*p**7 + 3/40*p**5. Factor i(x).
x*(x + 1)**4/4
Suppose 6*h = 4*h - 0*h. Let o(t) be the second derivative of 3/10*t**6 - 9/70*t**7 + 3/20*t**5 + 0 + 6*t + 6/5*t**2 - 3/4*t**4 + h*t**3. Factor o(j).
-3*(j - 1)**3*(3*j + 2)**2/5
Let o(s) = -s**3 + s**2 + s - 7. Let f(y) = -3*y**3 + 3*y**2 - 18*y - 6. Let c(w) = f(w) - 6*o(w). Factor c(l).
3*(l - 2)**2*(l + 3)
Let s(c) = -2*c**2 + 7*c - 5. Let j(b) = -b**2. Let i(f) = 3*j(f) - s(f). Let l be i(-7). Factor 2*t**3 + 4 + 3 + 2*t - 2*t**2 - 4*t - l.
2*(t - 1)**2*(t + 1)
Let t(v) be the first derivative of v**6/630 - 2*v**5/105 + v**4/14 + 11*v**3/3 - 1. Let x(w) be the third derivative of t(w). Factor x(g).
4*(g - 3)*(g - 1)/7
Let t = 25 + -21. Let w = t - 4. Let -5 - 9*l + 4 - 3*l**3 + 9*l**2 + 4 + w = 0. What is l?
1
Let x = 3040 - 1770. Determine j so that -2*j**2 - 1265 + x - 2*j**2 - j**2 = 0.
-1, 1
Let z(w) = w**4 - w**3 - 2*w. Let k(u) = 2*u**3 + 73*u**2 - 131*u + 50. Let y(r) = k(r) - 3*z(r). Let y(b) = 0. Calculate b.
-5, 2/3, 1, 5
Suppose 3*o = 5*x - 62, -2*x + 5*o = -0*o - 40. Determine h, given that -6*h**4 - x - 45*h**2 + 35*h + 25*h**3 + 6*h**4 - 5*h**4 = 0.
1, 2
Let p(g) be the second derivative of 0 - 1/3*g**3 + g**2 + 1/24*g**4 + g. Factor p(h).
(h - 2)**2/2
Let l = -223 - -225. Let k(h) be the second derivative of 0*h**3 + 0*h**l + 1/80*h**5 - 1/24*h**4 + 0 + 6*h. Factor k(t).
t**2*(t - 2)/4
Suppose -16*g = -31 - 17. Factor -6 - 21*x**2 - g + 23*x**2 + 17*x.
(x + 9)*(2*x - 1)
Let f(c) be the first derivative of -c**5/10 - c**4/8 + c**3/2 + c**2/4 - c + 138. What is s in f(s) = 0?
-2, -1, 1
Let a be (-24)/(-10) + (-43)/(-5) + -8. Let o(s) be the third derivative of -6*s**2 + 0*s + 1/2*s**5 - 1/6*s**4 - 1/3*s**a + 0. Factor o(m).
2*(3*m - 1)*(5*m + 1)
Let z = 36662 + -476598/13. Factor 0 - z*t - 2/13*t**2.
-2*t*(t + 4)/13
Let z(x) = -15*x**2 + 5*x + 65. Let w(d) = -805*d + 33 - 8*d**2 + 807*d + 0. Let r(i) = 5*w(i) - 3*z(i). Let r(v) = 0. Calculate v.
-2, 3
Let c(o) be the third derivative of o**5/420 - 13*o**4/42 + 338*o**3/21 - 19*o**2. Factor c(b).
(b - 26)**2/7
Let l(u) be the first derivative of u**2 - u**4 - 2/3*u**3 + u + 1/3*u**6 + 1/5*u**5 - 15. Solve l(f) = 0.
-1, -1/2, 1
Let x(k) be the first derivative of k**6/40 + k**5/10 + k**4/8 + 23*k**2/2 - 17. Let f(c) be the second derivative of x(c). Determine i so that f(i) = 0.
-1, 0
Let v(f) be the first derivative of -f**6/4 + 66*f**5/5 - 897*f**4/4 + 1256*f**3 - 10203*f**2/4 + 2166*f + 583. Suppose v(p) = 0. What is p?
1, 4, 19
Let k**3 - 11*k**4 + 14*k**2 + k**3 - 3 - 2*k**5 + 21*k**4 - 16*k**4 - 5 = 0. Calculate k.
-2, -1, 1
Let a(l) be the first derivative of -2/3*l**3 - 14 + 0*l**2 + 0*l - 2/3*l**5 - 1/9*l**6 - 7/6*l**4. Factor a(g).
-2*g**2*(g + 1)**2*(g + 3)/3
Suppose 10*d + 15 = 13*d. Suppose 0 = -2*p - 6, -2*s + 15 = -d*p - 4. Determine k, given that 4/7*k**3 + 0*k**s + 0*k**4 - 2/7*k - 2/7*k**5 + 0 = 0.
-1, 0, 1
Let g(a) = a**2 - 47*a + 1. Let s(c) = 0*c - 7 - 23*c + 1 + 7. Let i(m) = -4*g(m) + 9*s(m). Let i(l) = 0. Calculate l.
-5, 1/4
What is t in -4/9 + 2/9*t - 2/9*t**4 - 2/9*t**3 + 2/3*t**2 = 0?
-2, -1, 1
Suppose 0 = c - 2*c + 4*t - 348, 5*c - t = -1797. Let h = c + 1806/5. Factor -h + 3/5*n**2 + 3/5*n.
3*(n - 1)*(n + 2)/5
Let q(w) be the third derivative of 0*w**5 - 1/70*w**7 + 0*w + 0*w**6 + 1/112*w**8 + 0*w**4 + 0 + 0*w**3 + 44*w**2. Factor q(n).
3*n**4*(n - 1)
Let n(x) be the second derivative of x**4/24 + 71*x**3/12 + 35*x**2/2 + 24*x - 3. Determine j, given that n(j) = 0.
-70, -1
Let d(o) be the first derivative of o**6/57 - 66*o**5/95 - 17*o**4/19 - 299. Factor d(f).
2*f**3*(f - 34)*(f + 1)/19
Suppose -2*n - h + 16 = h, 2*h + 4 = 3*n. Suppose -5*z = -5*r - 20, -n*z + 3*r + 8 = -7. Factor 4*v**z - 14*v**2 + 14*v**2 - v**3.
3*v**3
Let w(q) = 8*q - 17. Let f be w(4). Determine u so that -41*u**3 + 13*u**4 - 20 + 80*u + 19*u**3 - 43*u**3 + f*u**2 + 7*u**4 = 0.
-1, 1/4, 2
Let h be 10/(-2)*(-154)/(-55). Let u be (h - -2)/(-4) + (-2)/2. Factor -1/2 + 1/4*l**u - 1/4*l.
(l - 2)*(l + 1)/4
Factor 28/5*q + 72/5 - 4/5*q**2.
-4*(q - 9)*(q + 2)/5
Let g be 1/7 - (4740/(-42) + 5). Let a = -209/2 + g. Factor -3*b + 9/4*b**4 + 2 + 15/4*b**3 - a*b**2.
(b + 1)*(b + 2)*(3*b - 2)**2/4
Let r(n) be the second derivative of 1/105*n**7 + 0*n**3 + 0 + 7/30*n**4 - 4/5*n**2 - 1/25*n**6 - 1/50*n**5 + 7*n. Determine u, given that r(u) = 0.
-1, 1, 2
Let w be 2 - (120/57 - (-20)/2470*-13). Factor w - 1/4*j**2 + j.
-j*(j - 4)/4
Let j be (3/(-4))/1*4*-1. Let m be 6 - -1*(-9)/j. Factor -1/4*p**4 + 0 - 3/4*p**2 + 1/4*p + 3/4*p**m.
-p*(p - 1)**3/4
Let u(h) = -6*h**4 + 40*h**3 + 464*h**2 + 1176*h + 8. Let a(l) = -2*l**4 + 14*l**3 + 154*l**2 + 393*l + 3. Let p(f) = 8*a(f) - 3*u(f). Factor p(m).
2*m*(m - 12)*(m + 4)**2
Let b(l) = l**3 - 7*l**2 + 2*l - 11. Let m be b(7). Factor 12*t - 9*t**3 + 2*t**m - 5*t**3 - 3*t**4 + 3*t**3.
-3*t*(t - 1)*(t + 2)**2
Let p(i) be the first derivative of 0*i - 8 - 10/3*i**3 - i**5 + 0*i**2 + 15/4*i**4. Suppose p(s) = 0. Calculate s.
0, 1, 2
Factor -2*l**3 - 3025 + 6*l**3 - 9*l**3 - 135*l**2 + 124*l - 1279*l.
-5*(l + 5)*(l + 11)**2
Let j(f) be the second derivative of -16*f**6/45 - 2*f**5/5 + f**3/9 - 87*f. Determine c so that j(c) = 0.
-1/2, 0, 1/4
Solve 2*k**5 + 4*k**4 + 13*k**2 - 49*k**3 + 47*k**3 - 6*k**5 - k**2 + 22*k**3 = 0.
-1, 0, 3
Let 32/7*b - 128/7 - 2/7*b**2 = 0. What is b?
8
Suppose 0 = -5*a + 25, k + 3*a + 8 = 5*a. Factor -21*v + 11*v**2 + 16*v**2 - 17 - 24*v**k + 47.
3*(v - 5)*(v - 2)
Factor -24/7 - 4/7*d**2 + 20/7*d.
-4*(d - 3)*(d - 2)/7
Let d(s) = -s**3 + 3*s**2 + 1. Let b(y) = 40*y**3 - 45*y**2 - 685*y + 300. Let q(j) = -b(j) - 30*d(j). Solve q(h) = 0.
-11, 1/2, 6
Let k(s) be the first derivative of -7 - 5/4*s**4 - 20*s + 5/3*s**3 + 10*s**2. What is z in k(z) = 0?
-2, 1, 2
Let p = 126003105/167882 + -3/15262. Let m = p + -750. Solve -m*o**2 + 0 + 4/11*o**3 + 6/11*o**4 - 4/11*o = 0 for o.
-1, -2/3, 0, 1
Let s(r) be the first derivative of -6*r + 10 + 0*r**3 - 3/4*r**4 + 9/2*r**2. Let s(i) = 0. What is i?
-2, 1
Suppose r + 3*r = -r + 20. Factor -1/5*o**3 + 0*o - 1/5*o**r + 2/5*o**2 + 0.
-o**2*(o - 1)*(o + 2)/5
Let j(a) be the first derivative of -a**5/20 + 9*a**4/8 + 5*a**3 + 31*a**2/4 + 21*a/4 - 433. Factor j(f).
-(f - 21)*(f + 1)**3/4
Let p(n) = -8*n**2 - 2*n + 7. Let h(b) = -55*b**2 - 15*b + 50. Let y be (-6)/10 + 234/65. Let v(o) = y*h(o) - 20*p(o). Let v(f) = 0. What is f?
-2, 1
Let p(s) = -s + 2. Let v be p(4). Let d = 2 - v. Factor -3*o**d - 40*o - 9*o**2 - 12 + 16*o + 6*o**3 + 6*o**4.
3*(o - 2)*(o + 1)**2*(o + 2)
Let 8/9*j**2 + 1/3*j**3 - 1/9*j**4 - 4/3*j - 16/9 = 0. Calculate j.
-2, -1, 2, 4
Factor -1/4*j**3 - 3/4*j - 5/4*j**2 + 9/4.
-(j - 1)*(j + 3)**2/4
Let b(f) be the third derivative of -f**7/210 - f**6/60 + f**5/20 + f**4/3 + 2*f**3/3 - 184*f**2. Factor b(c).
-(c - 2)*(c + 1)**2*(c + 2)
Determine h, given that 5/3*h**3 - 1/2*h**4 - 1/6*h**5 - 3/2*h + 5/6 - 1/3*h**2 = 0.
-5, -1, 1
Suppose -655/3*s**3 - 490/3*s - 1735/3*s**2 - 40/3 + 3800/3*s**4 - 880/3*s**5 = 0. What is s?
-1/4, -2/11, 1, 4
Let v(h) be the first derivative of h**6/2 - 3*h**4/4 + 162. Factor v(p).
3*p**3*(p - 1)*(p + 1)
Suppose -3/2*i**4 - 5/3*i**3 + 0*i**2 + 1/6*i**5 + 0*i + 0 = 0. Calculate i.
-1, 0, 10
Let o be (8/24)/(1/36). Let v be 0 - (-9 - o/(-4)). Find w, given that -2 + 9*w**4 - 1 - 3*w**5 + 2*w**2 + 0 + 9*w - 8*w**2 - v*w**3 = 0.
-1, 1
Suppose 37 = 5*f + o - 4*o, 5*f = -3*o + 13. Suppose 45*i = 60 + 30. Suppose -i*r**2 + r**4 + 3/2*r**3 - 1/2*r**f - 2*r + 0 = 0. What is r?
-1, 0, 2
Let z(s) be the first derivative of -10 + 10/9*s**3 - 2*s + 11/6*s**2. Factor z(x).
(2*x + 3)*(5*x - 2)/3
Let t(z) be the first derivati