e of g(s). Factor w(p).
2*p*(p + 1)*(p + 2)**2/9
Let h be (((-285)/2)/5)/(-1). Let k = 29 - h. Factor -1/2*w**2 + k*w**4 + 0 + 0*w + 0*w**3.
w**2*(w - 1)*(w + 1)/2
Let c(q) be the first derivative of 1/7*q**2 - 9 + 0*q + 4/21*q**3 + 1/14*q**4. Find b, given that c(b) = 0.
-1, 0
Let u(n) be the first derivative of -9/2*n**2 - 1/4*n**4 - 18 - 4*n - 2*n**3. Factor u(r).
-(r + 1)**2*(r + 4)
Factor -8/11*n**2 + 10/11*n**3 + 0*n + 0 - 2/11*n**4.
-2*n**2*(n - 4)*(n - 1)/11
Let u(k) = -k**5 + k**4 - k**3 - k**2 + k + 1. Let d(f) = -7*f**5 + 10*f**4 - 11*f**3 - 12*f**2 + 12*f + 8. Let s(j) = -3*d(j) + 24*u(j). Solve s(q) = 0 for q.
-2, 0, 1
Let s be 21/2 + -2 - (-12)/(-24). Determine q, given that 24 + 499*q**2 + 2*q**3 - 505*q**2 - s*q + 0*q = 0.
-2, 2, 3
Let p(c) = 2*c**2 + 77 - 48 + 2*c**2 - 13*c**2 - 3*c + c**3. Let v be p(9). Factor -4/13 - 6/13*q - 2/13*q**v.
-2*(q + 1)*(q + 2)/13
What is y in -99/5 + 24/5*y + 3/5*y**2 = 0?
-11, 3
Let l(f) = f**5 + 21*f**4 + 9*f**3 - 53*f**2 - 33*f + 3. Let m(y) = y**5 + y**4 + y**3 - y**2 + y + 1. Let h(u) = -l(u) + 3*m(u). Factor h(i).
2*i*(i - 9)*(i - 2)*(i + 1)**2
Let o(w) = -8*w**3 - 8*w**2 + 3*w + 3. Let u(i) = 5*i**3 + 12*i - 8*i + 10*i**3 - 5 - 9*i + 15*i**2. Let n(h) = 5*o(h) + 3*u(h). Factor n(t).
5*t**2*(t + 1)
Let h(z) be the first derivative of -5/2*z**2 - 10/3*z**3 + 8 + 0*z - 5/4*z**4. Factor h(c).
-5*c*(c + 1)**2
Let v(l) be the first derivative of l**7/280 - l**6/120 - l**5/10 + l**4/2 + 13*l**3/3 - 13. Let o(h) be the third derivative of v(h). Factor o(u).
3*(u - 2)*(u - 1)*(u + 2)
Let x(f) be the first derivative of f**9/4032 - f**7/560 + f**5/160 - 2*f**3/3 - 2. Let d(i) be the third derivative of x(i). Factor d(k).
3*k*(k - 1)**2*(k + 1)**2/4
Let i(q) be the second derivative of q**4/24 + 3*q**3 + 81*q**2 - q - 16. Factor i(u).
(u + 18)**2/2
Suppose -3*s = -x + 53 - 26, 4*x + 4*s + 36 = 0. Let w(g) = g**2 - 3*g - 7. Let k be w(5). Factor 0*a - 2/3*a**k + 0 - 2/3*a**4 + x*a**2.
-2*a**3*(a + 1)/3
Suppose 13*d - 32 = 33. Solve -102*x**3 - 36*x + 49*x**4 - 4*x**2 + 74*x - 30*x + 49*x**d = 0.
-2, -2/7, 0, 2/7, 1
Let k(u) be the first derivative of 2*u**4/7 + 10*u**3/3 + 50*u**2/7 - 250*u/7 - 182. Factor k(x).
2*(x + 5)**2*(4*x - 5)/7
Let l(w) = w**3 - 5*w**2 - 6*w + 2. Suppose 0 = -4*h - 3*j + 15, 3*h = -2*h + 4*j + 42. Let x be l(h). Factor 0 - 4/3*o**3 + 0*o**x + 2/3*o**5 + 2/3*o + 0*o**4.
2*o*(o - 1)**2*(o + 1)**2/3
Let n(h) = -43*h**2 + 256*h + 15. Let q be n(6). Let g(a) be the second derivative of 1/18*a**4 + a + a**2 + 4/9*a**q + 0. Solve g(b) = 0.
-3, -1
Factor -s**2 - 1/8*s**5 + 15/8*s**3 + 0 + 0*s - 3/4*s**4.
-s**2*(s - 1)**2*(s + 8)/8
Determine r, given that -72/7*r + 1/7*r**2 + 71/7 = 0.
1, 71
Let o(d) be the first derivative of -49/5*d + 6 + 7/5*d**2 - 1/15*d**3. Solve o(g) = 0.
7
Find a, given that 680 - 34*a**2 - 232 - 224 + 26*a**3 + 21*a - 229 + a**5 - 9*a**4 = 0.
1, 5
Let k(r) = -11*r - 8. Let f be k(-3). Factor -6*d**3 - 3 + 21*d**2 + 13 + d**3 - f*d - d**2.
-5*(d - 2)*(d - 1)**2
Let q(k) be the second derivative of k**8/6720 - k**7/1260 + k**6/720 + k**4/3 + 24*k. Let g(m) be the third derivative of q(m). Solve g(x) = 0.
0, 1
Let d = 17848 + -17846. Factor 50/3*v + 16/3 + d*v**2.
2*(v + 8)*(3*v + 1)/3
Let u = 282 - 10151/36. Let o(n) be the second derivative of u*n**4 + 1/18*n**3 - 1/90*n**6 - 1/60*n**5 + 0*n**2 + 4*n + 0. Determine m, given that o(m) = 0.
-1, 0, 1
Factor 25/2 + 55*d + 121/2*d**2.
(11*d + 5)**2/2
Suppose -4 = 4*d, 3*d + 7 = 4*n + 4*d. Let v(k) be the second derivative of 4*k + 8/21*k**4 + 0*k**n + 4/21*k**3 + 0 + 1/10*k**5. Suppose v(z) = 0. Calculate z.
-2, -2/7, 0
Let a be (-1265)/(-66)*(-156)/15. Let d = -198 - a. Factor -4/9*t**2 + 8/9*t + d.
-4*(t - 3)*(t + 1)/9
Let t(v) be the third derivative of -v**7/210 - v**6/30 - v**5/15 + v**3/6 - 11*v**2. Let g(w) be the first derivative of t(w). Factor g(i).
-4*i*(i + 1)*(i + 2)
Let j = -12 - -14. Factor -26*s**j + 5*s**5 + 25*s**2 - 3*s**4 - 4*s**5 + 3*s**3.
s**2*(s - 1)**3
Let k(f) be the first derivative of f**3 - 408*f**2 + 55488*f + 6. Factor k(q).
3*(q - 136)**2
Let u(d) be the first derivative of -2*d**3/27 - 26*d**2/9 + 112*d/9 - 182. What is f in u(f) = 0?
-28, 2
Let t(o) be the first derivative of o**5/4 - 17*o**4/16 + 4*o**3/3 - o**2/2 + 435. Factor t(p).
p*(p - 2)*(p - 1)*(5*p - 2)/4
Suppose -10*x = x. Let c(j) be the first derivative of 1/2*j**5 - 3 + 2/3*j**3 + x*j**2 + 3/2*j**4 + 0*j. Suppose c(s) = 0. Calculate s.
-2, -2/5, 0
Let p(l) = -6*l**4 - 19*l**3 - 61*l**2 - 84*l - 41. Suppose -5*r = 16 - 66. Let q(w) = w**4 + w**3 + 1. Let m(y) = r*q(y) + 2*p(y). Find x, given that m(x) = 0.
-6, -1
Let c(v) = 6*v + 4. Let o(k) be the third derivative of 0*k + 1/60*k**5 + 4*k**2 - 7/24*k**4 + 0 - 5/6*k**3. Let d(q) = 3*c(q) + 2*o(q). Factor d(p).
2*(p + 1)**2
Let o(g) be the first derivative of 2*g**3/45 - 7*g**2/5 - 44*g/15 + 171. Factor o(l).
2*(l - 22)*(l + 1)/15
Suppose l + v - 3 = 0, 15 = -4*l - l + 5*v. Factor 4*s**4 + 6*s**5 - 4*s**3 - 2 + 6*s**4 - 2*s - 12*s**2 + l + 4.
2*(s - 1)*(s + 1)**3*(3*s - 1)
Let f(d) be the first derivative of -16 + 2/5*d**4 - 4/5*d - d**2 + 1/15*d**6 - 4/15*d**3 + 8/25*d**5. Solve f(v) = 0.
-2, -1, 1
Let l(x) be the third derivative of x**6/120 - 11*x**5/30 + 121*x**4/24 + x**2 - 3. Factor l(w).
w*(w - 11)**2
Determine y so that -36*y - y**2 + 75*y + 19 + 1 - 31*y = 0.
-2, 10
Suppose 189*v - 187*v - 10 = 0. Let g(y) be the second derivative of 0 + 1/36*y**4 + y + 0*y**3 + 0*y**2 + 1/30*y**6 - 1/20*y**v - 1/126*y**7. Factor g(j).
-j**2*(j - 1)**3/3
Let d(a) be the second derivative of 3*a**5/20 - 13*a**4/14 + 10*a**3/7 + 12*a**2/7 + 135*a. Factor d(k).
3*(k - 2)**2*(7*k + 2)/7
Suppose 6*d**3 - 15*d**3 + 6*d**3 - 4*d**2 + 7*d**3 = 0. What is d?
0, 1
Find b such that 6*b**2 - 54*b - 2/9*b**3 + 162 = 0.
9
Factor 0 + 225/2*s + 1/2*s**3 + 15*s**2.
s*(s + 15)**2/2
Let g be ((-24)/(-28))/((-32)/(-304)) + (-18)/6. What is q in g*q - 3/7 - 108/7*q**2 = 0?
1/6
Let m(p) be the first derivative of -p**6/540 + p**4/36 - 3*p**3 + 9. Let f(g) be the third derivative of m(g). Suppose f(v) = 0. Calculate v.
-1, 1
Let v(b) be the third derivative of -b**6/120 + b**5/4 + 7*b**3/2 + 12*b**2. Let d be v(15). Factor 24*t**3 - 16*t**4 + 0*t + 25*t**5 - d*t**5 - 16*t**2 + 4*t.
4*t*(t - 1)**4
Let j = -2396 - -45530/19. Factor 2/19*f**5 + 0*f**2 + 0*f + 0 - j*f**4 + 4/19*f**3.
2*f**3*(f - 2)*(f - 1)/19
Let v(d) = 13*d + 10*d**2 - 11 + d**2 + 7. Let k(r) = -23*r**2 - 27*r + 9. Let m(p) = -6*k(p) - 13*v(p). Determine u, given that m(u) = 0.
-1, -2/5
Factor -32/7*i - 34/7*i**2 + 2/7.
-2*(i + 1)*(17*i - 1)/7
Let n(l) be the second derivative of 0 + 20*l + 14/3*l**3 - 6*l**2 + 1/5*l**5 - 5/3*l**4. Factor n(y).
4*(y - 3)*(y - 1)**2
Let n(k) be the third derivative of k**5/180 - 5*k**4/72 - k**3/3 - 208*k**2. Suppose n(t) = 0. Calculate t.
-1, 6
Suppose -3*q + 301 = 16. Let c = q + -93. Determine f, given that 20*f - c*f**2 - 49/4*f**5 + 4 + 217/4*f**4 - 64*f**3 = 0.
-2/7, 1, 2
Let c be (-27)/(270/(-20)) - (-10)/(-9). Factor 4 - c*k**2 - 2/9*k**3 + 2/3*k.
-2*(k - 2)*(k + 3)**2/9
Let r(z) be the second derivative of z**4/28 - 9*z**3/7 + 243*z**2/14 - 2*z + 10. Factor r(m).
3*(m - 9)**2/7
Let z(l) = 11*l**2 - 3*l - 7. Suppose 0 = 4*s + 18 + 10. Let u(h) = -10*h - 4 - 23*h + 31*h + 6*h**2. Let q(r) = s*u(r) + 4*z(r). Factor q(n).
2*n*(n + 1)
Let h(t) be the first derivative of 0*t**4 + 0*t**3 + t**2 + 3 - 1/60*t**5 - 1/240*t**6 + 0*t. Let p(a) be the second derivative of h(a). Solve p(c) = 0.
-2, 0
Factor 9/4*r - 1/4*r**4 + 0 - 1/4*r**3 + 9/4*r**2.
-r*(r - 3)*(r + 1)*(r + 3)/4
Let w(p) be the first derivative of 2*p**3 + 0*p - 3/4*p**4 + 0*p**2 - 5. Factor w(b).
-3*b**2*(b - 2)
Solve -1 - 5*m**4 + 15*m**2 + 17/2*m + 1/2*m**3 = 0 for m.
-1, 1/10, 2
Let n = 19 - 13. Determine y so that 11 - n*y + 18 - 5*y**2 + 2*y**2 - 32 = 0.
-1
Let b(u) = u**2 + 147*u - 1570. Let o be b(10). Determine q, given that 0 + 2*q**4 + 10/3*q**3 - 4/3*q**2 + o*q = 0.
-2, 0, 1/3
Let w be 5 + (0 - (-8)/(-4)). Suppose -5*x + 19 = -w*i, -4*x + 4 = 2*i - 20. Suppose 11*c - 9*c - 3 + i*c**2 - 1 = 0. Calculate c.
-2, 1
Let o(c) be the second derivative of -12/11*c**2 + 1/66*c**4 + 40*c + 1/3*c**3 + 0. Factor o(t).
2*(t - 1)*(t + 12)/11