ive of j**8/120 + 19*j**7/420 + 2*j**6/45 - j**5/15 - 19*j**3/3 + j**2. Let w(h) be the first derivative of d(h). Factor w(n).
2*n*(n + 1)*(n + 2)*(7*n - 2)
Let b(m) be the first derivative of 2*m**3/21 + 2*m**2 - 102*m/7 - 22. Suppose b(d) = 0. Calculate d.
-17, 3
Let s be ((-23)/(322/(-66)) + -5)/(6/(-7)). Suppose -a + a**2 + s - 1/3*a**3 = 0. What is a?
1
Let j(s) = 4*s**2 + 15*s - 46. Let o(b) = 2*b**2 + 8*b - 24. Let f(x) = -4*j(x) + 10*o(x). Factor f(l).
4*(l - 2)*(l + 7)
Determine t, given that -1/6*t**4 - 1/3 - 3/2*t**2 + 5/6*t**3 + 7/6*t = 0.
1, 2
Let d = 25 - 11. Suppose 0*w - 4*w - 2*k = -d, -1 = k. Find f such that w*f**3 + 108*f + 15 + 16 + 36*f**2 + 77 = 0.
-3
Let u(z) = 4*z**3 - 264*z**2 - 5*z - 5. Let x(p) = -12*p**3 + 792*p**2 + 16*p + 16. Let v(h) = 16*u(h) + 5*x(h). Suppose v(w) = 0. What is w?
0, 66
Let j = 33 - 31. Suppose 1 + 14*v**3 - 4 - 3*v**5 - j*v**3 - 7*v**4 - 13 + 32*v**2 = 0. Calculate v.
-2, -1, 2/3, 2
Let n(w) be the third derivative of w**7/1575 + w**6/300 + w**5/450 - w**4/60 - 2*w**3/45 + 80*w**2 + 2*w. What is h in n(h) = 0?
-2, -1, 1
Let a(v) be the first derivative of -v**5/10 + 3*v**4/4 + 31*v**3/6 - 9*v**2 + 345. Solve a(m) = 0.
-4, 0, 1, 9
Let r(t) be the second derivative of 6*t + 9/2*t**2 - 1/4*t**4 - t**3 + 0. Factor r(k).
-3*(k - 1)*(k + 3)
Let l(w) be the second derivative of -w**4/120 - 7*w**3/30 + 3*w**2/4 + 138*w. Determine j, given that l(j) = 0.
-15, 1
Let x = 932 + -550. Find n, given that -6*n**3 + 2*n**4 + 382 - x = 0.
0, 3
Let h be (-50)/(-45) + (-16170)/(-9261). Factor -4/7*w**4 - h*w**2 + 8/7*w + 16/7*w**3 + 0.
-4*w*(w - 2)*(w - 1)**2/7
Factor -3*m**3 + 957*m**2 - 1886*m**2 + 959*m**2.
-3*m**2*(m - 10)
Let v = 137 + -129. Factor v*p**2 + 2 + 5*p - 14*p**2 - p + 8*p**2.
2*(p + 1)**2
Determine a, given that 2889/2*a**2 + 243*a - 1458 + 27/2*a**4 - 971/4*a**3 - 1/4*a**5 = 0.
-1, 1, 18
Let x(w) = 2*w**4 - 9*w**3 - 21*w**2 - 20*w - 3. Let k(j) = 3*j**4 - 18*j**3 - 43*j**2 - 40*j - 5. Let h(a) = 6*k(a) - 10*x(a). Factor h(t).
-2*t*(t + 2)**2*(t + 5)
Let v(y) = y**3 - 10*y**2 + 23*y + 42. Let s(r) = -r**3 - 2*r**2 + r. Let q(x) = -4*s(x) - v(x). Factor q(a).
3*(a - 2)*(a + 1)*(a + 7)
Let m(n) be the first derivative of -4*n**5/5 - 11*n**4 + 56*n**3/3 + 48*n**2 + 215. Let m(l) = 0. What is l?
-12, -1, 0, 2
Let c = -8855/2 + 4428. Factor d - c*d**2 - 1/2.
-(d - 1)**2/2
Let l be (0 + 1)*12*8/32. Suppose -5*n = 5*h - 35, 2*h = -n + l*n - 2. Factor -6*k**n + 128/3*k - 32/3 + 32*k**3 - 176/3*k**2.
-2*(k - 2)**2*(3*k - 2)**2/3
Find a such that 3/4*a**5 + 3/4*a + 0 - 3/2*a**3 + 0*a**2 + 0*a**4 = 0.
-1, 0, 1
Let f(o) be the first derivative of o**6/15 - 3*o**5/10 + o**4/2 - o**3/3 + 14*o + 12. Let i(x) be the first derivative of f(x). Factor i(z).
2*z*(z - 1)**3
Let h be (2 - -1) + 0 + -1. Let j(m) = -m**2 + 32*m + 476. Let o be j(43). Find z, given that 0 + 2/9*z - 2/9*z**o - 2/9*z**4 + 2/9*z**h = 0.
-1, 0, 1
Let r = 0 - 6. Let k = r + 9. Factor -3*z**4 - z - 4*z - k*z**3 + 5*z.
-3*z**3*(z + 1)
Solve 10*t**3 - 26*t**2 + 2*t**4 + 68*t - 54*t + 0*t**4 = 0.
-7, 0, 1
Determine y so that 12*y + 2/3*y**2 + 64/3 = 0.
-16, -2
Suppose 5*r = -4*q - 8, -14*q + 5*r + 32 = -10*q. Let p(h) be the first derivative of -81/2*h**2 + 9*h**q + 81*h + 4 - 3/4*h**4. Solve p(l) = 0 for l.
3
Suppose 14/11 - 12/11*j + 2/11*j**4 + 12/11*j**3 - 16/11*j**2 = 0. What is j?
-7, -1, 1
Let r be 1602/99 + -13 - (-4)/(-22). Solve 32/5 - 16/5*t - 72*t**2 + 248/5*t**4 + 4*t**r - 84/5*t**5 = 0 for t.
-1, -1/3, 2/7, 2
Let c(r) = -25*r**4 + 115*r**3 - 525*r**2 + 225*r + 3450. Let t(z) = z**4 - z**3 + z - 1. Let f(h) = c(h) + 20*t(h). Factor f(b).
-5*(b - 7)**3*(b + 2)
Let b(r) be the first derivative of 8/9*r + 1/27*r**6 - 19 + 16/9*r**2 + 50/27*r**3 + 14/45*r**5 + 19/18*r**4. Factor b(w).
2*(w + 1)**3*(w + 2)**2/9
Solve 136*s**3 + 3183624*s + 121773618 + 2/9*s**4 + 31212*s**2 = 0.
-153
Let b = 12468 - 12468. Determine u so that 1/2*u + 1/2*u**2 + b = 0.
-1, 0
Let t(f) be the third derivative of f**5/15 + 13*f**4/3 + 50*f**3/3 + 16*f**2 - 4. Let t(h) = 0. Calculate h.
-25, -1
Let r(n) be the first derivative of 2*n**6/3 - 8*n**5/5 - 4*n**4 + 8*n**3/3 + 6*n**2 - 7. Factor r(f).
4*f*(f - 3)*(f - 1)*(f + 1)**2
Suppose -2*q + 4 = m, -5*q - 546*m = -553*m - 29. Factor 0 + 2/3*f**2 - 4/3*f**q + 4/3*f - 2/3*f**4.
-2*f*(f - 1)*(f + 1)*(f + 2)/3
Let y = 298 + -155. Let t = y + -141. Find r such that -1/6*r**t - 1/3 + 1/2*r = 0.
1, 2
Let z(t) = -t - 3. Let g be z(-6). Let d be (8 - 25/5) + -2 + 1. Determine s, given that s**2 - 4 - s**g + 4*s**3 - d*s**3 + 2*s**2 = 0.
-2, 1
Let h(g) = -g**2 + 11*g + 6. Let i(r) = r + 1. Let u(j) = -h(j) + 6*i(j). Let o be u(6). Suppose -3*z**2 - 1 - 2 + o*z + 0 = 0. What is z?
1
Let p(u) = u**4 + u**2 + u. Let q(c) = 25*c**4 + 100*c**3 + 130*c**2 + 5*c. Let a(w) = -5*p(w) + q(w). Factor a(j).
5*j**2*(2*j + 5)**2
Let i(y) be the first derivative of 2*y**5/45 - y**4/18 - 2*y**3/27 + y**2/9 - 53. Factor i(x).
2*x*(x - 1)**2*(x + 1)/9
Let g be (-15 + 5)/(-2) - 5. Suppose 6*s + 14 - 26 = g. Factor -6/7*u**s + 9/7*u - 3/7*u**3 + 0.
-3*u*(u - 1)*(u + 3)/7
Suppose o + 5*b - 27 = 0, -3*o + 0*b = 2*b - 16. Factor -4*g**3 + 3*g**3 - 48*g**2 - 50 - 45*g + 36*g**o.
-(g + 2)*(g + 5)**2
Let j be 125/35 + (-12)/(-28). Find o such that 114*o + 10*o**3 - 15*o**2 + 6 + 14 + 5*o**j - 134*o = 0.
-2, 1
Suppose -6*w + 25 = g + 14, 2*w - 1 = -3*g. Find r such that -2/3*r**4 - 2/3 + 4/3*r**w + 1/3*r**5 - 2/3*r**3 + 1/3*r = 0.
-1, 1, 2
Let f(o) = -o**3 + 7*o**2 + 5*o - 8. Let m be f(7). Factor 2*g - m*g**2 - 3*g - 21*g**2 + 4*g**3 + 51*g**2.
g*(g + 1)*(4*g - 1)
Let h(m) be the first derivative of m**4/12 - 2*m**3/3 + 2*m**2 - 8*m/3 - 38. Factor h(o).
(o - 2)**3/3
Factor 2/7*i**2 + 62*i + 0.
2*i*(i + 217)/7
Determine g so that -5/2*g**2 - 1/2*g**3 + 3*g + 0 = 0.
-6, 0, 1
What is q in -32*q - 3*q**2 + 55*q - 29*q = 0?
-2, 0
Let w(a) = a**2 - 4*a + 2. Suppose 4*b - 8 = -3*h - 2*h, 5*b + 27 = 3*h. Let l be w(h). Factor k**2 + 0*k**l - 134 + k**3 + 134.
k**2*(k + 1)
Let k(v) = 7*v**2 + 2*v + 1. Let o(f) be the second derivative of -5*f**4/4 - 2*f**3/3 - f**2 - f. Let j = 8 - -5. Let i(w) = j*k(w) + 6*o(w). Factor i(p).
(p + 1)**2
Let p(j) be the first derivative of 0*j**3 + 3/2*j**4 + 0*j**2 - 35 + 0*j - 5/2*j**6 + 9/5*j**5. Factor p(d).
-3*d**3*(d - 1)*(5*d + 2)
Suppose 0 = -0*w - w + 4. Let x(s) be the second derivative of 2*s - 1/4*s**w + 0 - 3/2*s**3 - 3*s**2. Find j, given that x(j) = 0.
-2, -1
Let j(m) be the second derivative of m**4/20 + 2*m**3/5 - 27*m**2/2 + 62*m. Factor j(u).
3*(u - 5)*(u + 9)/5
Suppose -640000/3 - 320/3*p**3 - 4/3*p**4 - 128000/3*p - 3200*p**2 = 0. What is p?
-20
Let m(r) be the third derivative of r**7/945 - r**6/270 - 29*r**5/270 - 7*r**4/18 - 20*r**2 + 2*r. Find i, given that m(i) = 0.
-3, -2, 0, 7
Factor -2*u**5 - 17 + 11 + 32*u**3 + 4*u**5 - 26 - 32*u + 14*u**4 + 16*u**2.
2*(u - 1)*(u + 2)**4
Let b(q) be the third derivative of 0 - 7*q**2 + 0*q**4 + 0*q**3 - 1/390*q**5 + 0*q. Solve b(v) = 0.
0
Solve -1/4*j**2 + 4 - 3/2*j = 0.
-8, 2
Suppose -2 = 2*s, 0 = 2*x - 9*s + 4*s - 5. Factor x + 3/2*c + 3/4*c**2.
3*c*(c + 2)/4
Let h = 11427 + -22853/2. Factor 0*u**2 + 1/4*u**3 - 3/4*u + h.
(u - 1)**2*(u + 2)/4
Suppose 3*g + 14 = 8. Let f(j) = 3*j**4 + 3*j**3 - j**2 - 5*j + 2. Let p(u) = u**2 - u + 1. Let c(k) = g*p(k) + f(k). Find v, given that c(v) = 0.
-1, 0, 1
Let h(q) be the first derivative of 5/8*q**4 - 8 - 5/4*q**2 + 0*q**3 + 0*q. Suppose h(d) = 0. Calculate d.
-1, 0, 1
Let g(w) be the second derivative of w**4/84 + 4*w**3/7 - 54*w. Let g(h) = 0. What is h?
-24, 0
Let o(j) be the second derivative of -j**5/70 + 2*j**4/21 - 5*j**3/21 + 2*j**2/7 - 163*j. Let o(y) = 0. What is y?
1, 2
Let i(b) be the third derivative of -b**6/420 + 13*b**5/210 - 23*b**4/84 + 11*b**3/21 + b**2 + 48*b. Factor i(d).
-2*(d - 11)*(d - 1)**2/7
What is j in 55*j**3 - 13/2 + 3/2*j**5 - 1/2*j + 39*j**2 + 47/2*j**4 = 0?
-13, -1, 1/3
Let d(o) be the second derivative of o**6/6 + 9*o**5/4 - 5*o**4/4 - 145*o**3/6 - 45*o**2 - 19*o - 1. Let d(j) = 0. What is j?
-9, -1, 2
Suppose -y + 3 = 2*b - 6, 3*y + 2*b - 15 = 0. Let w(s) = -s + 7. Let p be w(7). Solve p*o**3 + y*o**4 - 4*o**3 + 3*o**2 + 3*o**3 - 5*o**3 = 0 for o.
0, 1
Let z(o) = -o**3 - 6*o**2