 1/4*n**5 + 1/4*n**4 + 0*n.
-n**4*(n - 1)/4
Let r(f) be the first derivative of 48*f**2 - 1/2*f**6 - 3*f**4 - 3*f**5 + 16*f**3 + 48*f - 110. Determine c so that r(c) = 0.
-2, -1, 2
Let w = 232 + -226. Let c(y) = 3*y**2 - 51*y - 24. Let b(v) = -5*v. Let x(m) = w*b(m) - c(m). Suppose x(k) = 0. Calculate k.
-1, 8
Let a(w) be the first derivative of -5*w**4/12 - 365*w**3/9 - 1140*w**2 - 2160*w - 2532. Find n such that a(n) = 0.
-36, -1
Suppose -2*w - 5 = d, -5*d - 2*w = -5*w - 40. Let q = 820/7 + -117. Factor 2/7*b**2 - 3/7*b - 3/7*b**4 + 2/7*b**3 + q + 1/7*b**d.
(b - 1)**4*(b + 1)/7
Let n(z) be the third derivative of 11/3*z**4 + 0*z + 7/60*z**6 - 78*z**2 + 0 - 16/3*z**3 + 4/3*z**5. Let n(f) = 0. What is f?
-4, -2, 2/7
Let j(c) be the first derivative of -193 + 2/21*c**3 + 3/7*c**2 - 80/7*c. Solve j(v) = 0 for v.
-8, 5
Let k(i) be the first derivative of i**5/25 + 3*i**4/2 + 24*i**3/5 - 27*i**2 - 729*i/5 + 3936. Find z, given that k(z) = 0.
-27, -3, 3
Let h = 6 + -9. Let s(l) = l**2. Let y(k) = 1 - 8 + 8*k + 0*k**2 - 12*k**2 + 13*k**2. Let a(d) = h*y(d) + 6*s(d). Factor a(v).
3*(v - 7)*(v - 1)
Let c(j) be the third derivative of -j**5/6 + 43*j**4/8 + 13*j**3/6 + 6*j**2 - 12*j. Let z be c(13). Factor -13/3*m**3 - 1/3*m**4 - 12*m - 16*m**2 + z.
-m*(m + 1)*(m + 6)**2/3
Let m(x) = -x**3 - 110*x**2 - 2799*x + 181. Let c be m(-70). Determine n, given that -153/4*n**3 - 15/4*n**4 - 225/2*n**2 - c*n - 18 = 0.
-6, -2, -1/5
Factor 4449236*f + 9282178*f + 12987*f**2 + 5008827*f + 9014055921 + 3*f**3.
3*(f + 1443)**3
Let n = -358 - -1245. Let s = n + -885. Let -2*a + 12/5 + 2/5*a**s = 0. Calculate a.
2, 3
Let o = 1741 - 1827. Let z be (-88)/(-170) + o/731. Factor -2/5*l**4 - 2/5*l + z*l**3 + 2/5*l**2 + 0.
-2*l*(l - 1)**2*(l + 1)/5
Suppose 0 = i - 92 + 104, 5*a - 3*i - 192 = 8*i. Find v such that -a*v**3 + 27 + 261/4*v**2 - 78*v - 9/4*v**4 = 0.
-9, 2/3, 1, 2
Factor -1591*b**3 + 3*b**2 + 4*b**5 - 28*b**4 - 2*b**2 + 1587*b**3 + 24*b**4 + 3*b**2.
4*b**2*(b - 1)**2*(b + 1)
Factor 1234/5*q - 2/5*q**2 + 1236/5.
-2*(q - 618)*(q + 1)/5
Suppose 99*m**2 - 1016*m**3 - 1026*m**3 + 2039*m**3 - 99 + 3*m = 0. What is m?
-1, 1, 33
Let y(j) be the first derivative of -j**7/5880 - j**6/280 - j**5/35 - 5*j**4/42 + 37*j**3/3 + 61. Let d(n) be the third derivative of y(n). Factor d(g).
-(g + 2)**2*(g + 5)/7
Find s such that 44/3*s + 42*s**3 - 130/3*s**2 - 2/3*s**5 - 38/3*s**4 + 0 = 0.
-22, 0, 1
Let r(x) be the third derivative of x**6/24 + 17*x**5/4 - 95*x**4/4 - 1060*x**3/3 + 1823*x**2 - 2*x - 2. Factor r(f).
5*(f - 4)*(f + 2)*(f + 53)
Let d be 2/13 - (-2 + 90185/195). Let u = -460 - d. Factor 0*h**2 - 1/6 + u*h**3 - 1/3*h + 1/6*h**4.
(h - 1)*(h + 1)**3/6
Let t(f) be the first derivative of 1/3*f**3 - 1/8*f**4 + 1/8*f**2 + 6 + 1/24*f**6 - 1/10*f**5 - 1/2*f. Suppose t(q) = 0. Calculate q.
-1, 1, 2
Let -50*q - 5*q**4 + 1/3*q**5 - 65/3*q**2 + 23*q**3 + 0 = 0. What is q?
-1, 0, 5, 6
Let v(g) be the first derivative of 33*g**5/40 + 135*g**4/16 + 2*g**3 + 701. Solve v(m) = 0.
-8, -2/11, 0
Let w be 0 + 3 + -2 + -1. Let j = 13151/11640 - 7/1455. What is v in -j*v**4 - 3/8*v**2 + w*v + 9/8*v**3 + 3/8*v**5 + 0 = 0?
0, 1
Find n such that 60516*n**3 - 31160*n**2 + 482*n + 5205*n - 288 - 455*n = 0.
6/41, 2/9
Let s = -5/29359 - -1409267/205513. Let -44/7*g - 20/7*g**3 + 2 + 2/7*g**4 + s*g**2 = 0. What is g?
1, 7
Suppose 4*x**3 - 1079 + 8*x**2 - 8*x - 2*x**4 + 1079 - 5*x**3 + 3*x**3 = 0. What is x?
-2, 0, 1, 2
Let g(l) be the first derivative of -32*l**2 - 7*l - 1 - 1/3*l**4 - 16/3*l**3. Let h(y) be the first derivative of g(y). Factor h(r).
-4*(r + 4)**2
Let b(m) be the second derivative of -m**7/42 - 4*m**6/15 + 83*m**5/20 + 413*m**4/6 + 688*m**3/3 + 320*m**2 - 2*m - 22. What is a in b(a) = 0?
-8, -1, 10
Let c(q) = -4. Let y(n) = -1. Let x(h) = c(h) - 3*y(h). Suppose 0 = 2*p - 28 + 4. Let m(f) = -2*f**2 + 10*f + 6. Let r(s) = p*x(s) + 2*m(s). Factor r(a).
-4*a*(a - 5)
Suppose 4*z - 39 + 118 = 3*w, -5*w = -5*z - 125. Let s be (2/w)/((-149)/(-3129)). Factor -2/9*n**4 + 0*n + 2/9*n**3 + 4/9*n**s + 0.
-2*n**2*(n - 2)*(n + 1)/9
Let s(i) be the third derivative of 0*i**5 + 18 - 1/320*i**6 + i**2 + 1/1680*i**7 + 0*i + 0*i**3 + 0*i**4. Factor s(j).
j**3*(j - 3)/8
Let n(x) = -5*x**2 - 11. Let p(j) = -27*j**2 - 282*j - 66. Let h(a) = 6*n(a) - p(a). Suppose h(o) = 0. What is o?
0, 94
Factor 5 - 35 + 621118*y**2 - 1325*y - 621338*y**2.
-5*(y + 6)*(44*y + 1)
Suppose -p**2 + 1/4*p**3 - 247/2 - 259/4*p = 0. What is p?
-13, -2, 19
Let i(t) be the third derivative of t**5/360 - 73*t**4/144 - 41*t**3/2 - 4157*t**2 + t. Find d, given that i(d) = 0.
-9, 82
Find b such that -114*b**2 - 35*b**3 + 579*b**2 + 1008*b + 300 - 2188*b = 0.
2/7, 3, 10
Let f = -726170 + 2178518/3. Factor w**3 - 4*w + 1/6*w**2 + 1/6*w**4 + f.
(w - 1)**2*(w + 4)**2/6
Let s(w) be the third derivative of 0*w - 49*w**2 - 4/3*w**3 - 243/10*w**5 + 2 + 9*w**4. Solve s(p) = 0 for p.
2/27
Let m(z) = -7*z**2 + 3 - 5 + z**3 + 2 + 13*z + 2. Let b be m(6). Factor -187 - 2*k**2 + b*k + 4*k - 101.
-2*(k - 12)**2
Let w(k) be the third derivative of k**8/504 + 2*k**7/105 + 13*k**6/180 + 2*k**5/15 + k**4/9 + 130*k**2 + 6. Factor w(p).
2*p*(p + 1)**2*(p + 2)**2/3
Suppose -2 = v + 2*z - z, 4*z = 4*v + 16. Let d = 0 - v. Factor -21*o + 24*o**4 + 12*o**d + 5*o**5 - 2*o**5 + 6*o**5 - 18*o**2 - 6.
3*(o - 1)*(o + 1)**3*(3*o + 2)
Let j = -3385 + 3395. Let f(h) be the first derivative of 0*h**3 + 2/9*h**5 + 0*h**4 + j + 0*h - 1/27*h**6 + 0*h**2. Determine y so that f(y) = 0.
0, 5
Let o(v) be the third derivative of -v**7/105 + 9*v**6/10 - 112*v**5/5 - 392*v**4/3 + 1242*v**2. Let o(f) = 0. What is f?
-2, 0, 28
Find h, given that -22*h - 5*h**2 + 25*h**3 - 55*h + 4*h**4 - 28*h - 2609 + 2699 - 9*h**4 = 0.
-2, 1, 3
Factor -114 - 1/3*h**2 - 39*h.
-(h + 3)*(h + 114)/3
Suppose 3915*u - 4201*u + 572 = 0. Suppose 2*v + 4*n + 6 = 0, v - 4*n - 24 = -9. Factor -3/7*j - 1/7*j**v + 5/7*j**u - 9/7.
-(j - 3)**2*(j + 1)/7
Let i(g) be the first derivative of -g**4/8 + 15*g**3/4 - 39*g**2/2 - 32*g + 169. Let t(f) be the first derivative of i(f). Factor t(p).
-3*(p - 13)*(p - 2)/2
Factor -326700/7 - 1980/7*c - 3/7*c**2.
-3*(c + 330)**2/7
Let h be (155 + -50)*30/84. Factor h*c + 1/2*c**3 - 125/2 - 15/2*c**2.
(c - 5)**3/2
Let q(g) = 4*g - 8. Let d be q(6). Let s(u) = u**3 - 16*u**2 - u + 20. Let m be s(d). Factor -2*i**2 + 2*i**3 - m*i - 151 + 151.
2*i*(i - 2)*(i + 1)
Let s(a) be the first derivative of 2*a**3/9 + 86*a**2/3 + 166*a + 2741. Factor s(f).
2*(f + 3)*(f + 83)/3
Suppose 1 = 2*s + 2*r - 15, 0 = r - 7. Let v(j) = 4*j**2 + 14*j. Suppose 0 = -3*m + m + 8. Let d(t) = t**2 - 1. Let z(b) = m*d(b) + s*v(b). Factor z(u).
2*(u + 2)*(4*u - 1)
Let v be -60 + 20017/333 - (-1066)/126. Suppose -108/7 + 188/7*j**2 + v*j - 16/7*j**4 - 124/7*j**3 = 0. What is j?
-9, -3/4, 1
Let w(j) be the first derivative of -12*j**4 + 18/5*j**5 + 32/3*j**3 + 118 - 1/3*j**6 + 0*j + 0*j**2. Let w(b) = 0. Calculate b.
0, 1, 4
Factor 10984*b - 477013*b - 547475*b + 3584*b**2 + 1671572 - 73100 + 207116*b - 4*b**3.
-4*(b - 447)**2*(b - 2)
Let g(d) = d - 14. Let t(c) = -3*c**2 + 306*c - 147. Let u(h) = -12*g(h) - t(h). Factor u(j).
3*(j - 105)*(j - 1)
Find t, given that 0*t + 0*t**2 + 1/2*t**5 + 0*t**3 + 0 + 118*t**4 = 0.
-236, 0
Let j(l) = 13*l**2 + 21*l - 6. Let a be 6/15 - (-208)/80. Let m(p) = -2*p**2 - p - 1. Let h(w) = a*j(w) + 21*m(w). What is g in h(g) = 0?
1, 13
Factor 4*r**2 - 875*r - 778*r - 1863 + 510*r - 1313 - 437*r.
4*(r - 397)*(r + 2)
Let j(a) be the first derivative of -a**5 - 125*a**4/2 + 265*a**3 - 10*a**2 - 1060*a + 717. Factor j(p).
-5*(p - 2)**2*(p + 1)*(p + 53)
Let s(q) = 13*q + 158. Let u be s(-12). Let g be u/7 + 1 + 45/(-35). Determine a so that g*a**2 + 0 + 6*a - 3/2*a**3 = 0.
-2, 0, 2
Suppose -4*t - 4*m - 28 = -8*t, -17 = -2*t + 3*m. Suppose -r - 4*a + 19 = 0, -t*r + 0*a + 4 = -2*a. Solve -15*g + 23 + 0*g - r + 5*g**2 - 5*g = 0 for g.
2
Suppose -227 = -3*k - 4*m, -k + 3*m + 93 = -0*m. Let f = k + -75. Solve 0*b**2 - f*b - 9*b**2 - 9 + 12*b**2 = 0 for b.
-1, 3
Suppose -17*m + 87 = -117. Factor -154*g**3 + 150*g**3 - 6*g + 20*g**2 - m*g - 6*g.
-4*g*(g - 3)*(g - 2)
Let p(f) be the first derivative of f**3 - 27*f**2/2 - 30*f + 223. Factor p(b).
3*(b - 10)*(b + 1)
Let b = 28 - 0. Suppose