. Factor g(r).
-r*(r + 1)**3*(r + 2)/5
Let d(f) be the first derivative of -4/21*f**3 - 3/2*f**2 + 0*f - 1/21*f**4 + 2 - 1/210*f**5. Let c(g) be the second derivative of d(g). Factor c(j).
-2*(j + 2)**2/7
Suppose -m + 3 = -r, 4*r + 3*m - m - 12 = 0. Suppose 3*s - 5*d - 21 = 0, -d + 2 = -r. Factor 0*l**4 + 7*l**3 + 4*l**5 - 4*l**4 - 10*l**3 - s*l**2 - 17*l**3.
4*l**2*(l - 3)*(l + 1)**2
Solve 16/19*o - 4/19*o**3 + 8/19*o**2 + 0 - 2/19*o**4 = 0 for o.
-2, 0, 2
Determine g, given that -15112*g + 14888*g - 802 + 3938 + 4*g**2 = 0.
28
Let f(o) be the third derivative of o**9/3780 - o**8/1680 - o**7/630 + o**6/180 + 7*o**4/12 - 13*o**2. Let y(m) be the second derivative of f(m). Factor y(z).
4*z*(z - 1)**2*(z + 1)
Factor -45/8 - 5/4*i**2 - 1/8*i**4 + 2*i**3 - 9*i.
-(i - 15)*(i - 3)*(i + 1)**2/8
Let d(b) be the second derivative of -b**5/5 - 7*b**4/3 + 10*b**3/3 + 150*b**2 + 33*b + 1. Factor d(z).
-4*(z - 3)*(z + 5)**2
Let s = -17/6 - -157/30. Suppose s*c - 2/5*c**2 - 18/5 = 0. What is c?
3
Let b = -150/467 - -4019/2335. Determine m, given that 2/5 + 3*m**4 - 19/5*m**3 - m**2 + b*m = 0.
-2/5, -1/3, 1
Let m(z) be the third derivative of -z**4/24 + z**3/2 + 8*z**2. Let n be m(0). Solve j**3 + 2*j**n - 91*j**5 + 3*j**4 - j**3 + 92*j**5 = 0.
-2, -1, 0
Let r(c) = -27*c**2 - 3854*c + 842. Let i(v) = -84*v**2 - 11563*v + 2529. Let h(b) = 6*i(b) - 17*r(b). Factor h(g).
-5*(g + 86)*(9*g - 2)
Let j be 3*2 + -10 + 9. Suppose -4*o + 3*z + 20 = -2*o, 5*o - j*z - 40 = 0. Determine l so that -5*l**o - 26*l**2 - 2*l**5 - 3*l**5 + 26*l**2 = 0.
-1, 0
Factor 10*c**2 - 2/9*c**3 - 10 + 2/9*c.
-2*(c - 45)*(c - 1)*(c + 1)/9
Let z(j) = 2*j**2 - 296*j + 10956. Let m(f) = -2*f**2 + 296*f - 10955. Let g(b) = 4*m(b) + 3*z(b). Factor g(p).
-2*(p - 74)**2
Let w(h) = -h**5 - h**4 - 6*h**3 - 10*h**2 + 8*h - 6. Let t(b) = -b**5 - 6*b**3 - 9*b**2 + 8*b - 5. Let k(o) = 6*t(o) - 5*w(o). Find l such that k(l) = 0.
-1, 0, 2
Let j(a) = 17*a**2 + 13*a - 23. Suppose 11*l = 15*l - 28. Let r(u) = 8*u**2 + 7*u - 12. Let s(n) = l*r(n) - 3*j(n). Let s(k) = 0. What is k?
-3, 1
Let g(w) = -w**2 - w + 1. Let c(x) = -9*x**2 - 2*x + 5. Let m(v) = -9*v**2 - v + 5. Let b(r) = -5*c(r) + 4*m(r). Let t(o) = -b(o) - 5*g(o). Factor t(a).
-a*(4*a + 1)
Solve -14/17*h**3 + 2/17*h**4 - 12/17 + 14/17*h + 10/17*h**2 = 0.
-1, 1, 6
Let s(u) be the first derivative of -u**5/5 - u**4/4 + 2*u**3 + 2*u**2 - 8*u + 437. Factor s(h).
-(h - 2)*(h - 1)*(h + 2)**2
Factor 1/3 + 1/3*h**2 - 2/3*h.
(h - 1)**2/3
Let g(j) = j**3 + 3. Let w be g(0). Suppose w = -2*f + 9. Factor -4*d**3 + 5*d**2 + 4*d**3 - 5 - 3*d - d**f - 4.
-(d - 3)**2*(d + 1)
Suppose 0 = -2*g + 7 + 3. Suppose 4*y - 17 = g*k - 0*k, -3*k - 15 = -4*y. Solve s**y - 1/2*s**5 + 0*s**4 - 1/2*s + 0 + 0*s**2 = 0 for s.
-1, 0, 1
Let o(s) = -s**3 - 26*s**2 + 47*s - 20. Let j(b) = -b**3 + 2*b**2 - 2*b + 1. Let z(n) = 2*j(n) + o(n). Solve z(w) = 0.
-9, 2/3, 1
Find k, given that -27/2*k + 1/2*k**2 + 13 = 0.
1, 26
Determine j, given that -48*j - 46*j**2 + 494*j**2 - 851 + 851 + 76*j**3 = 0.
-6, 0, 2/19
Let t(u) = 3*u**2 + 58*u - 97. Let a be t(-21). Let g(l) be the second derivative of -3/2*l**2 + 1/20*l**5 + 0 - a*l - 1/6*l**3 + 1/4*l**4. Factor g(o).
(o - 1)*(o + 1)*(o + 3)
Let b = 25 + -18. Suppose 0 = -b*d + 9 + 19. Suppose q**3 - 7*q**3 + 2*q**5 - 4*q**d + 6*q + 8*q**2 + 2*q = 0. Calculate q.
-1, 0, 2
Let a(l) = -11*l**3 + 21*l**2 - 15*l + 5. Let d(f) = -10*f**3 + 20*f**2 - 15*f + 5. Let s(g) = 5*a(g) - 6*d(g). Suppose s(v) = 0. What is v?
1
Let v(u) be the second derivative of -u**5/30 + u**4/3 - 4*u**3/3 - 17*u**2/2 - 9*u. Let q(r) be the first derivative of v(r). Factor q(w).
-2*(w - 2)**2
Let z(b) be the second derivative of 0*b**3 - 9 + 1/78*b**4 + 0*b**2 + 1/65*b**5 - 4*b. Solve z(n) = 0.
-1/2, 0
Let h(m) be the first derivative of -2*m**7/245 - m**6/30 - m**5/21 - m**4/42 + 11*m**2/2 - 5. Let t(i) be the second derivative of h(i). Factor t(p).
-4*p*(p + 1)**2*(3*p + 1)/7
Let o(n) be the first derivative of 2*n**5/5 - n**4/2 - 2*n**3/3 + n**2 + 142. Factor o(k).
2*k*(k - 1)**2*(k + 1)
Let h = 1237/2 + -618. Let u(c) be the third derivative of -1/24*c**4 - h*c**3 + 0 - 1/336*c**8 - 1/70*c**7 + 5*c**2 + 1/60*c**6 + 0*c + 1/10*c**5. Factor u(n).
-(n - 1)**2*(n + 1)**2*(n + 3)
Let b = 21803/40 - 545. Let s(g) be the first derivative of 1/8*g**3 - b*g**5 + 0*g + 1 + 0*g**4 + 0*g**2. Factor s(k).
-3*k**2*(k - 1)*(k + 1)/8
Let p(q) be the second derivative of -q**4/24 - 13*q**3/6 + 155*q**2/4 - 415*q. What is o in p(o) = 0?
-31, 5
Factor 768 - 3/2*f**3 - 288*f + 36*f**2.
-3*(f - 8)**3/2
Let t(r) be the first derivative of -r**4/90 - r**3/15 - 2*r**2/15 + 14*r - 11. Let o(m) be the first derivative of t(m). Determine l, given that o(l) = 0.
-2, -1
Suppose 112769 - 115894 + 5*q**3 - 76*q**2 + 3375*q - 179*q**2 = 0. Calculate q.
1, 25
Let q(n) be the third derivative of 0 - 1/165*n**5 + 2/33*n**3 - 1/132*n**4 + 3*n**2 + 0*n + 1/660*n**6. Suppose q(h) = 0. Calculate h.
-1, 1, 2
Let a(s) be the third derivative of -s**6/135 - s**5/27 + s**4/18 - s**2 + 240*s. Factor a(x).
-4*x*(x + 3)*(2*x - 1)/9
Let q(u) = -5*u**3 - 21*u**2 - 36*u - 23. Let y(b) = -56*b**3 - 230*b**2 - 394*b - 254. Let m(h) = -68*q(h) + 6*y(h). Find j, given that m(j) = 0.
-10, -1
Let a(p) be the third derivative of 0 - 19*p**2 + 11/36*p**4 - 2/45*p**5 + 1/3*p**3 + 0*p. Suppose a(i) = 0. What is i?
-1/4, 3
Let d(f) be the first derivative of -5*f**3/3 - 5*f**2 - 5*f - 310. Find g such that d(g) = 0.
-1
Let q(o) = 15*o**4 + 860*o**3 + 1120*o**2 - 295*o - 560. Let h(x) = -x**2 + x. Let l(r) = -5*h(r) - q(r). Determine c so that l(c) = 0.
-56, -1, 2/3
Let k(l) be the second derivative of l**5/50 + 83*l**4/30 + 301*l. Solve k(w) = 0 for w.
-83, 0
Let y = 34 + -19. Factor 86 + 79 + y + 5*w**2 + 60*w.
5*(w + 6)**2
Factor -2*y**2 - 2/15*y**3 + 0 - 52/15*y.
-2*y*(y + 2)*(y + 13)/15
Solve -4/9*i**4 + 0 - 10/9*i**3 + 10/9*i**5 + 4/9*i**2 + 0*i = 0.
-1, 0, 2/5, 1
Let o(x) = 6*x**4 + 24*x**3 + 30*x**2 + 7*x. Let a(s) = -3*s**4 - 12*s**3 - 15*s**2 - 3*s. Suppose 122 = 3*r + 131. Let h(p) = r*o(p) - 5*a(p). Factor h(m).
-3*m*(m + 1)**2*(m + 2)
Suppose -30 = -4*p - 6. Factor 7*b + p*b**2 - 2*b - b - 6*b.
2*b*(3*b - 1)
Let d(n) be the third derivative of n**7/840 - n**6/120 + n**5/60 + 16*n**2 - 3*n. Factor d(l).
l**2*(l - 2)**2/4
Let f(x) be the third derivative of x**6/40 - 3*x**5/20 - x**4/2 + 949*x**2. What is j in f(j) = 0?
-1, 0, 4
Suppose -8*r + 21 + 75 = 0. Let g be (-2 - r/(-4)) + 11. Find m, given that -8 + g*m**2 + 13 - 8*m - 5 = 0.
0, 2/3
Let o(g) be the second derivative of 0 + 2*g + 1/120*g**4 - 1/30*g**3 - 3/20*g**2. Find c, given that o(c) = 0.
-1, 3
Let u(q) be the third derivative of -q**5/12 + 5*q**4/4 - 20*q**3/3 + 61*q**2. Factor u(f).
-5*(f - 4)*(f - 2)
Let w(g) be the second derivative of 28*g - 4*g**2 + 1/10*g**5 + 3*g**3 + 0 - g**4. Let w(r) = 0. Calculate r.
1, 4
Suppose 4*a - 6 = 2. Factor k**4 + 3*k**3 + 4*k**3 - k**3 - 2*k**2 + 7*k**a.
k**2*(k + 1)*(k + 5)
Let l(j) = -2*j - 10. Let u be l(-9). Let v be 4/2*12/u. What is s in -2*s**v - 2 + 6*s**2 - 15 + 9 = 0?
-1, 2
Let s(k) be the second derivative of k**5/10 - 4*k**4 + 23*k**3/3 + 96*k. Suppose s(z) = 0. Calculate z.
0, 1, 23
Let i = -20815/4 - -5175. Let l = i - -29. Let 1/2*y**2 + 1/4*y + 0 + l*y**3 = 0. What is y?
-1, 0
Let u(r) be the third derivative of r**7/1785 - 7*r**6/1020 + 8*r**5/255 - r**4/17 + 13*r**2 - 5*r. Factor u(o).
2*o*(o - 3)*(o - 2)**2/17
Let m be (-6 + 53)/((-1)/(-2) - 1). Let w = 96 + m. Factor -3/5*z**w + 24/5*z - 48/5.
-3*(z - 4)**2/5
Let a(o) = -10*o**3 - 40*o**2 - 58*o - 26. Let u(r) = -40*r**3 - 159*r**2 - 233*r - 105. Let n(h) = -18*a(h) + 4*u(h). Suppose n(i) = 0. Calculate i.
-2, -6/5, -1
Let b(s) be the second derivative of 2/15*s**6 + 0 + 1/63*s**7 + 0*s**2 + 2/3*s**4 + 13/30*s**5 + 4/9*s**3 + 5*s. Solve b(q) = 0 for q.
-2, -1, 0
Let s(f) be the third derivative of 5/96*f**4 + 1/240*f**5 + 0*f + 20*f**2 + 0 - 1/4*f**3. Factor s(c).
(c - 1)*(c + 6)/4
Let p = -98 - -106. Suppose -6*j + p = -2*j. Solve -5*o**4 + 0*o + 0 + 4*o**3 - 4/5*o**j = 0.
0, 2/5
Let m(k) = 15*k**3 - 40*k**2 + 55*k - 5. Let h(o) = 13*o**3 - 39*o**2 + 54*o - 4. Let r(p) = -5*h(p) + 4*m(p). Determine a so that r(a) = 0.
0, 2, 5
Let f be ((-26)/