- 14045. Let a(n) = 6*k(n) + 13*o(n). Factor a(r).
-5*(r - 53)**2
Let i(d) be the first derivative of -3*d**4/8 - 7*d**3/2 + 55. Factor i(o).
-3*o**2*(o + 7)/2
Let c(u) = u**4 - u**2 + 1. Let j = -38 + 42. Let v(m) = 13*m**4 + 7*m**3 - 6*m**2 + 4. Let d(h) = j*c(h) - v(h). Factor d(o).
-o**2*(o + 1)*(9*o - 2)
Let i(t) = -t**2 + 9*t - 5. Let b be i(7). Suppose -2*k + 7 = -4*y + 35, k = y - b. Find q such that 5*q**4 + y*q**3 - 3*q**5 - 3*q**2 - 2*q**2 - 2*q**5 = 0.
-1, 0, 1
Let m(x) = 50*x**2 - 66*x - 7. Let v(d) = 7*d**2 - d - 1. Let i(y) = 5*m(y) - 35*v(y). Factor i(a).
5*a*(a - 59)
Let z be (-2)/(-2) + 40 + (-544)/17. Suppose z*t + 3/2*t**2 - 21/2 = 0. What is t?
-7, 1
Let v(b) be the first derivative of -b**4/2 + 8*b**3/3 - b**2 - 12*b + 18. Let v(h) = 0. Calculate h.
-1, 2, 3
Factor -12*g**4 - 29*g**2 - 4*g**5 + 36*g**3 - 32*g**2 + 41*g**2.
-4*g**2*(g - 1)**2*(g + 5)
Suppose 0 = -4*w + 32 + 96. Let h = 34 - w. Solve 3/2*g**3 + 0*g**h + 0*g + 3/2*g**4 + 0 = 0 for g.
-1, 0
Let g(v) be the first derivative of -8 + 0*v**4 + 3/35*v**5 + 0*v**2 - 1/14*v**6 + 0*v + 0*v**3. Factor g(b).
-3*b**4*(b - 1)/7
Let d(p) = -4*p**4 + 2*p**3 + 3*p**2 - 4*p - 7. Let j(o) = -o**4 - 1. Let m = 97 + -98. Let r(f) = m*d(f) + 3*j(f). Let r(t) = 0. What is t?
-1, 2
Let h(q) = 12*q - 369. Let a be h(31). Determine j so that -2/11*j**a - 2/11*j**4 + 0 + 0*j + 4/11*j**2 = 0.
-2, 0, 1
Let j be 5/(5 + 25)*2. Let q(t) be the second derivative of 0*t**3 + 0 + 1/18*t**4 + 2*t - j*t**2. Factor q(y).
2*(y - 1)*(y + 1)/3
Let z = 2839/5670 - 2/2835. Let x(r) be the first derivative of -11 + 0*r**2 + z*r - 1/6*r**3. Factor x(w).
-(w - 1)*(w + 1)/2
Let b(c) be the second derivative of -1/600*c**6 + 0*c**5 + c**2 + 1/15*c**3 + 2*c + 0 + 1/40*c**4. Let p(i) be the first derivative of b(i). Factor p(r).
-(r - 2)*(r + 1)**2/5
Let w = -2/949 - -953/1898. Factor -1/2*h**4 + 0 + 1/2*h**2 + w*h**3 - 1/2*h.
-h*(h - 1)**2*(h + 1)/2
Let o(s) be the third derivative of -s**6/60 - s**5/6 - s**4/2 - 215*s**2. Find a such that o(a) = 0.
-3, -2, 0
Let g(i) = i**3 + 6*i**2 - 9*i - 10. Let p be g(-7). Suppose 0 = -3*w + p*c + 17, -4*c - 10 + 2 = 0. Factor 0*s**3 + s**w + 3*s**3 - 3*s**3 - s.
s*(s - 1)*(s + 1)
Let n(a) = -5*a**4 - 7*a**3 + 2*a**2 + 7*a - 3. Let g(c) = 11*c**4 + 15*c**3 - 4*c**2 - 15*c + 7. Let t(f) = -3*g(f) - 7*n(f). Find u such that t(u) = 0.
-2, -1, 0, 1
Solve 4/5*n + 6/5*n**3 + 0 + 14/5*n**2 - 14/5*n**4 - 2*n**5 = 0 for n.
-1, -2/5, 0, 1
Let b(w) be the first derivative of 18 + 0*w**3 + 0*w**2 + 1/10*w**4 + 0*w. Suppose b(k) = 0. Calculate k.
0
Let b = 18 + -18. Suppose -g + 13 - 1 = b. Factor 7 + g*x + 2 - 9*x**2 + 12*x**2.
3*(x + 1)*(x + 3)
Let n(j) be the third derivative of 25*j**5/12 + 25*j**4 + 120*j**3 - j**2 + 136. Suppose n(z) = 0. What is z?
-12/5
Let s(q) = -q**2 + 8*q + 5. Let j be s(8). Let o**3 + 3*o**5 - 4*o**j - o**4 + o**4 = 0. What is o?
-1, 0, 1
Let 6477/5*i**2 - 1681/5 + 4/5*i**4 - 1025*i + 65*i**3 = 0. What is i?
-41, -1/4, 1
Let y(z) be the second derivative of z**6/1080 + z**5/120 - 5*z**4/36 + z**3 + 27*z. Let i(g) be the second derivative of y(g). Factor i(f).
(f - 2)*(f + 5)/3
Suppose 12 = -10*k + 14*k. Suppose -c + 4*o - 4 = -5*c, -k*c - 2*o = -4. Let -56*z + 121*z - 57*z + z**c + 16 = 0. What is z?
-4
Let c = 80 + -90. Let g be (2/c)/(2 - 3 - 0). Let 0*w**3 - g*w**4 + 0*w + 0 + 1/5*w**2 = 0. What is w?
-1, 0, 1
Suppose 0 = -5*h + 4*i + 37, -h + 0*h + i = -8. Suppose -4*c + 2*k + 16 = -0*k, 18 = -c - h*k. Factor 8/7 - 2/7*l**c + 0*l.
-2*(l - 2)*(l + 2)/7
Let v = 4677 + -4674. What is r in 0 - 4*r + 16*r**4 + 166/5*r**2 - 366/5*r**v + 32/5*r**5 = 0?
-5, 0, 1/4, 2
Let a(i) = -9*i**2 - 44*i + 7. Let v be a(-5). Let y(m) be the first derivative of 1/3*m**3 - m + 0*m**v + 5. Let y(r) = 0. What is r?
-1, 1
Let x(a) be the second derivative of -a**4/24 + 34*a**3/3 - 1156*a**2 + 5*a + 4. Factor x(i).
-(i - 68)**2/2
Factor -s**3 - 13/2*s**2 + 0 + 13/2*s**4 + s.
s*(s - 1)*(s + 1)*(13*s - 2)/2
Let w(f) = 5 - 2*f + 12 - 19. Let h be w(-2). Factor 4/3 + 1/3*z**h + 4/3*z.
(z + 2)**2/3
Let z(w) be the second derivative of 0*w**3 - 2/35*w**5 - w + 0*w**2 + 0 - 2/147*w**7 + 0*w**4 - 2/35*w**6. Factor z(h).
-4*h**3*(h + 1)*(h + 2)/7
Let l(c) = -c**2 + 7*c + 11. Let b = 19 - 11. Let p be l(b). Factor 5 + 6*k + 2*k**3 + 0*k**3 + 6*k**2 - p.
2*(k + 1)**3
Let j be (-4)/22 - (-1820)/6864. Let m(s) be the second derivative of 0 + 0*s**2 + 3*s - 1/72*s**4 - j*s**3. Factor m(n).
-n*(n + 3)/6
Let 27/5 - 6/5*d - 1/5*d**2 = 0. Calculate d.
-9, 3
Let 2772 - 1365 - 1377 - 32*f + 2*f**2 = 0. What is f?
1, 15
Let 316/3*z**3 + 0 - 56*z**2 + 4/3*z**5 - 320/3*z + 56*z**4 = 0. Calculate z.
-40, -2, -1, 0, 1
Let z(x) be the second derivative of -3/20*x**5 + 0*x**6 + 0*x**2 + 0*x**3 - 6*x + 0*x**4 + 0 + 1/14*x**7. Let z(j) = 0. What is j?
-1, 0, 1
Suppose 1/2*v**2 + 45 + 19/2*v = 0. Calculate v.
-10, -9
Let i(k) = -8*k**3 + 11*k**2 - 3*k - 5. Let x(n) = -9*n**3 + 12*n**2 - 3*n - 6. Let q(g) = 6*i(g) - 5*x(g). Solve q(h) = 0.
0, 1
Factor -329/6*w - 15 - 49/6*w**2.
-(7*w + 2)*(7*w + 45)/6
Let n = -20 + 5. Let t = 18 + n. Factor -3*j**t + 2*j**3 + 5*j**2 - 4*j**2.
-j**2*(j - 1)
Determine w so that 4*w**3 - 11995*w**2 + 14*w**4 + 11939*w**2 - 6*w - 10*w = 0.
-2, -2/7, 0, 2
Factor -1/3*w**3 + 0 - 13/3*w**2 + 14/3*w.
-w*(w - 1)*(w + 14)/3
Let u = -9727 - -29236/3. Factor 13310/3*p**2 - 1210/3*p**3 + 161051/3 - 1/3*p**5 - 73205/3*p + u*p**4.
-(p - 11)**5/3
Factor 0 + n + 3/2*n**2 + 1/2*n**3.
n*(n + 1)*(n + 2)/2
Suppose -2*l + 52 = -2*y - 2*y, 0 = 5*l + y - 119. Let d be (3/l*2)/((-21)/(-56)). Suppose 2*g**3 + 2/3*g + 2*g**2 + d*g**4 + 0 = 0. Calculate g.
-1, 0
Let w(i) be the second derivative of -i**5/150 + i**4/18 - 8*i**3/45 + 4*i**2/15 + 417*i. Factor w(b).
-2*(b - 2)**2*(b - 1)/15
Let s(f) be the first derivative of f**3 + 309*f**2 + 31827*f + 122. Factor s(h).
3*(h + 103)**2
Let i(j) be the first derivative of -j**5/20 + j**4/2 + j**3/12 - j**2 - 56. Determine p so that i(p) = 0.
-1, 0, 1, 8
Let v(k) be the third derivative of k**8/3864 - k**6/460 + k**5/345 - 128*k**2. Factor v(o).
2*o**2*(o - 1)**2*(o + 2)/23
Let p(l) be the second derivative of l**7/280 + l**6/40 + 3*l**5/40 + l**4/8 - 25*l**3/6 - 11*l. Let g(c) be the second derivative of p(c). Factor g(q).
3*(q + 1)**3
Let u(z) be the second derivative of -z**5/100 - z**4/15 + z**3/6 - 25*z. Factor u(y).
-y*(y - 1)*(y + 5)/5
Let t(g) = 2*g**4 - 9*g**3 + 4*g**2 + 3*g. Let y(f) = f**4 - 8*f**3 + 3*f**2 + 4*f. Let d(l) = -2*t(l) + 3*y(l). Determine h so that d(h) = 0.
-6, -1, 0, 1
Factor 8/3*u + 1/3*u**2 - 3.
(u - 1)*(u + 9)/3
Let k = -5849/4 + 1471. Let s = k + -85/12. Factor -s*p**3 + 4*p**2 + 2/3 - 3*p.
-(p - 1)**2*(5*p - 2)/3
Let x = -54707/4 + 13677. Determine p, given that x + 5/4*p**2 + 3/2*p = 0.
-1, -1/5
Let o be (-5 - -4) + 6/(-4). Let h = o + 8/3. Solve 1/6*r**2 - 1/6 + h*r**3 - 1/6*r = 0 for r.
-1, 1
Suppose -20 = 4*d - 4, -5*d = -3*c + 26. Determine o so that -3 - 328*o**c - 3*o**3 + 337*o**2 - 9 = 0.
-1, 2
Find n such that 1/4*n**2 - 23/4 + 11/2*n = 0.
-23, 1
Suppose -21*u - 19*u = 118*u. Factor 0 - 1/6*b**5 + 1/6*b**3 - 1/6*b**4 + 1/6*b**2 + u*b.
-b**2*(b - 1)*(b + 1)**2/6
Let c(x) be the third derivative of -3*x**7/140 + x**6/10 + 7*x**5/8 + x**4/4 - 5*x**3 + 4*x**2 - 12. Determine s, given that c(s) = 0.
-2, -1, 2/3, 5
Let y be ((-2)/5)/(2/30). Let t = -4 - y. Factor 3*z**2 - 2*z**t - 3*z**2 - 2*z + 4.
-2*(z - 1)*(z + 2)
Let l(s) = 2*s - 50. Let t be l(-12). Let p = -70 - t. Factor 2/3*q**p + 0 + 4/3*q**3 + 0*q + 2/3*q**2.
2*q**2*(q + 1)**2/3
Let y(v) be the first derivative of -v**4/7 - 20*v**3/21 + 50*v**2/7 + 500*v/7 - 14. Factor y(t).
-4*(t - 5)*(t + 5)**2/7
Let b(a) = 894*a - 46. Let f be b(8). Factor 7106 - 3*x**4 - f + 3*x - 3*x**3 + 3*x**2.
-3*x*(x - 1)*(x + 1)**2
Let w(b) be the first derivative of -4/9*b + 5 + 1/9*b**2 + 2/27*b**3. Factor w(u).
2*(u - 1)*(u + 2)/9
Let w(c) = 3*c**2 - 4*c - 12. Let y be w(-4). Let m = 54 - y. Suppose 1/2*t**m + 0 + 1/2*t = 0. Calculate t.
-1, 0
Let p(o) be the first derivative of -o**6/120 + o**5/15 - o**4/6 - o**2 + 10. Let r(j) be the second derivative of p(j). Factor r(n).
-n*(n - 2)**2
Let p(q) be the third derivative of -q**6/60 - q**5/6 - q**4/6 + 8*q**3/3 - 373*q**2