- -68/8407. Factor k*z**3 - 2/15*z**4 + 0*z + 0 - 4/3*z**2.
-2*z**2*(z - 5)*(z - 2)/15
Suppose -4*t = 6 - 14. Let u(o) be the first derivative of -t*o**3 + 7*o**3 + 18*o**2 + 12*o - 3 + 2. Factor u(a).
3*(a + 2)*(5*a + 2)
Find y, given that 128/7*y + 8/7*y**2 - 384/7 - 4/7*y**3 = 0.
-6, 4
Let q(p) be the first derivative of -13*p**5/15 - 49*p**4/12 - 40*p**3/9 + 2*p**2 - 11334. Factor q(y).
-y*(y + 2)**2*(13*y - 3)/3
Suppose -2*w + 1 + 5 = 0. Let b be 7/5 + 369*30/(-8550) + (-18)/(-190). Factor b*o**w - 2/5*o**2 + 0 + 0*o.
o**2*(o - 2)/5
Factor 7963*r**2 + 4*r**4 - 144*r - 8*r**3 + 52*r**3 - 7867*r**2.
4*r*(r - 1)*(r + 6)**2
Let d(w) = 107*w**2 - 1007*w - 1982. Let i(y) = 16*y**2 - 144*y - 283. Let a(x) = -3*d(x) + 20*i(x). Determine p so that a(p) = 0.
-2, 143
Let f(n) be the second derivative of 2*n**7/105 + n**6/15 - 7*n**5/15 + 2*n**4/3 + 85*n**2 + 89*n. Let r(z) be the first derivative of f(z). Factor r(p).
4*p*(p - 1)**2*(p + 4)
Let w(d) be the first derivative of d**4/8 + 3*d**3/2 + 6*d**2 + 13*d - 43. Let m(c) be the first derivative of w(c). Factor m(f).
3*(f + 2)*(f + 4)/2
Let x(z) be the third derivative of -20/3*z**4 + 0 - 23*z**2 + 19/30*z**5 - 100/3*z**3 + 0*z - 1/60*z**6. Factor x(a).
-2*(a - 10)**2*(a + 1)
Let b be (-20 - 3357/(-168))/(2/(-7)). Let h(a) be the first derivative of 0*a**3 + b*a**4 - 3/8*a**2 - 1/2*a - 19. Solve h(t) = 0 for t.
-1, 2
Let o(a) = -24*a + 6. Let z be o(-28). Suppose z*m**5 + 18*m**4 - 702*m**5 - 26*m**2 + 8*m**4 - 2*m**2 + 2 + 24*m**3 = 0. What is m?
-1, -1/4, 1/3, 1
Let z be (-3)/(-30) - (9 - 266/30)/((-60)/1605). Let 0 + z*d**3 - d**4 - 5/3*d**2 - d = 0. What is d?
-1/3, 0, 1, 3
Let k be (-3810)/(-24) - 2/(-8). Suppose -960 = 12*c - 18*c. Factor -25*h**2 + k + c - 309 - 45*h.
-5*(h + 2)*(5*h - 1)
Let b(p) = p**3 + 23*p**2 + p + 25. Let y be b(-23). Determine v so that 485*v - 125*v + 75*v**2 + 3*v**3 + y*v**3 + 540 = 0.
-6, -3
Let k be ((-342)/10)/(-3) - 15/(-25). Factor a**3 - 50*a - k*a**3 + 6*a**3 - 28*a**2 - 35*a - 62*a**2.
-5*a*(a + 1)*(a + 17)
Let t(v) be the second derivative of 1/35*v**5 + 2/21*v**4 + 0 + 0*v**2 - 2/7*v**3 + 120*v. Suppose t(o) = 0. Calculate o.
-3, 0, 1
Let f(q) be the first derivative of q**5/40 + 7*q**4/16 - 41*q**3/3 + 305*q**2/8 - 297*q/8 + 2121. Determine j, given that f(j) = 0.
-27, 1, 11
Let d(f) be the second derivative of 0*f**3 - 1/105*f**7 + 0*f**2 + 9*f - 1/100*f**5 + 0*f**4 - 3 - 1/50*f**6. Let d(s) = 0. Calculate s.
-1, -1/2, 0
Let z = 468318 - 468315. Find t such that -12/5 - 16/5*t + 1/5*t**z - 3/5*t**2 = 0.
-2, -1, 6
Let c(g) = g**4 - g - 1. Let v(f) = 9*f**4 + 9*f**3 - 30*f**2 - 6*f - 6. Suppose 44 = 5*a + 14. Let r(s) = a*c(s) - v(s). Suppose r(u) = 0. What is u?
-5, 0, 2
Let y(h) be the first derivative of -1/2*h**2 + 46 + 0*h - 7/6*h**3. Factor y(v).
-v*(7*v + 2)/2
Let j(s) be the third derivative of -s**8/336 + 13*s**6/120 - 4*s**5/15 - s**4/2 + 8*s**3/3 + 1010*s**2. Solve j(c) = 0.
-4, -1, 1, 2
Let z(s) = 6*s + 62. Let d be z(-10). Let -7*w**2 + 6 + 2*w**d - 105*w**3 - 3*w - w**2 + 108*w**3 = 0. Calculate w.
-1, 1, 2
Let v be 1/23 - (-1967)/103408. Let h(x) be the first derivative of v*x**4 - 16 - 1/20*x**5 + 0*x + 1/12*x**3 - 1/8*x**2. Factor h(j).
-j*(j - 1)**2*(j + 1)/4
Let h = 2685 - 2685. Let d(m) be the third derivative of h + 0*m**6 + 0*m - 18*m**2 + 0*m**3 + 0*m**4 + 0*m**5 - 1/420*m**7. Solve d(l) = 0 for l.
0
Let r(f) be the second derivative of -5*f**3/6 + 5*f**2/2 - 10*f. Let u be r(0). Let -32*y - 9*y**2 + 2*y**4 + 17*y + 3*y**3 - u - 1 + y**4 = 0. What is y?
-1, 2
Let k(v) = 323*v + 40. Let m be k(1). Let d = m + -360. Factor 0 - 8/3*x**d + 0*x - 14/9*x**4 + 8/9*x**2.
-2*x**2*(x + 2)*(7*x - 2)/9
Let s(l) be the third derivative of l**5/150 - 7*l**4/90 - 29*l**3/9 + 4*l**2 - 83*l + 4. Factor s(d).
2*(d + 5)*(3*d - 29)/15
Let k(g) be the second derivative of -g**7/168 + 23*g**6/12 - 907*g**5/80 + 337*g**4/24 + 227*g**3/6 - 113*g**2 + 44*g + 12. Determine u so that k(u) = 0.
-1, 1, 2, 226
Suppose 1693*p = 1695*p - 3388. Find h, given that h**2 + 1763 + 3*h**2 - 3385 + p - 76*h = 0.
1, 18
Let q(c) be the first derivative of -2*c**3/9 + 19*c**2/2 - 28*c/3 + 339. Suppose q(j) = 0. Calculate j.
1/2, 28
What is m in -87*m + 2743195*m**3 - 42*m**2 - 2743198*m**3 - 57*m = 0?
-8, -6, 0
Factor 3*x**3 + x**3 - 3*x**3 + 1423790 + 2447928 + 465*x**2 - 147843 + 72075*x.
(x + 155)**3
Factor 97*y**3 + 17412 + 99*y**3 + 2996*y**2 + 8508 + 15264*y.
4*(y + 5)*(7*y + 36)**2
Let u(z) be the first derivative of z**7/1470 - z**6/63 + 11*z**5/70 - 6*z**4/7 - 47*z**3/3 + 121. Let t(l) be the third derivative of u(l). Factor t(n).
4*(n - 4)*(n - 3)**2/7
Let x(t) be the third derivative of -7/8*t**3 - 5/48*t**4 + 0*t - 1/240*t**5 - 16*t**2 - 1. Determine d so that x(d) = 0.
-7, -3
Let q(k) be the first derivative of -k**5/30 + k**4/24 + 5*k**3/3 + 4936. Factor q(b).
-b**2*(b - 6)*(b + 5)/6
Suppose 0 = 173*j + 70*j. Let w(n) be the second derivative of 0 + 0*n**3 + 1/80*n**5 + j*n**2 + 1/24*n**4 - 27*n. Factor w(h).
h**2*(h + 2)/4
Let 0 + 0*k - 637/6*k**3 + 1/6*k**4 + 0*k**2 = 0. What is k?
0, 637
Let u(q) be the first derivative of -q**5/25 - 183*q**4/10 - 14884*q**3/5 - 907924*q**2/5 - 127. Find t, given that u(t) = 0.
-122, 0
Let v(j) be the first derivative of -4*j**5/25 + 68*j**4/5 - 1988*j**3/5 + 19864*j**2/5 + 45968*j/5 - 2299. Determine n, given that v(n) = 0.
-1, 17, 26
Let m be -3*(-5)/(-30)*0. Let z be (-9)/(-4)*(8 - 4). Factor -15 - 5*t**2 + 16*t + m*t**2 - 5*t + z*t.
-5*(t - 3)*(t - 1)
Let d(g) = 2*g**3 - 39*g**2 + 42*g - 24. Let k(m) = 7*m**3 - 115*m**2 + 127*m - 70. Let l(h) = 11*d(h) - 4*k(h). Find s, given that l(s) = 0.
1/2, 2, 8/3
Suppose 0 = -10*y + 4*y + 126. Suppose 13*z - y*z = -33384. Find x, given that 3*x**3 + 4413*x + 320 + 60*x**2 + 2*x**3 - z*x = 0.
-4
Let w(x) = -6 + 141*x**3 + 29 + 12*x - 20*x**2 - 142*x**3 + 33*x + 2. Let q be w(-22). Factor -2/21*c**q - 8/21*c + 0 + 10/21*c**2.
-2*c*(c - 4)*(c - 1)/21
Determine r, given that 324/5 - 33/5*r**4 + 9*r**2 + 432/5*r - 93/5*r**3 - 3/5*r**5 = 0.
-6, -3, -1, 2
Factor 126*i - 1284/5 + 6/5*i**3 + 648/5*i**2.
6*(i - 1)*(i + 2)*(i + 107)/5
Let v(j) = 4*j**2 - 1. Let m = -25 - -26. Let k be v(m). Factor -7 + 0*u**2 - 2*u**2 - k*u**2 + 27.
-5*(u - 2)*(u + 2)
Let t(s) be the second derivative of 3*s**4 - 20*s**3 + 3/10*s**5 + 21*s - 1 - 1/10*s**6 + 48*s**2. What is v in t(v) = 0?
-4, 2
Let o(g) be the first derivative of g**4/4 + 7*g**3/2 - 12*g**2 + 29*g + 5. Let i(j) be the first derivative of o(j). Factor i(x).
3*(x - 1)*(x + 8)
Solve -1/3*i**5 - 11/6*i + 13/6*i**3 + 5/3 - 11/6*i**2 + 1/6*i**4 = 0 for i.
-5/2, -1, 1, 2
Let o(h) be the third derivative of -1/60*h**6 + 0*h**5 + 0*h**3 + 0*h + 1/12*h**4 - 3*h**2 + 0. What is t in o(t) = 0?
-1, 0, 1
Let g(y) = -11*y - 11. Let i be g(-5). Let q = 48 - i. Find d such that 9*d**3 - 3*d**3 + 0*d**2 - 3*d**q - 6*d**2 + 3*d**3 = 0.
0, 1, 2
Factor 18 - 4 + 72*m + 52*m + 22 + 167*m + 93*m**2.
3*(m + 3)*(31*m + 4)
Suppose -2*u - 41 + 1073 = 0. Find a such that 154*a**4 + 560*a + u*a**3 + 580*a**2 - 6*a**4 + 16*a**5 + 244*a**2 + 96 = 0.
-3, -2, -1/4
Let h(x) be the first derivative of x**4/8 + x**3 - 15*x**2/4 + 73*x - 6. Let o(k) be the first derivative of h(k). Find p such that o(p) = 0.
-5, 1
Suppose -94*s + 56 = -66*s. Let r(m) be the first derivative of -m**s + 3*m + 16 - 1/3*m**3. Find k such that r(k) = 0.
-3, 1
Suppose -60*n + 80*n - 60 = 0. Factor 0*d**2 + 24 + 32*d + n*d**2 - 56*d - 4 + d**2.
4*(d - 5)*(d - 1)
What is r in r**2 + 4*r - 23316 + 2*r + 23316 = 0?
-6, 0
Let g(k) = -24*k**2 - 20*k + 4. Let p(l) = 25*l**2 + 23*l - 5. Let q(d) = -5*g(d) - 4*p(d). Let q(o) = 0. What is o?
-2/5, 0
Factor 123*n**3 + 557*n**3 - 4*n**4 + 568*n - 1140*n**2 - 104*n**3.
-4*n*(n - 142)*(n - 1)**2
Let p(w) = w**3 + 2*w**2 - 5*w + 4. Suppose -14*i + 12*i = -8. Let l be (-4)/3*(2/i + -2). Let f(q) = -q**2 - 1. Let n(z) = l*p(z) + 2*f(z). Factor n(a).
2*(a - 1)**2*(a + 3)
Factor 0 - 1/5*x**3 + 136*x**2 + 0*x.
-x**2*(x - 680)/5
Factor 26903*t - 8*t**4 - 56292*t**2 - 28168*t**2 + 1646*t**3 - 48121*t.
-2*t*(t - 103)**2*(4*t + 1)
Let i(l) = -l**2 + 2. Let v(f) = 7*f - 146. Let t be v(20). Let n(w) = 5*w**2 + 9*w - 26. Let d(x) = t*i(x) - n(x). Determine z, given that 