c + 5*d + 10 = 0, -2*d = c + c - 10. Factor -421*k**2 + 391*k**2 + 3*k**3 + k**3 - c*k**3.
-k**2*(k + 30)
Let o(l) = -l**3 - 15*l**2 - 4*l + 2. Let f be o(-15). Let h = f - 60. Factor 2*m**h - 26*m - 2*m**5 - 4 + 2*m**2 + 8*m**3 + 20*m.
-2*(m - 2)*(m - 1)*(m + 1)**3
Find q such that 0*q**2 + 3439*q**5 - 4*q**2 - 5*q + 6*q**3 - 3440*q**5 + 4*q**4 = 0.
-1, 0, 1, 5
Let y be -18 - 660/77 - -27. Let i be (-20)/(-4)*6/105. Factor 5/7*p + i*p**2 + y.
(p + 1)*(2*p + 3)/7
Let p(r) = 5*r**2 - 26*r + 39. Let g be 26/7*((-39)/(-3) + 1). Let d(s) = 44*s**2 - 238*s + 350. Let z(i) = g*p(i) - 6*d(i). Suppose z(o) = 0. What is o?
1, 18
Suppose 4*w = 5*h - w + 270, -5*w - 178 = 3*h. Let k = 85 - h. Suppose 133*z + 98*z**2 + 3 - 11 + 98*z**3 - k*z = 0. Calculate z.
-1, -2/7, 2/7
Suppose -97 - 443 = -6*c. Let q be -5 + 650/c - (-2)/(-9). Factor -2/5*w + 2/15*w**q - 4/3.
2*(w - 5)*(w + 2)/15
Let i(u) = 419*u + 24776. Let k be i(-59). Find a such that 605 - k*a + 5/4*a**2 = 0.
22
Let z(r) = 3*r**5 + 5*r**4 - 3*r**3 - 11*r**2 - 10*r - 2. Let l(v) = 8*v**5 + 10*v**4 - 9*v**3 - 21*v**2 - 20*v - 5. Let b(i) = -2*l(i) + 5*z(i). Factor b(d).
-d*(d - 5)*(d - 2)*(d + 1)**2
Suppose 0 = -z, -3*z = 5*h - 234 - 501. Let w = h + -130. Suppose 6*l**2 - 5*l**2 + 3*l**2 - 4 - 4*l**3 - 13*l + w*l = 0. Calculate l.
-1, 1
Let z(s) be the first derivative of -s**6/720 + 7*s**5/240 + s**4/6 - 74*s**3/3 + 32. Let y(v) be the third derivative of z(v). Factor y(k).
-(k - 8)*(k + 1)/2
Let f(u) be the second derivative of 0 + 1/5*u**5 - 3*u**2 - 5/4*u**4 - 4*u + 17/6*u**3. Find x, given that f(x) = 0.
3/4, 1, 2
Factor -12005*n - 557155*n**5 + 6860*n**2 + 557150*n**5 - 1470*n**3 + 72*n**4 + 68*n**4.
-5*n*(n - 7)**4
Let j(k) = 4*k**3 + k**2 + k. Let v(y) = -42*y**3 + 79*y**2 - 107*y - 184. Let a(g) = 22*j(g) + 2*v(g). Factor a(l).
4*(l - 2)*(l + 1)*(l + 46)
Let v be -1*((-20020)/231 - -84). Factor v + 1/3*g**2 - 3*g.
(g - 8)*(g - 1)/3
Let -5*x**3 - 65/2*x - 93/4*x**2 - 1/4*x**4 - 14 = 0. What is x?
-14, -4, -1
Let v(p) = 26*p**3 + 351*p**2 + 298*p - 55. Let c(l) = l**3 + l**2 - 7*l. Let k(g) = 4*c(g) + v(g). Solve k(o) = 0.
-11, -1, 1/6
Let r(m) be the first derivative of m**6/30 - 56*m**5/25 + 363*m**4/10 + 1624*m**3/15 + 841*m**2/10 - 991. Factor r(a).
a*(a - 29)**2*(a + 1)**2/5
Let j(q) be the second derivative of -q**4/48 + 19*q**3/24 - 15*q**2/2 + 5*q + 10. Factor j(m).
-(m - 15)*(m - 4)/4
Suppose -m - 8*z + 13*z + 582 = 0, -3*z = -m + 592. Let u = m - 605. Let 2/3*t**2 - 4/3*t - u = 0. Calculate t.
-1, 3
Determine i so that 55617*i - 27816*i - 3*i**2 - 27651*i = 0.
0, 50
Suppose -6*l + 15 = -l. Factor 13591*c**3 - 8*c**2 + c - 13587*c**l + 3*c.
4*c*(c - 1)**2
Determine y, given that 1/2*y**4 - 45/2*y**2 + 30 - 2*y - 6*y**3 = 0.
-2, 1, 15
Let x(s) be the first derivative of -3*s**4/2 + 20*s**3/3 + 29*s**2 + 32*s + 4192. Factor x(o).
-2*(o + 1)**2*(3*o - 16)
Suppose 47*g + 1120 - 5*g**2 - 389*g - 208*g = 0. Calculate g.
-112, 2
Factor 0*b + 0 + 1/5*b**5 + 21/5*b**2 - 5*b**3 + 3/5*b**4.
b**2*(b - 3)*(b - 1)*(b + 7)/5
Let y = 31674 - 31670. Find l, given that 2/3*l**5 + 4*l**2 - 4/3*l**y + 0*l - 10/3*l**3 + 0 = 0.
-2, 0, 1, 3
Let d(o) be the second derivative of -2/33*o**3 - 9/110*o**5 - 1/231*o**7 + 0*o**2 - 1/33*o**6 - 14 - 7/66*o**4 - o. Factor d(w).
-2*w*(w + 1)**3*(w + 2)/11
Let j be ((-3 - -4) + (-1 - -1))*11. Suppose 0 = j*o - 127 - 38. Let 13 + 21 - o*d**2 - 80*d + 26*d - 10 = 0. Calculate d.
-4, 2/5
Let d(g) be the first derivative of 15/2*g**2 + 5 + 5/8*g**4 - 1/20*g**5 - 9*g - 37/12*g**3. Factor d(f).
-(f - 3)**2*(f - 2)**2/4
Let s(n) = -n**2 - 5*n + 9. Let r(m) = m**2 + 6*m - 10. Let t(h) = -5*r(h) - 6*s(h). Factor t(p).
(p - 2)*(p + 2)
Let n(x) be the first derivative of -5/3*x**3 - 15125*x + 275*x**2 - 210. Find s, given that n(s) = 0.
55
Find l such that -186/7 + 2/7*l**2 - 184/7*l = 0.
-1, 93
Suppose 12/7*l**4 + 1152/7 + 96/7*l - 3/7*l**3 + 1/7*l**5 - 286/7*l**2 = 0. What is l?
-8, -2, 3
Let c(u) be the first derivative of -u**5/420 + 31*u**4/168 - 5*u**3/7 - 30*u**2 - 102. Let i(j) be the second derivative of c(j). Factor i(o).
-(o - 30)*(o - 1)/7
Solve 2037 - 30*a**3 + 1799 - 2770*a - 3401 + 965*a**2 = 0.
1/6, 3, 29
Let n = 81585/4 + -81567/4. Factor -15/4 - n*u - 3/4*u**2.
-3*(u + 1)*(u + 5)/4
Let q = 63629/13840 + 7/2768. Let p be 24/(-16) + 17/10. Factor -p*v**3 - 143/5*v + q*v**2 + 121/5.
-(v - 11)**2*(v - 1)/5
Solve 33*o + 44*o**4 - 225*o**2 + 57*o**2 - 36*o**4 + 3*o**3 - 55*o**3 - 141*o = 0 for o.
-3/2, -1, 0, 9
Let b(s) be the second derivative of -s**5/80 - 115*s**4/48 - 3127*s**3/24 + 10443*s**2/8 - 19*s - 51. Factor b(f).
-(f - 3)*(f + 59)**2/4
Let t = -9191/17 + 541. Let z = 140310 - 2385264/17. Factor -t*b + 2/17 - 2/17*b**3 + z*b**2.
-2*(b - 1)**3/17
Let k(q) be the first derivative of -q**7/2240 - q**6/480 - q**5/320 + 2*q**3/3 - 12. Let w(i) be the third derivative of k(i). Suppose w(n) = 0. Calculate n.
-1, 0
Let j = -129 + 120. Let b = j - -11. Solve 28*l**3 - 48*l + 9*l**3 - 9*l**b - 16*l**3 + 27*l**3 - 12 + 21*l**4 = 0.
-2, -1, -2/7, 1
Suppose 3*r = 3*v, 3*v + 160*r - 164*r + 3 = 0. Let h(b) be the first derivative of -1/8*b**4 + 0*b**2 + 4 + 0*b - 1/6*b**v. Factor h(u).
-u**2*(u + 1)/2
Let d = -599 + 600. Suppose -14*x = -d - 27. Factor -4/7*c**x + 0 + 4/7*c.
-4*c*(c - 1)/7
Let q(d) be the first derivative of -4*d**3/3 + 49*d**2/2 + d - 197. Let t(c) = -4*c**2 + 48*c - 2. Let o(s) = -3*q(s) + 4*t(s). Determine u so that o(u) = 0.
1/4, 11
Let p = -56 + 86. Let f(u) = -5*u**3 - 3*u**2 - 6*u + 4. Let x(c) = c**3 + c. Let k(q) = p*x(q) + 5*f(q). Let k(l) = 0. What is l?
-1, 2
Let v(h) = -h**4 + h**2 - h + 1. Let f = 34 - 16. Let c(u) = 15*u**4 + 24*u**3 - 81*u**2 + 72*u - 18. Let k(d) = f*v(d) + c(d). Factor k(o).
-3*o*(o - 3)**2*(o - 2)
Suppose -4*w + 2*x + 12 = -12, 2*w = 2*x + 10. Suppose 3*a + 16 = w*a - 2*u, -2*a + 12 = -3*u. Factor 2*z**2 + 2*z**a + 12*z + 13*z + 3*z**3 - 10 - 22*z**2.
5*(z - 2)*(z - 1)**2
Suppose 1809*z = 1808*z - 5. Let v(p) = -p**2 - 17*p - 55. Let o be v(z). Solve d**o + 0*d + 0 + 0*d**2 + 4/3*d**4 + 1/3*d**3 = 0.
-1, -1/3, 0
Let b = -616421/5 + 124850. Let a = b + -1565. Suppose 3/5*o**5 + 0*o + a*o**2 - 7/5*o**4 + 0*o**3 + 0 = 0. What is o?
-2/3, 0, 1, 2
Solve -1449/4 + 975/8*y - 3/8*y**2 = 0 for y.
3, 322
Factor -374/9*l**2 + 2/9*l**3 + 0 + 124/3*l.
2*l*(l - 186)*(l - 1)/9
Let i = 22058 + -111749/5. Let d = i + 292. Factor 0 + 0*f + d*f**3 + 1/5*f**2.
f**2*(f + 1)/5
Solve -2/5*i**2 + 0*i + 0 - 2/15*i**3 = 0.
-3, 0
Let m(a) = -a**3 + 5*a**2 + 178*a - 416. Let b be m(15). Let 18/5*z - 3/5*z**2 + 3/5*z**b - 21/5*z**3 + 0 + 3/5*z**5 = 0. What is z?
-3, -1, 0, 1, 2
Let t = 15808/69 - 5231/23. Find d such that -1/3*d**5 + t*d**3 + 2*d**2 + 0*d + 0 - 2/3*d**4 = 0.
-3, -1, 0, 2
Let s be (-9)/(-18) + (-982)/(-4). Suppose 152 = 3*m + 4*l, 5*m + 0*l = -3*l + s. Factor 15*y**3 + 93*y**2 - 165*y - 61*y**2 - m - 2 - 72*y**2.
5*(y - 5)*(y + 2)*(3*y + 1)
What is i in 5500 + 115*i + 92*i**3 - 4192*i**4 + 58*i**3 + 185*i - 905*i**2 + 4187*i**4 = 0?
-2, 5, 22
Let o(w) be the second derivative of -w**10/45360 + w**8/3360 + w**7/1890 + 14*w**4/3 + 8*w. Let z(u) be the third derivative of o(u). Factor z(g).
-2*g**2*(g - 2)*(g + 1)**2/3
Determine v so that -24*v - 4/7*v**2 + 196 = 0.
-49, 7
Let z(a) be the second derivative of -2*a - 97 - 76/15*a**4 + 29/3*a**3 - 10*a**2 + 7/5*a**5 - 14/75*a**6 + 1/105*a**7. Find p such that z(p) = 0.
1, 2, 5
Let l(n) be the second derivative of -11/5*n**2 + 3*n - 4/5*n**3 - 3 - 1/30*n**4. Factor l(h).
-2*(h + 1)*(h + 11)/5
Let c(v) be the first derivative of v**3 - 249*v**2 + 20667*v - 219. Factor c(h).
3*(h - 83)**2
Suppose -b + 25 = 4*b. Factor -85*u - 73*u + 138*u + 25*u**2 - b*u**3.
-5*u*(u - 4)*(u - 1)
Let c be 2 - 1 - (51 + -49)*(-1 - (-3)/(-6)). Find q, given that c - 2/3*q**2 + 11/3*q - 1/3*q**3 = 0.
-4, -1, 3
Let 104*l - 197*l + 96*l - 57 + 57*l**2 - 3*l**3 = 0. Calculate l.
-1, 1, 19
Find a such that 2*a - 3/8*a**4 - 23/8*a**2 - 1/2 + 7/4*a**3 = 0.
2/3, 1, 2
Let g = -149513/85 + 30501/17. Suppose g - 4*o**3 + 468/5*o**2 - 624/5*o = 0. What is o?
2/5, 1, 22
Let f(u) be the third derivative of u**5/120 + 29*u**4/8 + 2523*u**3/4 - 1965*u**2 - 2. Factor f(h).
(h + 87)**2/2
Determine g so that -1/2*g**5 -