k - 6)*(k + 2)*(k + 6)
Suppose -6*q + 2546 = -556. Let s be (4/22)/(705/q). Factor -s*x**2 + 8/15*x - 8/15.
-2*(x - 2)**2/15
Let f = -269738 + 539479/2. Factor 1/10*k**3 - f*k + 1/5*k**2 - 18/5.
(k - 4)*(k + 3)**2/10
Let n(v) = -103*v + 5564. Let q be n(54). Let w(l) be the second derivative of 5/8*l**4 - 9*l - 1/20*l**6 + 0 + 0*l**q + 3/4*l**3 + 3/40*l**5. Factor w(p).
-3*p*(p - 3)*(p + 1)**2/2
Let a be (48/(-18) + 1)*-24. Factor -52 + 152*r - 90*r**2 - 2*r**4 + a*r**3 + 6*r**4 - 106*r**2 + 52*r**2.
4*(r - 1)**3*(r + 13)
Let h(d) be the first derivative of d**4/3 - 12*d**3 - 93*d - 42. Let y(n) be the first derivative of h(n). Let y(v) = 0. Calculate v.
0, 18
Let d(x) be the second derivative of 2/3*x**3 + 0 + 1/120*x**5 - 15*x**2 - 5*x + 3/16*x**4. Let p(n) be the first derivative of d(n). Factor p(r).
(r + 1)*(r + 8)/2
Let r(l) = -12*l**4 - 20*l**3 - 12*l**2 + 8*l + 86. Let p(n) = n**4 + n**3 - 7. Let q(c) = 20*p(c) + 2*r(c). Find a such that q(a) = 0.
-2, 1
Let r(z) = -8*z**3 - 19*z**2 - 7*z + 199. Let d(p) = 13*p**3 + 35*p**2 + 14*p - 397. Let u(n) = 6*d(n) + 10*r(n). Factor u(s).
-2*(s - 7)**2*(s + 4)
Let t(i) be the third derivative of 1/630*i**7 + 4*i**2 - 12*i + 0*i**3 - 1/120*i**6 - 1/20*i**5 + 0 + 3/8*i**4. What is a in t(a) = 0?
-3, 0, 3
Let u(q) = 5*q**2 + q - 10. Let t be u(3). Factor -22*f + t - 6*f**2 + 17 - 47.
-2*(f + 4)*(3*f - 1)
Suppose 189/2 - 2277/4*o + 630*o**3 + 2607/4*o**2 + 75*o**4 = 0. What is o?
-7, -2, 3/10
Factor 11421 + 3056*r**2 - 7707 + 25870 - 14029*r + 4*r**4 - 16931*r + 5732*r**2 - 360*r**3.
4*(r - 43)**2*(r - 2)**2
Let o(f) = -7*f**2 + 12*f - 25. Let y(m) = m**2 - m + 3. Let x(w) = o(w) + 6*y(w). Let g be x(3). Factor 0*z + 0 + 2/3*z**g.
2*z**2/3
Let -1/6*a**2 + 103/6 + 17*a = 0. Calculate a.
-1, 103
Suppose 0 = -6*y + h + 27, -530*y = -529*y + 4*h + 33. Let a(g) = 3*g**2 + g. Let x be a(-1). Suppose 12 - 8/3*i**x + 2/3*i**y - 2*i = 0. What is i?
-2, 3
Let p(b) be the second derivative of b**5/50 + 29*b**4/15 + 19*b**3/5 + 9*b + 326. Solve p(c) = 0.
-57, -1, 0
Let g(a) be the first derivative of 5/42*a**4 + 2/105*a**5 + 2/7*a**3 + 4/21*a + 1/3*a**2 - 12. Factor g(o).
2*(o + 1)**3*(o + 2)/21
Let s(i) be the third derivative of -i**6/96 + 7*i**5/48 + 25*i**4/48 - 10*i**3/3 - 1639*i**2. Let s(c) = 0. Calculate c.
-2, 1, 8
Let d be (-7635)/315 + (-61)/(-21) + -3. Let n = 25 + d. Find i such that n*i**2 + 4/3*i + 2/3 = 0.
-1
Let f(q) be the third derivative of -q**8/6720 - 11*q**7/1260 - 121*q**6/720 - 29*q**4/24 - q**2 + q. Let x(w) be the second derivative of f(w). Factor x(g).
-g*(g + 11)**2
Let l(n) = n**2 + 28*n - 126. Let o be l(-32). Determine i so that -616 + 122*i - 116*i - 560 - 3*i**o + 120*i - 147 = 0.
21
Let j(g) be the second derivative of 1/30*g**6 + 1/6*g**4 + 3/16*g**5 - 1/8*g**3 + 0 + 0*g**2 - 98*g. Factor j(k).
k*(k + 1)*(k + 3)*(4*k - 1)/4
Let x = -12262 - -12266. Find z, given that 4/5*z**3 + 0 + 0*z - 2/5*z**x - 2/5*z**2 = 0.
0, 1
Let x(r) be the second derivative of r**5/5 - 28*r**4/3 + 104*r**3/3 - 9*r + 34. Factor x(l).
4*l*(l - 26)*(l - 2)
Let n(l) be the second derivative of l**5/5 + 5*l**4 - 68*l**3/3 - 152*l. Factor n(u).
4*u*(u - 2)*(u + 17)
Factor 118*s + 244*s + 145 - 184*s - 4*s**2 + 232*s + 169*s.
-(s - 145)*(4*s + 1)
Let i(g) be the first derivative of 3*g**4/8 + 3*g**3/2 - 12*g**2 + 18*g - 888. Suppose i(b) = 0. What is b?
-6, 1, 2
Let m(l) be the second derivative of l**4/6 - 31*l**3/6 + 21*l**2/2 + 11*l. Let s be m(16). Factor -69*y - 5*y**2 + 5*y**3 + s*y + 32*y.
5*y**2*(y - 1)
Let w(h) be the second derivative of 11*h**6/1440 - h**5/36 + 7*h**4/288 + h**3/36 - 43*h**2 + 24*h. Let q(g) be the first derivative of w(g). Factor q(f).
(f - 1)**2*(11*f + 2)/12
Let h(c) be the first derivative of c**4/10 - 1846*c**3/15 - 1849*c**2/5 - 370*c - 10823. Factor h(r).
2*(r - 925)*(r + 1)**2/5
Let w(o) = 2*o**2 - 19*o + 24. Let d be w(8). Suppose 3*p + 24 = n, -5*n - 3*p + d*p = -30. Factor -6/5*y + 3/5 - n*y**2.
-3*(3*y + 1)*(5*y - 1)/5
Factor -1008/5*f - 63504/5 - 4/5*f**2.
-4*(f + 126)**2/5
Solve -426/5 - 219/5*a - 3/5*a**2 = 0.
-71, -2
Suppose -k + 117 - 327 = 4*u, -840 = 4*k - 2*u. Let h be k/27 + -8 + 16. Let 2/9*o**2 - h - 2/9*o + 2/9*o**3 = 0. What is o?
-1, 1
Let c(u) = -u**2 + 69*u - 468. Let n be c(52). Let l = 833/2 - n. Factor l*i**2 + 7/2*i + 3.
(i + 1)*(i + 6)/2
Let 1804/7*t**2 + 0 + 2/7*t**3 + 406802/7*t = 0. Calculate t.
-451, 0
Suppose 5*j = 2*t - 25, -j = 3*t + 2*j - 69. Suppose -26*x + 22*x = -t. Factor x*o**2 - 19*o + 11 - 1 + 34*o.
5*(o + 1)*(o + 2)
Suppose -4*c = 4*k, -44*c = -2*k - 42*c + 8. Factor -2/13*v**3 + 8/13*v**k - 36/13 + 6/13*v.
-2*(v - 3)**2*(v + 2)/13
Solve 4*s**4 + 180*s**2 - 385*s + 105*s**3 - 5*s**2 + 324*s - 224*s + s**4 = 0 for s.
-19, -3, 0, 1
Let u(n) be the second derivative of 841/24*n**3 + 2*n + 0*n**2 + 1/80*n**5 - 29/24*n**4 + 40. Factor u(q).
q*(q - 29)**2/4
Let n(c) = c**3 + 15*c**2 + 27*c + 17. Let o be n(-13). Suppose o*t = -3*t + 91. Factor -18 - 9*d**3 - 12*d**3 + t*d**2 - 17*d**2 - 86*d**2 - 87*d.
-3*(d + 1)*(d + 3)*(7*d + 2)
Let c(r) = 3*r**3 + 28*r**2 + 9*r + 4. Let x be c(-9). Let n be 48/(-200)*(-65)/26. What is v in 0 + 0*v**2 + 7/5*v**3 - 4/5*v - n*v**x = 0?
-2/3, 0, 1, 2
Suppose -16/5*y + 2*y**2 - 26/5 = 0. What is y?
-1, 13/5
Let h = 526662/7 + -75234. Suppose -32/7*b + 2/7*b**3 - h - 6/7*b**2 = 0. What is b?
-2, -1, 6
Let p(h) = 7*h**2 + 129*h - 16. Let n(j) = -2*j**2 - 43*j + 13. Let o(v) = -10*n(v) - 3*p(v). Factor o(u).
-(u - 41)*(u - 2)
Let o(s) be the third derivative of s**5/12 + 955*s**4/12 + 182405*s**3/6 + 449*s**2. Factor o(u).
5*(u + 191)**2
Let l(x) = -33*x**2 + 3314*x. Let d(t) = 19*t**2 - 1658*t. Let m(y) = 5*d(y) + 3*l(y). Determine g, given that m(g) = 0.
0, 413
Let r(j) = -j**3 + 23*j**2 - 38*j - 3. Let m be r(21). Suppose -m + 176 = 19*d. Factor 0*u + d*u**3 + 0 + 5/6*u**4 + 20/3*u**2.
5*u**2*(u + 2)*(u + 4)/6
Suppose 135*x + 153 + 466 = 671*x - 453. Factor 0*u**x - 2/7*u**4 + 0*u - 22/7*u**3 + 0.
-2*u**3*(u + 11)/7
Suppose 0 = 37*h - 450 - 68. Let c(a) be the third derivative of 0*a - h*a**2 + 55/24*a**4 + 0 - 1/2*a**5 + 1/24*a**6 - 5*a**3. Find k such that c(k) = 0.
1, 2, 3
Let m(z) be the first derivative of -12*z**5/5 + 11*z**4 + 28*z**3/3 - 22*z**2 - 16*z + 2643. Suppose m(q) = 0. What is q?
-1, -1/3, 1, 4
Suppose -47*b - 144 = -59*b. Suppose z**2 + 394 - b*z + 47 - 30*z = 0. What is z?
21
Let t(c) be the second derivative of -c**5/50 - 173*c**4/30 - 493*c**3 + 7569*c**2/5 + 46*c. Factor t(a).
-2*(a - 1)*(a + 87)**2/5
Let q(k) be the second derivative of -k**6/36 - k**5/8 + 5*k**4/12 - 67*k**3/3 + 40*k. Let j(m) be the second derivative of q(m). Solve j(i) = 0 for i.
-2, 1/2
Let b be (-12)/(-8)*(-14)/(-3). Suppose b*l = l + 12. Factor -3*a + 0 + 1 + 25*a**l - 7*a.
(5*a - 1)**2
Suppose -7 = -3*b - 79. Let l = 26 + b. Factor 6*c**3 - 3*c**l + 0*c**2 - 11*c**4 + 8*c**4.
-3*c**2*(c - 1)**2
Determine w so that -1/10*w**2 + 30 - 299/10*w = 0.
-300, 1
Let m(s) be the third derivative of 25/6*s**4 + 32*s**2 + 1/6*s**6 - 31/12*s**5 + 0 + 35/6*s**3 + 0*s. Factor m(y).
5*(y - 7)*(y - 1)*(4*y + 1)
Let d(h) be the first derivative of -h**3 + 33*h**2 + 225*h - 722. Let d(v) = 0. What is v?
-3, 25
Factor -1/3*q**3 + 32*q**2 - 94 - 185/3*q.
-(q - 94)*(q - 3)*(q + 1)/3
Let r(k) = -9*k**2 - 572*k - 1106. Let t be r(-2). Factor -3/8*o - 1/4 - 1/8*o**t.
-(o + 1)*(o + 2)/8
Let h(b) be the first derivative of -b**7/735 + b**6/140 + b**5/210 - b**4/28 + 9*b**2 + b + 17. Let i(u) be the second derivative of h(u). Factor i(f).
-2*f*(f - 3)*(f - 1)*(f + 1)/7
Let i be (-7740)/(-3010)*56/48. Factor 0 + 2/15*z**2 - 2/15*z**4 + 2/15*z - 2/15*z**i.
-2*z*(z - 1)*(z + 1)**2/15
Suppose -35 = 2*y + 5*d, 7*d - 4*d = -27. Find r, given that 5/4*r - 3/2*r**3 + 3/2 - 2*r**2 + 1/2*r**4 + 1/4*r**y = 0.
-3, -1, 1, 2
Let t(o) be the first derivative of -41 - 10*o**2 - 2/3*o**3 + 48*o. Factor t(h).
-2*(h - 2)*(h + 12)
Let i(d) = 4*d**3 + 58*d**2 - 33*d - 852. Let x be i(-14). Determine j, given that -4/3*j**x + 24*j - 108 = 0.
9
Factor -396*y + 168/5*y**2 + 1040 + 4/5*y**3.
4*(y - 5)**2*(y + 52)/5
Let f(v) be the second derivative of 119 + 2*v + 5/4*v**3 + 1/24*v**4 + 0*v**2. Solve f(g) = 0 for g.
-15, 0
Suppose -2*d + 3*d + 5*g = -24, 2*d