6. Factor p*r - 4/23*r**2 + 2/23.
-2*(r - 1)*(2*r + 1)/23
Suppose -16/3 - 22/3*q**3 + 2*q**4 + 8*q + 4*q**2 = 0. What is q?
-1, 2/3, 2
Suppose -5 = -w, -4*i - 2*w = -5*w + 11. Let l be 4 + (i - 2/2). Factor 2*j**4 - j**4 + 7*j**4 - 4*j**3 - l*j**5.
-4*j**3*(j - 1)**2
Let i(c) be the third derivative of -c**5/12 - 7535*c**4/12 - 11355245*c**3/6 - 130*c**2 + 2*c. Factor i(y).
-5*(y + 1507)**2
Suppose -t - 28*t - 29 = 0. Let d be -13 - -16 - (3 - (t + 1)). Solve 0*o + 2/15*o**3 - 8/15*o**2 + d = 0.
0, 4
Let y be (-63 - 12474/(-196))*(65/6 - -2). Factor -12*g**4 + 21/4*g**5 - 3/2*g**2 + 0 + y*g**3 + 0*g.
3*g**2*(g - 1)**2*(7*g - 2)/4
Let q(i) = -i**3 + 14*i**2 - 45*i - 13. Let v be q(6). Let o(l) be the second derivative of 0 - 1/18*l**4 - 1/30*l**v + 0*l**2 + 9*l + 0*l**3. Factor o(g).
-2*g**2*(g + 1)/3
Suppose -4*t + 0*t = 0. Suppose 3*k - 2*y = 4*k + 5, t = 4*k - 3*y - 24. Suppose -r - 12*r**k + 0*r**3 + 8*r**2 - 3*r + 8*r**3 = 0. What is r?
0, 1
Let f(q) be the second derivative of -1/210*q**5 - 2/7*q**2 + 12*q - 1/21*q**4 + 0 - 11/63*q**3. What is r in f(r) = 0?
-3, -2, -1
Factor 2/19*b**2 + 98/19*b + 188/19.
2*(b + 2)*(b + 47)/19
Let p(c) be the first derivative of c**5/3 + 105*c**4/4 + 1765*c**3/9 + 1055*c**2/2 + 570*c - 2425. Let p(g) = 0. What is g?
-57, -3, -2, -1
Let i be (-1794)/(-624)*(-28)/(-2). Let r = -38 + i. What is k in -1/2*k**3 - r*k**4 + 3/2*k - k**5 + 2*k**2 + 1/4 = 0?
-1, -1/4, 1
Suppose 5*m = -3*y - 104 + 94, -6 = 4*y + 3*m. Factor y + 1/8*f**3 - 1/4*f - 1/8*f**2.
f*(f - 2)*(f + 1)/8
Let y(u) be the first derivative of 64/5*u**4 - 146/15*u**3 + 0*u - 2/5*u**5 + 170 - 10*u**2. Let y(n) = 0. Calculate n.
-2/5, 0, 1, 25
Suppose -161*l + 166*l - 90 = 0. Suppose -23*z**2 - 42*z - l*z + 27*z**2 + 56 = 0. What is z?
1, 14
Let l(q) = -9*q**2 + 92*q - 91. Let y(d) = 265*d**2 - 210*d**2 + 545 - 65*d - 485*d. Let s(v) = 25*l(v) + 4*y(v). Factor s(a).
-5*(a - 19)*(a - 1)
Let x(c) be the third derivative of c**8/2520 + c**7/180 + c**6/60 + c**5/60 + 17*c**4/12 - 54*c**2. Let r(m) be the third derivative of x(m). Factor r(o).
4*(o + 3)*(2*o + 1)
Suppose -2*c - 39*b + 36*b = 22, 3*c + 2*b = -8. Factor 1/3*z**c + 8/3*z + 0 - 2*z**2 - z**3.
z*(z - 4)*(z - 1)*(z + 2)/3
Let x(l) be the third derivative of -l**7/8820 + l**6/840 - l**5/210 - 35*l**4/24 - 2*l**2 + 45. Let j(u) be the second derivative of x(u). Factor j(k).
-2*(k - 2)*(k - 1)/7
Let o(u) be the second derivative of u**6/135 - 25*u**5/3 + 139873*u**4/54 + 94000*u**3/9 + 141376*u**2/9 + 121*u - 1. Factor o(z).
2*(z - 376)**2*(z + 1)**2/9
Let n(a) be the first derivative of 2*a**5/65 + 3*a**4 - 162*a**3/13 + 4*a**2/13 + 648*a/13 - 2407. Let n(u) = 0. Calculate u.
-81, -1, 2
Let k(s) be the first derivative of 1/10*s**4 + 141 + 14*s - 1/5*s**2 - 14/3*s**3. Factor k(h).
2*(h - 35)*(h - 1)*(h + 1)/5
Let n(r) = -28*r + 91. Let a be n(3). Suppose 1 - 3*c**4 - 273*c**3 + 136*c**3 + 9*c**2 - 3*c + 140*c**3 - a = 0. What is c?
-1, 1, 2
Let f be (-20)/4 + 1912 - -1. Determine s, given that 241*s**4 - 10 + f*s**2 - 236*s + 543*s**4 - 2464*s**3 + 26 - 8 = 0.
1/14, 1, 2
Let m(u) = -25*u + 208. Let h be (5 - (5 + 4)) + 12. Let y be m(h). Factor 8*t**3 - 4/3*t**4 + y*t - 44/3*t**2 + 0.
-4*t*(t - 3)*(t - 2)*(t - 1)/3
Let r(g) be the third derivative of 1/276*g**6 - 2*g + 0*g**3 - 1/3864*g**8 + 0 + 1/230*g**5 + 0*g**4 - 49*g**2 + 1/2415*g**7. Find j, given that r(j) = 0.
-1, 0, 3
Let o(p) = -456*p + 2280. Let m(s) = 24*s - 120. Let j(q) = 56*m(q) + 3*o(q). Let t be j(5). Find v such that 2/11*v**3 + 0*v**2 - 2/11*v + t = 0.
-1, 0, 1
Let l(u) = 2*u. Let y be l(0). Let n be (-4 - 10/(-2)) + (y - 1). Factor q**2 + 2 + n - 3*q**2 - 7*q + 2*q**3 + 5*q.
2*(q - 1)**2*(q + 1)
Let d = -215027 - -1075177/5. Factor 78/5*c - 6*c**2 - d - 6/5*c**3.
-6*(c - 1)**2*(c + 7)/5
Let j = -388 - -390. Let a(w) be the first derivative of -4/15*w - 22/15*w**3 - 17/15*w**j - 28. Factor a(b).
-2*(3*b + 1)*(11*b + 2)/15
Let i(w) = -w**2 - 143*w + 624. Let r(f) = f**2 + 288*f - 1249. Let m(d) = -9*i(d) - 4*r(d). Determine v, given that m(v) = 0.
-31, 4
Let w = -17 - -32. Suppose 4*n + w = 4*z + 71, 5*n - 34 = -4*z. Find y such that 17*y - 49*y**2 - 11*y**2 + n*y**3 - 5*y**5 + 15*y**4 + 23*y = 0.
-2, 0, 1, 2
Let q be (-36)/(-14) - ((-225)/35 - -6). Suppose 3*z + 41 = 3*a + 11, 0 = 4*a - q*z - 35. Factor -3/4*g + g**3 + 0*g**4 - 1/2 - 1/4*g**a + 1/2*g**2.
-(g - 2)*(g - 1)*(g + 1)**3/4
Let k = 859622 - 6876971/8. Factor 1/8*u**3 + 1/8*u**4 + 0 - k*u**2 + 3/8*u.
u*(u - 1)**2*(u + 3)/8
Let g = -44 - -35. Let c = 12 + g. Determine j so that 111 + 12*j**c - 111 + 4*j**4 - 16*j = 0.
-2, 0, 1
Factor -628*b**2 + 401*b - 231*b + 151*b**3 + 0*b**3 + 49*b**3 + 254*b + 4*b**4.
4*b*(b - 2)*(b - 1)*(b + 53)
Factor -16015*r**2 - 16011*r**2 - 184*r + 32022*r**2.
-4*r*(r + 46)
Let c(s) be the second derivative of s**4/18 - 32*s**3 + 6912*s**2 - 2333*s. Factor c(n).
2*(n - 144)**2/3
Let h = 185604 - 2041634/11. Factor 0 - 6/11*k + h*k**2.
2*k*(5*k - 3)/11
Let q(p) be the first derivative of -p**9/3024 + p**8/112 - 2*p**7/35 + 11*p**6/90 + 154*p**3/3 + 100. Let m(i) be the third derivative of q(i). Factor m(c).
-c**2*(c - 11)*(c - 2)**2
Let x be (-4 - -88)/3 + 0. Let r be x/9 + 7/(-63). Factor 9 - 3*b**2 + 3*b**r + 0 - 6*b**2 + 3.
3*(b - 2)**2*(b + 1)
Let j be 1 + 2 + 0 - (-858)/33. Find n such that 10*n**2 - 45*n + 9*n**3 - 11*n**3 + 8 + j*n = 0.
1, 2
Let i = -628 - -630. Suppose 0*d - 3*d + 208 = 4*f, f + 4*d - 39 = 0. Let -14*v + 6*v**2 - 31*v**i + 4*v + f*v**3 - 20*v**4 = 0. Calculate v.
-1/4, 0, 1, 2
Let v(q) = -2*q**3 - 2*q**2 + 36*q - 16. Let p be v(3). Let b(f) be the first derivative of -45/2*f**2 - 5/4*f**4 - p*f - 10*f**3 + 6. Factor b(t).
-5*(t + 1)**2*(t + 4)
Factor -a**2 - 9/4 - 37/4*a.
-(a + 9)*(4*a + 1)/4
Let l(o) be the second derivative of 99/2*o**3 + o + 14 + 363/2*o**2 - 21/4*o**4 + 3/20*o**5. Find i such that l(i) = 0.
-1, 11
Suppose -692*n + 703*n = 11. Let p(y) = 2 + y**3 + 0 - 3. Let l(w) = -5*w**3 - 30*w**2 - 75*w + 2. Let r(q) = n*l(q) + 2*p(q). Factor r(a).
-3*a*(a + 5)**2
Let r(g) be the first derivative of g**4/2 - 68*g**3/3 + 64*g**2 - 108. Factor r(u).
2*u*(u - 32)*(u - 2)
Let l(z) be the third derivative of z**5/240 + 623*z**4/96 - 26*z**3 - 2*z**2 - 64*z - 15. Suppose l(w) = 0. Calculate w.
-624, 1
Suppose -18 + 30 = 6*h. Factor 21*b**h + 20*b - 41*b**2 + 25*b**2 - 60.
5*(b - 2)*(b + 6)
Let z(w) be the third derivative of w**6/24 - 181*w**5/12 + 40495*w**4/24 + 41405*w**3/6 + 493*w**2. Suppose z(x) = 0. Calculate x.
-1, 91
Suppose 94 + 3*c**2 + 156 + 418 - 92 - 294*c = 0. What is c?
2, 96
Let h = -667 + 1012. Suppose -108 - 72 + 170*w + 5*w**2 + h = 0. Calculate w.
-33, -1
Solve 0 + 100/7*m**3 - 14*m**2 - 2/7*m**4 + 0*m = 0 for m.
0, 1, 49
Suppose -3*q + 0*q = -5*h + 10, -5*q = 0. Factor -40*j**h + 7*j**3 - 44*j + 7865 - 3*j**3 - 7865.
4*j*(j - 11)*(j + 1)
Suppose 176/5*x**2 + 0 + 4/5*x**3 + 492/5*x = 0. Calculate x.
-41, -3, 0
Let u(w) be the third derivative of 1/4*w**4 + 0*w + 15/16*w**3 + 189*w**2 + 0 + 1/160*w**5. Find b such that u(b) = 0.
-15, -1
Let n(k) be the first derivative of -1/21*k**3 - 1521/7*k + 207 - 39/7*k**2. Factor n(y).
-(y + 39)**2/7
Let o(t) be the second derivative of 3*t**5 + 155*t**4/12 - 25*t**3/2 - 1127*t. Suppose o(v) = 0. What is v?
-3, 0, 5/12
Find m, given that -84*m + 33/4*m**4 - 39/4*m**5 - 30*m**2 + 60*m**3 - 12 = 0.
-2, -1, -2/13, 2
Let d(x) = 18*x**3 + 264*x**2 + 378*x - 135. Let l(f) = -37*f**3 - 529*f**2 - 758*f + 269. Let a(m) = -5*d(m) - 3*l(m). Determine q, given that a(q) = 0.
-11, -2, 2/7
Let t(k) be the second derivative of -k**5/30 - 7*k**4/3 - 9*k**3 - 40*k**2/3 - 325*k. Factor t(l).
-2*(l + 1)**2*(l + 40)/3
Let h(w) be the second derivative of w**6/120 + w**5/16 - 17*w**4/8 + 40*w**3/3 - 28*w**2 - 6524*w. Factor h(f).
(f - 4)**2*(f - 1)*(f + 14)/4
Let u(s) be the third derivative of -s**8/20160 + s**7/560 - s**6/40 - 9*s**5/4 + 83*s**2. Let m(j) be the third derivative of u(j). Factor m(x).
-(x - 6)*(x - 3)
Suppose 4 - 6 = -2*h. Let g be (5/30*50)/h. Factor -10/3 - 20/3*c**2 + 5/3*c**3 + g*c.
5*(c - 2)*(c - 1)**2/3
Let s be (17*2)/((-8)/(4 + -8)). Factor -1 + 81*t - s*t**2 + 1 + t**3 - t**2.
t*(t - 9)**2
Let f be 120/(4/8*-2). Let j be (5/3)/((-100)/f). Find v,