Factor 181*q**2 + 16*q + 192*q**3 - 92*q**2 - q**4 + 154*q**2 - 72*q**3 + 106*q.
-q*(q - 122)*(q + 1)**2
Let g(a) = a**4 + 42*a**3 + 493*a**2 + 1830*a - 2354. Let j(c) = -c**4 - 43*c**3 - 493*c**2 - 1829*c + 2350. Let z(m) = 4*g(m) + 3*j(m). Factor z(i).
(i - 1)*(i + 13)**2*(i + 14)
Let k be 28/15 - 3/(11/(308/(-105))). Let i(u) be the third derivative of 0 - 19*u**2 - 7/30*u**5 - 5/2*u**4 - k*u**3 + 0*u. Factor i(r).
-2*(r + 4)*(7*r + 2)
Suppose 156 = -3*y - 9*j + 7*j, -2*j - 6 = 0. Let m be 0 - 5 - 280/y. Factor 1/5*a**4 - m*a**3 + 0*a + 0 + 2/5*a**2.
a**2*(a - 2)*(a - 1)/5
Suppose -109*b - 112 = -128*b + 40. Let q(u) be the second derivative of 5/6*u**3 - 1/4*u**5 + 0*u**4 + b*u + 0*u**2 + 0. Find i such that q(i) = 0.
-1, 0, 1
Suppose -3*m - 27 = 3*q, -5*q + 63 = m + 72. Suppose q*j - 3/2 + 3/8*j**2 = 0. What is j?
-2, 2
Determine t, given that 3197*t + 39*t**2 - 589*t + 32*t**2 - 850208 - 73*t**2 = 0.
652
Let w(a) be the second derivative of -1 + 4*a**2 - 2*a + 1/5*a**6 + 4*a**3 - 1/2*a**4 - 4/5*a**5. Factor w(v).
2*(v - 2)**2*(v + 1)*(3*v + 1)
Let y(v) be the first derivative of -203 - 61/2*v**4 - 44/3*v**3 + 36*v**2 + 25/3*v**6 + 12*v**5 - 16*v. Suppose y(s) = 0. What is s?
-2, -1, 2/5, 1
Let s(u) = -u**3 - 4*u**2 + 5*u + 27. Let i be s(-6). Let g = 71 - i. Let 0*o**g + 3*o**2 + 13 - 17 - 2*o**3 + 3*o**3 = 0. Calculate o.
-2, 1
Suppose -439978*q - 42 = -439999*q. Find u such that 3/2*u**q - 1/2*u**4 - 1/2*u + 1/2*u**3 - 1 = 0.
-1, 1, 2
Factor 0*g**2 + 17341 + 556*g + 2*g**2 + 21301.
2*(g + 139)**2
Let p = 313 - 307. Suppose -20*m = p*m. Factor 0 - 2/13*a**5 + 2/13*a**4 + m*a + 0*a**2 + 4/13*a**3.
-2*a**3*(a - 2)*(a + 1)/13
Let u(r) be the third derivative of 1/840*r**6 + 1/6*r**3 - 17*r**2 + 0 + 1/84*r**5 - 13/168*r**4 + 0*r. What is k in u(k) = 0?
-7, 1
Let c(r) = r + 87. Let d be c(19). Let s = d - 102. Find i such that 0 - 6/7*i**s - 6/7*i**3 - 2/7*i**2 + 0*i - 2/7*i**5 = 0.
-1, 0
Let p = 100 + -97. Let q**4 + q**4 + 2105*q**p - 8*q - 2103*q**3 - 8*q**2 = 0. What is q?
-2, -1, 0, 2
Let c = -17 + 29. Let m = 3297 - 3282. Suppose 4*t**4 - 32*t**2 + 61 + m - c = 0. Calculate t.
-2, 2
Let k be (-188)/(-16) - 2/(-32)*4. Suppose 4 = 49*s - 51*s + 3*c, 2*s + c = k. Factor -7/2*d - s*d**2 + 1/2.
-(d + 1)*(8*d - 1)/2
Let w(i) be the first derivative of -i**6/180 - 47*i**5/135 - 176*i**4/27 + 512*i**3/27 + 103*i**2 - 57. Let a(f) be the second derivative of w(f). Factor a(c).
-2*(c + 16)**2*(3*c - 2)/9
Let d be (-1 - (-20)/36)*72/(-16). Find a, given that 6*a**3 - 4*a**3 + 206*a - 198*a**d - 71874 + 6328*a = 0.
33
Let x(q) be the third derivative of q**7/630 - q**6/18 + 17*q**5/60 + q**4/18 - 34*q**3/9 - 3*q**2 + 33*q - 18. Factor x(h).
(h - 17)*(h - 2)**2*(h + 1)/3
Let r(y) be the first derivative of -y**4/10 - 49*y**3/15 - 147*y**2/5 - 27*y + 3860. Factor r(g).
-(g + 9)*(g + 15)*(2*g + 1)/5
Let a(t) be the third derivative of 0*t - 14/5*t**3 + 13/100*t**5 + 1/200*t**6 + 17*t**2 - 6 - 2/5*t**4. Factor a(f).
3*(f - 2)*(f + 1)*(f + 14)/5
Find a such that -5406/7*a**2 - 208/7*a**3 + 208/7*a + 5408/7 - 2/7*a**4 = 0.
-52, -1, 1
Factor -355*t**3 - 12223106 - 65*t**4 - 150*t**2 + 12223106.
-5*t**2*(t + 5)*(13*t + 6)
Let i = 8/305 - -9704/2135. Let a(v) be the first derivative of 1/2*v**4 - i*v**2 - 39 - 74/21*v**3 + 24/7*v. Solve a(z) = 0 for z.
-1, 2/7, 6
Let b be (-18)/(-3) + (-4)/(0 + 1). Let g be (b/22)/(6/264*22). Determine i, given that 6/11*i**2 + g*i**4 + 6/11*i**3 + 0 + 2/11*i = 0.
-1, 0
Let b = 267680 - 267678. Let 1/4*w**4 - w**b + 1/4*w**5 + 0 + 0*w - w**3 = 0. Calculate w.
-2, -1, 0, 2
Let w(m) be the first derivative of 6/5*m**2 + 124 + 32/5*m - 2/15*m**3. Factor w(l).
-2*(l - 8)*(l + 2)/5
Let m(f) = -f**5 - f**4 - f**3 + 8*f**2 + 2. Let z(c) = 2*c**5 + 19*c**4 - 69*c**3 - 24*c**2 + 432*c - 6. Let v(s) = -3*m(s) - z(s). Factor v(b).
b*(b - 6)**3*(b + 2)
Let x(v) be the first derivative of v**4/34 + 128*v**3/51 + 1043*v**2/17 + 1960*v/17 - 2789. Factor x(g).
2*(g + 1)*(g + 28)*(g + 35)/17
Let d = 1349/114576 + -3/341. Let k(v) be the third derivative of 0*v + 0*v**7 + d*v**8 + 1/30*v**5 + 0 + 0*v**4 + 0*v**3 - 2*v**2 - 1/40*v**6. Factor k(z).
z**2*(z - 1)**2*(z + 2)
Let t(s) be the first derivative of -s**7/42 - s**6/8 + s**5/12 + 5*s**4/8 + 7*s**2 - 1. Let f(a) be the second derivative of t(a). What is w in f(w) = 0?
-3, -1, 0, 1
Let s(a) be the first derivative of -1/3*a**3 + 0*a - 87 - 9/4*a**4 + 9/2*a**2 + 1/5*a**5. Factor s(o).
o*(o - 9)*(o - 1)*(o + 1)
Determine q so that 1268*q**2 + 7*q**4 + 3876*q + 1082*q**3 - 8704 + 3994*q - 7784*q**2 - 6*q**4 + 5178*q = 0.
-1088, 2
Let -28*s - 25*s - s**2 - 11716 + 11056 = 0. What is s?
-33, -20
Let t(f) be the third derivative of -f**6/30 + 193*f**5/5 - 37249*f**4/2 + 14378114*f**3/3 + 1689*f**2 - 2. Factor t(a).
-4*(a - 193)**3
Let g(c) be the first derivative of c**6/2160 - c**5/20 + 9*c**4/4 + 68*c**3/3 + 41. Let t(h) be the third derivative of g(h). Factor t(o).
(o - 18)**2/6
Let k(b) be the third derivative of b**6/660 - 2*b**5/55 - 43*b**4/132 - 10*b**3/11 - 716*b**2. Suppose k(u) = 0. Calculate u.
-2, -1, 15
Let x be (-130)/(-5) + 0 - -1 - (28 + -22). Let o(u) be the second derivative of 5/4*u**5 + 1/6*u**6 + 35/6*u**3 + x*u + 5*u**2 + 15/4*u**4 + 0. Factor o(s).
5*(s + 1)**3*(s + 2)
What is m in -9*m**5 + 220*m**4 + 13113*m - 6266*m**3 - 18945*m + 11880*m**2 + 7*m**5 = 0?
0, 1, 54
Let c(k) be the first derivative of -28*k**3/3 + 540*k**2 + 468*k - 10704. Factor c(h).
-4*(h - 39)*(7*h + 3)
Suppose 8*c - 15*c - 12*c + 38*c = -16*c. Factor -2/7*h + c - 15/7*h**3 - 17/7*h**2.
-h*(h + 1)*(15*h + 2)/7
Let g(p) = p**4 + p**3 - 3*p**2 + 3*p. Let k(b) = b**3 + b - 1. Suppose 11*q + 1 - 45 = 0. Let r(h) = q*k(h) - 2*g(h). Let r(j) = 0. What is j?
-1, 1, 2
Suppose -35 = 4*j + 42 - 89. Let w(m) be the second derivative of 30*m - 72/5*m**2 - 8/5*m**j + 0 - 1/15*m**4. Determine f, given that w(f) = 0.
-6
Let o = 1596 + -2414. Let g = -815 - o. Factor -1/3*n + 1/3*n**2 + 1/3*n**g - 1/3.
(n - 1)*(n + 1)**2/3
Suppose -496/9*r - 494/9 - 2/9*r**2 = 0. What is r?
-247, -1
Let b(a) be the third derivative of -a**5/40 + 143*a**4/16 + 36*a**3 - 15*a**2 - 8*a. Factor b(o).
-3*(o - 144)*(o + 1)/2
Let x(s) = 2*s**2 - 40*s + 40. Let y(j) = j**3 - 3*j**2 - 6*j - 1. Let f be y(5). Let u be x(f). Factor 6*c**2 - 3*c**u + 2 - 14.
3*(c - 2)*(c + 2)
Find c, given that 53/11*c - 53/11*c**3 - 1/11*c**4 + 169/11*c**2 - 168/11 = 0.
-56, -1, 1, 3
Let h(t) be the third derivative of 1/960*t**6 - t**2 - 74 - 13/240*t**5 + 0*t**3 + 0*t + 25/192*t**4. Solve h(f) = 0.
0, 1, 25
Let g be 24/(-42) + ((-1105)/7)/(-5). Factor -g*q**3 + 9*q**2 - 43*q**2 - 86*q - 26*q - 104 + 29*q**3.
-2*(q + 2)**2*(q + 13)
Let m(l) be the first derivative of l**4/2 - 64*l**3/3 + 221*l**2 + 1156*l - 1332. Factor m(t).
2*(t - 17)**2*(t + 2)
Let n(y) = -y**2 + 9*y - 2. Let f be n(4). Suppose 8*g = f - 2. Solve 0 + 3/10*v**g + 1/5*v + 1/10*v**3 = 0 for v.
-2, -1, 0
Let c = -78/1219 - -13721/4876. Factor -1/2 + 21/4*h + c*h**2.
(h + 2)*(11*h - 1)/4
Let q(y) be the first derivative of 5*y**6/8 + 1077*y**5/20 + 417*y**4/8 - 215*y**3/2 - 849*y**2/8 + 213*y/4 + 6323. Suppose q(f) = 0. Calculate f.
-71, -1, 1/5, 1
Let r = -1100 + 257. Let f = r - -845. Find t such that -6/7*t + 9/7 - 3/7*t**f = 0.
-3, 1
Let o(b) be the third derivative of 0*b - 3 + 10/21*b**3 + 1/7*b**4 + 1/840*b**6 + 3/140*b**5 - 2*b**2. Determine x so that o(x) = 0.
-5, -2
Let g = 869959/63 - 132646/9. Let h = g - -931. Suppose -8*m**4 + 16/7 + 106/7*m**3 - 68/7*m**2 - 8/7*m + h*m**5 = 0. What is m?
-2/5, 1, 2
Let a(j) = 3*j**4 - 123*j**3 - 46*j**2 + 5*j + 5. Let m(l) = 2*l**4 - 108*l**3 - 46*l**2 + 4*l + 4. Let f(s) = 4*a(s) - 5*m(s). Suppose f(i) = 0. What is i?
-23, -1, 0
Let b(o) be the third derivative of -o**7/350 + 651*o**6/100 - 423801*o**5/100 + 308*o**2. Factor b(s).
-3*s**2*(s - 651)**2/5
Find i, given that -18444*i - 100920 + 681/2*i**2 - 3/2*i**3 = 0.
-5, 116
Let w(y) = 9*y**4 - 41*y**3 - 301*y**2 - 636*y - 365. Let x(r) = 14*r**4 - 62*r**3 - 450*r**2 - 954*r - 548. Let m(b) = 8*w(b) - 5*x(b). Solve m(i) = 0 for i.
-3, -2, -1, 15
Let k(n) be the third derivative of 1/735*n**7 - 2/21*n**4 - 1/60*n**6 + 0 - 139*n**2 + 0*n + 1/15*n**5 + 0*n**3. Let k(m) = 0. What is m?
0, 1,