 -22378100 - 3*n**2 + 22376867 - 4*n + 424*n.
-3*(n - 137)*(n - 3)
Let o(x) be the first derivative of x**3/6 + 3*x**2/4 - 14*x + 1410. What is d in o(d) = 0?
-7, 4
Let u(k) = 7*k - 8*k - k**2 - 3397 + 3399 - 2*k. Let v be u(-3). Factor 4/13*z**v - 4/13 - 6/13*z.
2*(z - 2)*(2*z + 1)/13
Find c such that -2/5*c**2 + 258/5*c - 200 = 0.
4, 125
Let g(u) = 4*u**4 - 264*u**3 - 274*u**2 + 6*u + 12. Let r(k) = -k**4 + k**3 + 3*k**2 - k - 2. Let b(d) = -g(d) - 6*r(d). Let b(f) = 0. What is f?
-128, -1, 0
Let f(o) be the first derivative of 2/15*o**5 - 8/9*o**3 - 4/3*o**2 + 0*o + 1/6*o**4 + 175. Factor f(z).
2*z*(z - 2)*(z + 1)*(z + 2)/3
Let v(c) be the first derivative of -c**7/1260 - c**6/54 - 4*c**5/45 - 73*c**3 + 9. Let t(u) be the third derivative of v(u). Suppose t(b) = 0. Calculate b.
-8, -2, 0
Let h = 201463796/197785 - -1/39557. Let c = 1019 - h. Factor c*a**2 - 6/5 - 4/5*a.
2*(a - 3)*(a + 1)/5
Let d(c) be the third derivative of -c**8/360 - 61*c**7/1575 - 29*c**6/300 + 41*c**5/90 - 5*c**4/18 - 6271*c**2. Find o, given that d(o) = 0.
-5, 0, 2/7, 1
Suppose 15 = -2*c + 25. Find s such that 132*s**3 - 144 + 408*s - 43*s**5 + 57*s**3 - 48*s**c + 94*s**5 - 417*s**2 - 39*s**4 = 0.
1, 3, 4
Let j(b) be the third derivative of -b**5/180 - b**4/24 + 14*b**3/9 - 3465*b**2. Factor j(g).
-(g - 4)*(g + 7)/3
Let 1/3*b**2 - 14/3*b + 8 = 0. Calculate b.
2, 12
Suppose -133/5*o**2 - 1/5*o**3 + 0 - 132/5*o = 0. Calculate o.
-132, -1, 0
Let t(l) be the second derivative of -l**4/6 - 1049*l**3/3 - 1048*l**2 - 4628*l. What is f in t(f) = 0?
-1048, -1
Let r(o) be the second derivative of -o**7/3360 + o**6/960 + o**4/12 + 15*o**3/2 + 85*o. Let t(y) be the third derivative of r(y). Factor t(w).
-3*w*(w - 1)/4
Let g(p) be the second derivative of p**8/33600 - p**7/2100 + p**6/400 - p**5/150 - 35*p**4/6 - 2*p - 39. Let i(h) be the third derivative of g(h). Factor i(s).
(s - 4)*(s - 1)**2/5
Suppose -7*s + 7667 = -190363. Let c be (-4)/(-38) + s/190 + -2. Suppose 28*t - c*t**2 - 4/3 = 0. Calculate t.
2/21
Determine h, given that 15680 + 285*h**2 + 5/2*h**3 + 8400*h = 0.
-56, -2
Let d(l) be the third derivative of 2*l**6/75 - 23*l**5/75 + 31*l**4/30 - 8*l**3/5 + 443*l**2. Suppose d(j) = 0. What is j?
3/4, 1, 4
Let r(a) be the third derivative of 1/330*a**6 + 2*a**2 - 93 + 0*a**4 + 1/1155*a**7 - 1/110*a**5 + 0*a**3 + 0*a. Factor r(o).
2*o**2*(o - 1)*(o + 3)/11
Let t(r) be the third derivative of 1/20*r**5 - 1/120*r**6 + 0 + 0*r**3 - 41*r**2 + 0*r**4 + 0*r. Solve t(v) = 0.
0, 3
Suppose 0 = -21*r - r - 12496. Let o = r - -570. Factor -108/5 - 36/5*v - 3/5*v**o.
-3*(v + 6)**2/5
Suppose 896*u - 6678 + 1389 = -867*u. Factor 0*w - 10/3*w**u + 4/3*w**2 + 0 + 2*w**4.
2*w**2*(w - 1)*(3*w - 2)/3
Let y(t) be the first derivative of 3*t**5/5 - 1995*t**4/2 + 440893*t**3 + 1328670*t**2 + 1330668*t - 2746. Determine x, given that y(x) = 0.
-1, 666
Suppose 5*h + 6*w - 335 = w, -4*h = -2*w - 274. Suppose 18*a + 16*a - h = 0. Factor -2/5*r**a + 8/5 + 6/5*r.
-2*(r - 4)*(r + 1)/5
Determine a, given that 851*a**3 + 76*a**4 + 1296*a**2 + 0 + 1003*a**3 - 864*a - 4*a**5 + 0 - 2358*a**3 = 0.
0, 1, 6
Factor -139 + 658*r + 241 + 344 - r**2 - 213*r.
-(r - 446)*(r + 1)
Let z(y) be the second derivative of -6*y**2 + 8*y - 1/4*y**4 - 1 + 1/30*y**6 - 10/3*y**3 + 3/10*y**5. Factor z(q).
(q - 2)*(q + 1)**2*(q + 6)
Let g be (-132)/(-2) + 5/(15/9). Suppose 5*m = -p + g, -14 = 2*m - p - 43. Determine d, given that 9*d**4 + 3*d**2 + m*d**4 - 18*d**4 - 18*d**2 + 10*d = 0.
-2, 0, 1
Let v(h) be the third derivative of 0*h + 47/78*h**4 + 28 + 2209/39*h**3 + 3*h**2 + 1/390*h**5. Factor v(u).
2*(u + 47)**2/13
Factor -3/7*z**2 - 7581 - 114*z.
-3*(z + 133)**2/7
Let a(l) be the second derivative of -31/60*l**5 - 1/3*l**2 - 1/60*l**6 + 49/72*l**4 + 0*l**3 + 68*l + 0 + 5/63*l**7. Find c such that a(c) = 0.
-2, -1/4, 2/5, 1
Let p(g) = -g + 12. Let m be p(-3). Factor 6*z**3 - 2*z + 20 + 42*z + 8*z**3 - 24*z**3 - 5*z**4 + m*z**2.
-5*(z - 2)*(z + 1)**2*(z + 2)
Let j(q) be the first derivative of 2*q**3/27 - 1016*q**2/9 + 516128*q/9 + 1011. Factor j(m).
2*(m - 508)**2/9
Let h(k) be the second derivative of 59 - 7/120*k**5 - 1/4*k**3 + k - 5/24*k**4 - 1/180*k**6 + 0*k**2. What is a in h(a) = 0?
-3, -1, 0
Let g(b) be the first derivative of -2*b**5/35 + 3*b**4/2 - 54*b**3/7 - 729*b**2/7 + 8748*b/7 + 47. Find q, given that g(q) = 0.
-6, 9
Find m such that 2/9*m**3 + 240 + 4*m**2 - 72*m = 0.
-30, 6
Let a(o) be the third derivative of 5/2*o**4 - 1/8*o**6 + 1/6*o**5 - 12*o**3 - 2*o**2 + 0 - 23*o + 1/336*o**8 + 0*o**7. Factor a(z).
(z - 2)**3*(z + 3)**2
Let y = -364896 + 729873/2. Solve -y*z + 27/8*z**3 + 3*z**4 - 81/2*z**2 - 3/8*z**5 + 0 = 0 for z.
-3, -1, 0, 6
Let p(k) be the first derivative of -k**6/1440 - k**5/480 + k**4/8 + k**3/3 - 25*k**2/2 - 41. Let g(d) be the third derivative of p(d). Factor g(u).
-(u - 3)*(u + 4)/4
Let f = -54722 - -109449/2. What is z in 2 - 11/2*z + z**3 + f*z**2 = 0?
-4, 1/2, 1
Let u(m) = -15*m**2 - 3*m - 9. Suppose 0 = -3*b + 14 + 31. Suppose b = -2*r + 25. Let o(w) = -8*w**2 - w - 5. Let c(q) = r*u(q) - 9*o(q). Factor c(v).
-3*v*(v + 2)
Let o = 146 + -78. Let r = o - 68. Suppose -y**5 + 2 - y + 18*y**3 - 16*y**3 + 2*y**4 - 4*y**2 + r*y**5 = 0. Calculate y.
-1, 1, 2
Let d(z) be the first derivative of -z**6/9 + 4*z**5/15 + 5*z**4/2 - 80*z**3/9 - 4*z**2/3 + 32*z + 325. Solve d(w) = 0 for w.
-4, -1, 2, 3
Let k(u) = -3*u - 120. Let p be k(-41). Let a be p/((-60)/(-8)) - (-4)/(-10). Determine b, given that 3/2 + a*b - 3/8*b**2 = 0.
-2, 2
Suppose 6*x - 3*x - u + 10 = 0, 5*u - 24 = 2*x. Let m be (148/(-185))/((-1)/x*-2). Factor -m*t**2 - 4/5*t + 8/5.
-4*(t - 1)*(t + 2)/5
Let k = -1284163/5 + 256835. Factor 3/5*q + k - 3/5*q**3 - 12/5*q**2.
-3*(q - 1)*(q + 1)*(q + 4)/5
Let z(g) = g**3 - 11*g**2 - 11*g - 3. Let c be z(12). Suppose -c = -5*s + 1. Factor -6 - 17*o**2 - 9*o**3 + 9*o - 25*o**2 + 45*o**s + 3*o**4.
3*(o - 2)*(o - 1)**2*(o + 1)
What is b in -2/11*b**2 + 1260/11 + 18/11*b = 0?
-21, 30
Suppose z + 2667 = 2673. Let q(p) be the second derivative of 2/5*p**z + 0 + 0*p**2 + 4*p - 2/5*p**5 + 0*p**3 - 1/3*p**4. Factor q(l).
4*l**2*(l - 1)*(3*l + 1)
Let h be -4 + -7 - (11/22 + -12 + -4). Factor -1104*g + 285/2*g**2 - h*g**3 - 384.
-3*(g - 16)**2*(3*g + 1)/2
Let c(f) = f**4 - f**2 + f. Let g(y) = -28*y**4 - 84*y**3 + 680*y**2 - 2192*y + 2592. Let i(o) = 32*c(o) + g(o). Factor i(r).
4*(r - 6)**3*(r - 3)
Let h be (42 + -15)*1/(-3). Let i be 6 + h + (-30)/(-6). Suppose 0*y + 1/3 - 1/3*y**i = 0. Calculate y.
-1, 1
Let g(n) be the second derivative of 277*n + 1/19*n**3 + 0 + 7/95*n**5 + 0*n**2 - 17/114*n**4. Factor g(k).
2*k*(k - 1)*(14*k - 3)/19
Factor 98*f**2 - 11250 - 3450*f - 2/3*f**3.
-2*(f - 75)**2*(f + 3)/3
Let u be 3/3 - (-11)/(-22). Let s(l) be the first derivative of 1/5*l**5 - 17 - 1/6*l**6 - 2/3*l**3 - 1/2*l**2 + u*l**4 + l. Factor s(b).
-(b - 1)**3*(b + 1)**2
Factor -342*u**3 - 53*u**3 + 48457*u**2 - 6750000*u + 73043*u**2 - 480*u**3 + 125000000 + 146*u**3.
-(9*u - 500)**3
Let p = 952711/357270 + 3/119090. Factor 1/3*m**3 + 16 - 5/3*m**2 - p*m.
(m - 4)**2*(m + 3)/3
Let g(d) be the second derivative of -3/140*d**5 + 1/294*d**7 + 116*d + 0 - 1/210*d**6 + 0*d**2 + 1/84*d**4 + 1/21*d**3. Factor g(a).
a*(a - 2)*(a - 1)*(a + 1)**2/7
Let b = 104807 + -104803. Solve -11/6*x**2 - 7/6*x**3 - 5/6*x - 1/6*x**b + 0 = 0.
-5, -1, 0
Find o, given that 13/3*o**2 + 1/3*o**4 - 5*o**3 + 130/3 + 53*o = 0.
-2, -1, 5, 13
Let u(v) = 7*v**2 - 14*v - 8. Let w be u(10). Factor -2205*k**2 - 358*k**3 - 317*k**3 - 34 - 10 - w*k + 8.
-3*(k + 3)*(15*k + 2)**2
Let z(i) be the first derivative of 0*i + 13 - 3*i**2 - 6*i**3 - 15/8*i**4. Suppose z(v) = 0. What is v?
-2, -2/5, 0
Let w(y) = 12*y**2 + 3. Let l(s) = -7*s**2 - 90*s - 1218. Let p(f) = l(f) + w(f). Find m such that p(m) = 0.
-9, 27
Let x(t) be the second derivative of 5*t**4/12 + 235*t**3/6 - 375*t**2 - 5*t + 53. Let x(y) = 0. What is y?
-50, 3
Let q be (-52 - (-1209)/78*4) + 34/(-4). Suppose -q*y**5 + 0 - 29*y**4 + 20*y**3 + 0*y**2 + 0*y = 0. Calculate y.
-20, 0, 2/3
Let d = -16 - -20. Let u(f) be the first derivative of -2*f**2 + f**4 + 4 - 4/3*f**3 + d*f. Suppose u(q) = 0. What is q?
-1, 1
Let v(a) = -5*a**2 + 115*a - 508. Let b be v(17). Let 4/3*i**b + 80/3 - 28*i = 0. W