3*(i - 1)*(i + 3)
Let q(c) = 5*c**2 - 3*c + 3. Let k be q(1). Let f be 3/5 - (-242)/55. Solve 267*l**2 - 1 + k*l - 4 - f*l**3 - 262*l**2 = 0.
-1, 1
Let l(d) = -3*d**2 + 1590*d + 6066. Let t(v) = -v**2 + 636*v + 2427. Let m(h) = 7*l(h) - 18*t(h). Factor m(y).
-3*(y + 4)*(y + 102)
Let s be (1 + 0)*(-18 - (17 - 35)). Let m(z) be the third derivative of 5*z**2 + s*z**4 + 4/21*z**3 + 0 - 1/140*z**6 + 0*z - 1/30*z**5. Factor m(c).
-2*(c + 1)*(c + 2)*(3*c - 2)/7
Let s(g) = -80*g + 2 + 2*g**2 + 32*g + 0*g**2 + 12*g + 12*g. Let v be s(12). Factor 1/6*k**3 - 11/6*k - 1 - 2/3*k**v.
(k - 6)*(k + 1)**2/6
Suppose 0 = -3*m - 3*y, -2*m = -10*y + 7*y - 20. Factor 45*u**m + 14*u**2 - 75*u**3 - 90 - 95 - 5*u**5 + 185 + 21*u**2.
-5*u**2*(u - 7)*(u - 1)**2
Let k(i) be the third derivative of -2*i**5/165 - 47*i**4/132 + 4*i**3/11 + 76*i**2 - 7. Factor k(m).
-2*(m + 12)*(4*m - 1)/11
Let g(x) be the first derivative of -x**6/540 + x**5/9 - x**4 - 2*x**3/3 - 17*x - 38. Let l(d) be the third derivative of g(d). Factor l(v).
-2*(v - 18)*(v - 2)/3
Factor -22/9*m + 0 + 28/9*m**4 - 8*m**3 - 2/9*m**5 + 68/9*m**2.
-2*m*(m - 11)*(m - 1)**3/9
Suppose 11*d - 1 = 21. Suppose 3621 + 352*k + 5648 - 1525 + 4*k**d = 0. What is k?
-44
Let v(j) be the third derivative of j**7/1050 + 23*j**6/100 + 34*j**5/25 + 203*j**4/60 + 9*j**3/2 - j**2 - 33*j. Factor v(p).
(p + 1)**3*(p + 135)/5
Let b(l) be the second derivative of l**4/2 + 10*l**3/3 + 9*l**2/2 + 3*l - 8. Let c(o) = -o**2 + o + 1. Let x(u) = 3*b(u) - 15*c(u). Factor x(w).
3*(w + 1)*(11*w + 4)
Determine t so that 40/9*t**3 + 34/3*t**2 - 8/9*t - 136/9 + 2/9*t**4 = 0.
-17, -2, 1
Suppose 2*x - 15323 = -5*s - 3568, -4*x - 11785 = -5*s. Find g such that g**3 + 3442*g + 432*g + 13602*g + 213*g**2 - s*g + 357911 = 0.
-71
Let w be (-2635)/434*10/(-17). Suppose -w*q**4 + 0 - 2/7*q**2 + 15/7*q**3 + 0*q = 0. Calculate q.
0, 1/5, 2/5
Let c = -142607 - -142754. Suppose 7203/2 + 3/2*h**2 - c*h = 0. Calculate h.
49
Let n be -8 - (-61)/8 - (-54)/16. Let l(z) be the second derivative of z**n + 4/15*z**6 + 0 + 0*z**2 + 19*z - 1/2*z**5 - 1/3*z**4. Suppose l(r) = 0. What is r?
-3/4, 0, 1
Let d be (6/3 + -2)*16/16. Let g be 5 - ((-966)/(-21))/(10 + d). Factor g - 6/5*u**4 + 6/5*u + 4/5*u**2 - 4/5*u**3 - 2/5*u**5.
-2*(u - 1)*(u + 1)**4/5
Let u(y) be the first derivative of -y**6/3 - 88*y**5/5 - 42*y**4 - 2838. Factor u(a).
-2*a**3*(a + 2)*(a + 42)
Let s(u) be the second derivative of 0*u**4 + 1/4*u**3 - 3/40*u**5 + 0*u**2 - 2 + u. Suppose s(m) = 0. What is m?
-1, 0, 1
What is o in 776/11*o - 98/11*o**3 + 1316/11*o**2 + 112/11 = 0?
-2/7, 14
Let x(p) be the second derivative of -1/8*p**2 - 1/4*p**3 + 0 - 36*p + 7/48*p**4. Suppose x(u) = 0. What is u?
-1/7, 1
Let r(g) be the third derivative of g**6/660 + g**5/55 - 10*g**4/33 - 8*g**2 + 65*g. Factor r(s).
2*s*(s - 4)*(s + 10)/11
Factor -1/3*c**2 - 2*c - 3.
-(c + 3)**2/3
Find a, given that -218/11*a**4 - 842/11*a - 1268/11*a**2 - 2/11*a**5 - 852/11*a**3 - 210/11 = 0.
-105, -1
Let i(l) be the first derivative of 2*l**4/5 + 26*l**3/15 - 18*l/5 - 2309. Factor i(z).
2*(z + 1)*(z + 3)*(4*z - 3)/5
Let v(n) be the second derivative of -n**7/42 + 7*n**6/15 + 98*n**5/5 + 201*n + 3. Find x such that v(x) = 0.
-14, 0, 28
Suppose 4*f + 15 = 5*s, -4*s - 30 + 42 = -f. Let v(c) be the second derivative of -8*c**4 - 14*c + f + 0*c**2 + 8/3*c**3 + 11/5*c**5. Factor v(j).
4*j*(j - 2)*(11*j - 2)
What is m in -3/2*m**2 - 789*m - 207507/2 = 0?
-263
Let k(o) be the first derivative of 11/8*o**4 + 1/12*o**6 - 1/3*o**3 - 3/5*o**5 + 122 - 3*o**2 + 4*o. Determine b, given that k(b) = 0.
-1, 1, 2
Suppose 0 = 3*x, 5*x = -2*q - 3 + 13. Solve 0 - 2/5*z**q + 0*z**2 - 2*z**4 - 8/5*z**3 + 0*z = 0 for z.
-4, -1, 0
Let v(d) be the second derivative of -d**6/15 - 11*d**5/5 - 61*d**4/6 + 64*d**3 - 108*d**2 - 6*d + 100. Factor v(b).
-2*(b - 1)**2*(b + 6)*(b + 18)
Let m = 31 + -30. Let s be 2 + (0 - (-1 + m))/(-1). Factor a**2 - 3*a**3 - 8 + 8*a**s - 3 + 5 + 3*a - 3*a**4.
-3*(a - 1)**2*(a + 1)*(a + 2)
Let h(f) be the first derivative of -2*f**3/15 - 29*f**2/5 + 192*f/5 + 369. Suppose h(r) = 0. Calculate r.
-32, 3
Suppose -13*y - 6*y = -20*y. Let s(p) be the third derivative of 1/72*p**4 + 20*p**2 - 1/180*p**5 + 1/630*p**7 + 0*p**3 + y + 0*p - 1/360*p**6. Factor s(b).
b*(b - 1)**2*(b + 1)/3
Let l(f) = -15*f**2 + 85*f + 150. Let d(m) = 130*m**2 - 765*m - 1350. Let o(h) = -4*d(h) - 35*l(h). Factor o(s).
5*(s + 2)*(s + 15)
Let u(j) be the first derivative of -j**6/3 + 164*j**5/5 - 1597*j**4/2 - 2296*j**3 - 1764*j**2 - 841. Suppose u(a) = 0. What is a?
-1, 0, 42
Suppose 4*b + 12 = 2*d, -3*b - 8 = -2*d + 2. Solve u**2 - 3 - 5 - d*u**3 - 11*u**2 - 16*u + 0*u**2 = 0 for u.
-2, -1
Let g be (9/6*26/(-91))/(243/(-189)). Factor 5/3 + g*n**3 + n**2 - 3*n.
(n - 1)**2*(n + 5)/3
Let m(a) = 46*a**2 - 399*a - 34822. Let f be m(-82). Factor -3/5*x**3 - f - 144*x**2 - 11520*x.
-3*(x + 80)**3/5
Let b(f) be the third derivative of f**5/30 - 41*f**4/4 - 250*f**3/3 + 96*f**2. Factor b(h).
2*(h - 125)*(h + 2)
Let v(y) be the first derivative of 3*y**4/20 + 24*y**3/5 - 3*y**2/10 - 72*y/5 - 406. Factor v(l).
3*(l - 1)*(l + 1)*(l + 24)/5
Let t(a) be the second derivative of 4*a**7/7 + 2*a**6/3 - 19*a**5/5 - 9*a**4 - 14*a**3/3 + 4*a**2 - 3430*a. Factor t(d).
4*(d - 2)*(d + 1)**3*(6*d - 1)
Let s = -993 + 1065. Suppose 7*v - s = -29*v. Suppose 1/2*d**v + 7/6*d - 1 = 0. What is d?
-3, 2/3
Let j(z) = -4*z**4 + 6*z**3 + 20*z**2 + 10*z - 2. Let i = -653 - -651. Let w(s) = 2*s**3 + s**2 - s + 1. Let t(d) = i*j(d) - 4*w(d). Solve t(h) = 0.
-1, -1/2, 0, 4
Let n = -530 + 532. Let k = -2 - -5. Factor n*c**4 + 2*c - 7*c + 5*c + 2*c**k.
2*c**3*(c + 1)
Let d = 262412/35 + -37486/5. Let 2/7*x - 4/7*x**2 + 2/7*x**4 - 4/7*x**3 + 2/7 + d*x**5 = 0. Calculate x.
-1, 1
Let n(r) = 42*r**2 - 376*r - 18. Let o be n(9). Determine q, given that 1/9*q**3 + 0*q**2 - 4/9*q + o = 0.
-2, 0, 2
Let n be ((-4)/18)/((13 - (-4886)/(-378))*-15). Factor 3/5*o**2 + 0 + 2/5*o - n*o**4 + 0*o**3.
-o*(o - 2)*(o + 1)**2/5
Let d be (400/88)/(-5)*-11. Let b be d + (-17)/2 + (-6)/4. Determine j so that 0*j - 2/3*j**2 - 2/3*j**3 + b = 0.
-1, 0
Let t(r) be the second derivative of -1/105*r**6 - 25/21*r**3 + 13/70*r**5 + 0 - 15/14*r**4 + 70*r + 250/7*r**2. Factor t(f).
-2*(f - 5)**3*(f + 2)/7
Let g(j) = j**3 - 13*j**2 + j - 11. Let q(s) = -s**3 + 7*s**2 - 4*s + 1. Let w be q(6). Let h be g(w). Factor -3*r**3 - h*r + 0*r**3 + 5*r**3.
2*r*(r - 1)*(r + 1)
Let t = 111231 + -111231. Find o, given that t - 8/7*o**3 - 2/7*o + o**2 + 3/7*o**4 = 0.
0, 2/3, 1
Let y(s) be the first derivative of s**3/3 + 239*s**2/2 - 482*s - 12652. Factor y(p).
(p - 2)*(p + 241)
Let i(m) be the third derivative of -m**5/120 - 32*m**4 - 49152*m**3 + 3587*m**2. Factor i(u).
-(u + 768)**2/2
Let h(r) be the third derivative of r**7/735 - 124*r**6/105 + 10576*r**5/35 - 121024*r**4/21 + 952576*r**3/21 - 1512*r**2. Factor h(b).
2*(b - 244)**2*(b - 4)**2/7
Let k be -2 - (0 + -2)/(8/156). Let r = k - 34. Determine h so that 4 + 16*h**2 - 6*h**4 - 2*h**5 + 14*h + 4*h**r - 2*h**4 + 4*h**4 = 0.
-1, 2
Let x be 6/1 - (((-4480)/12)/(-5))/((-1824)/(-144)). Suppose 12/19*k**2 - 8/19*k**4 - x*k**5 + 0 - 2/19*k**3 + 0*k = 0. Calculate k.
-3, -2, 0, 1
Determine q, given that 34747958/17*q**2 - 2/17*q**5 + 0*q + 1554/17*q**4 + 0 - 402486/17*q**3 = 0.
0, 259
Let d(s) be the first derivative of s**8/10080 - s**7/1008 + s**6/360 - 146*s**3/3 - 48. Let q(g) be the third derivative of d(g). Factor q(t).
t**2*(t - 3)*(t - 2)/6
Let c(i) be the first derivative of -1/9*i**3 - 45 - 7/3*i**2 - 13/3*i. Factor c(k).
-(k + 1)*(k + 13)/3
Let g(c) = c**2 + 9*c + 10. Let n be g(-9). Suppose -16*t = -11*t - n. Determine v so that 21*v**t - 13*v**2 + 28*v**2 - 8 + 12*v = 0.
-2/3, 1/3
Determine q so that 0 + 210*q + 3/2*q**5 - 6*q**2 - 423/2*q**3 + 6*q**4 = 0.
-14, -1, 0, 1, 10
Let a be -16 + 4 - (-16 - (-266)/(-70)). Determine d so that -1/5*d**4 - 9/5*d**3 - 18/5 - a*d - 29/5*d**2 = 0.
-3, -2, -1
Let x = -3188 + 3191. Let i(h) be the third derivative of 3/16*h**4 + 0*h + 1/80*h**5 + 0 + 10*h**2 + 9/8*h**x. Factor i(w).
3*(w + 3)**2/4
Let y(u) = u**3 + 5*u**2 - 9*u - 18. Let b be y(-6). Let v be (b + 18/66)*(-20)/(-30). Factor -v*c**2 + 2/11*c**3 - 16/11*c + 24/11.
2*(c - 2)**2*(c + 3