8
Let f(a) = -3*a**3 + 163*a**2 - 1186*a + 2744. Let h(d) = 20*d**3 - 1060*d**2 + 7708*d - 17836. Let w(l) = 32*f(l) + 5*h(l). Factor w(u).
4*(u - 7)**3
Suppose -5 = -8*f + 19. Determine z, given that -5*z**3 + 9*z**f + 20*z**2 + 0*z**3 = 0.
-5, 0
Solve 669/5*q**3 - 3/5*q + 0 - 666/5*q**2 = 0 for q.
-1/223, 0, 1
Let h(b) = 6*b**2 - 67*b + 140. Let l(n) = -11*n**2 + 135*n - 280. Let k(u) = 18*h(u) + 10*l(u). Factor k(f).
-2*(f - 70)*(f - 2)
Let y be (-3)/2 - 98/(-28). Suppose -5*n = -2*d + 6, -2 = -3*d - 4*n + 7. Factor -25*r**3 + 313*r**2 + 18 - 105*r - 39*r**d - 137*r**y.
-(r - 2)*(8*r - 3)**2
Suppose 3*b - 5 - 4 = 0. Solve 2*c + 273*c**2 + b*c**3 - 192 - 50*c - 261*c**2 = 0.
-4, 4
Let i(s) = 20*s - 20. Let p be i(3). Factor 67*h**2 - 35*h**3 - p*h + 66*h**2 - 15*h**4 - 43*h**2.
-5*h*(h - 1)*(h + 4)*(3*h - 2)
Let k(p) be the third derivative of 53*p**2 - 17/48*p**3 + 0*p - 1/480*p**5 - 3/32*p**4 + 2. Let k(u) = 0. Calculate u.
-17, -1
Let o(b) be the second derivative of 81/8*b**2 + 3/80*b**5 + 25/16*b**4 - 53/8*b**3 + 7 + 4*b. Factor o(t).
3*(t - 1)**2*(t + 27)/4
Suppose -47 = -y + 60. Factor y*q**2 + 31*q**3 + 12*q + 15*q**4 - 24 - 17*q**2 + 38*q**3.
3*(q + 1)*(q + 2)**2*(5*q - 2)
Let u(k) be the third derivative of k**5/30 + 19*k**4/12 + 6*k**3 - 1390*k**2. Find m, given that u(m) = 0.
-18, -1
Let d(j) be the second derivative of -j**6/50 - 63*j**5/50 - 9*j**4/5 + 101*j**3/5 - 369*j**2/10 - 8*j + 9. Solve d(z) = 0 for z.
-41, -3, 1
Let h(t) be the third derivative of 0 + 77*t**2 + 2*t - 4/5*t**3 - 13/60*t**4 - 1/300*t**5 + 1/600*t**6. Factor h(z).
(z - 6)*(z + 1)*(z + 4)/5
Factor 900*u**2 + 24*u**3 - u**4 + 4544*u + 13*u**3 + 9*u**3 + 7104 + 8*u**2 - u**4.
-2*(u - 37)*(u + 4)**2*(u + 6)
Let y be 1496/(-30) + (-24)/180. Let f be (-2 + (1235/y)/(-13))*-4. Find p, given that -4/15*p + f*p**2 - 2/15*p**3 + 0 = 0.
0, 1, 2
Suppose -4*r + 1340 = -3*r. Let m = -588 + 592. Solve r*n**2 - 1330*n**2 - n - m*n - 5 = 0 for n.
-1/2, 1
Let m(d) be the first derivative of d**3/3 - 329*d**2 + 5404. Factor m(b).
b*(b - 658)
Factor -26/9*m**2 + 0 - 28/3*m + 4/3*m**3 + 2/9*m**4.
2*m*(m - 3)*(m + 2)*(m + 7)/9
Factor 5*y**2 - 227 - 23*y**2 - 201*y - 125*y - 433 + 20*y**2.
2*(y - 165)*(y + 2)
Let k(z) be the first derivative of -28*z**5/5 + 2*z**4 + 84*z**3 - 36*z**2 + 815. Factor k(i).
-4*i*(i - 3)*(i + 3)*(7*i - 2)
Factor -144/5 - 286/5*r + 2/5*r**3 - 28*r**2.
2*(r - 72)*(r + 1)**2/5
Let m(a) be the second derivative of -a**4/30 + 19*a**3/15 - 2*a - 29. Find j, given that m(j) = 0.
0, 19
Let y(g) = -5*g**4 - 5*g**3 + 50*g**2 - 20. Let c(h) = 19*h**2 + h**3 - 20*h**2 - 2*h**3 + 1. Let d(b) = 20*c(b) + y(b). Suppose d(u) = 0. What is u?
-6, 0, 1
Let 31178/9*p**2 + 1024/3*p + 8 - 34322/9*p**3 = 0. What is p?
-6/131, 1
Let v(d) be the first derivative of -d**3/3 + 2*d**2 + d - 115. Let q(w) = 5*w**3 - 37*w**2 + 78*w - 38. Let j(z) = q(z) - 2*v(z). Factor j(t).
5*(t - 4)*(t - 2)*(t - 1)
Let r = -51169 - -255859/5. Factor 12/5 + 2/5*b**2 - r*b.
2*(b - 6)*(b - 1)/5
Let c(r) be the first derivative of r**5/20 - 2*r**4/3 - 19*r**3/6 - 5*r**2 + 195*r + 83. Let k(z) be the first derivative of c(z). Solve k(f) = 0.
-1, 10
Let s(c) be the first derivative of -3/4*c**4 + 6*c**2 + 3/5*c**5 + 0*c - 4*c**3 + 139. What is j in s(j) = 0?
-2, 0, 1, 2
Let y be 183/6 + 4 + (-35)/10. Suppose -y*b = -5*b. Factor 1/2*f - 1/2*f**2 + b.
-f*(f - 1)/2
Let -11716 - 2259*y - 686*y + 37*y - 6780 + 460*y - 81*y**2 = 0. What is y?
-136/9
Let p(k) = 2*k**2 - 17*k + 67. Let g be p(4). Determine o, given that g*o**2 + 16*o**3 - 11*o**2 - 13*o**4 + 9*o**4 = 0.
-1, 0, 5
Suppose 106*m - 68*m**4 - 208*m + 21*m**3 + 138*m**4 + 17*m**2 + 72 - 79*m**4 + m**5 = 0. Calculate m.
-2, 1, 3, 4
Let f(y) be the second derivative of y**6/24 + 3*y**5/2 + 25*y**4/2 + 140*y**3/3 + 177*y**2/2 - 8*y - 2. Let b(l) be the first derivative of f(l). Factor b(j).
5*(j + 2)**2*(j + 14)
Let x be (5/5)/(4830/(-1150)*2/(-18)). Solve -12/7 + x*i**2 + 12/7*i + 3/7*i**5 - 3/7*i**4 - 15/7*i**3 = 0.
-2, -1, 1, 2
Let g(i) be the second derivative of 3*i**5/20 + 3*i**4 + 41*i**3/2 + 63*i**2 + 8*i - 30. Let g(q) = 0. Calculate q.
-7, -3, -2
Let k be ((-15)/(-15))/((-3)/(-57)). Suppose 3*i = -k*i. Determine r so that -2/15*r**2 + 0*r + i = 0.
0
Let x(p) = 69*p - 171. Let h be x(2). Let o be 5 - h/55*-5. Factor 121/4 - 11/2*m + 1/4*m**o.
(m - 11)**2/4
What is i in 18/13*i**2 + 0 - 2/13*i - 54/13*i**3 + 54/13*i**4 = 0?
0, 1/3
Let m(j) be the third derivative of -j**6/240 - 173*j**5/120 + 44*j**4/3 - 59*j**3 + 9718*j**2 + 2. Factor m(y).
-(y - 2)**2*(y + 177)/2
Suppose 0 - 424/3*d - 28/3*d**2 = 0. What is d?
-106/7, 0
Let f(p) be the first derivative of -p**4/10 - 4*p**3/3 - 29*p**2/5 - 8*p - 5520. Factor f(s).
-2*(s + 1)*(s + 4)*(s + 5)/5
Suppose 64 = 2*t + 14*t. Suppose -t*o + 7*o - 4*m = 29, -4*o - 3*m = 3. Suppose 4/5*r**2 - 1/10*r**o - 21/10*r + 9/5 = 0. Calculate r.
2, 3
Let i = -137 - -218. Let 120*h**2 + i*h**3 + 17 - 8 + 51*h + 24*h**4 - 21*h**2 = 0. What is h?
-1, -3/8
Suppose 32 = -110*d + 169*d - 86. Suppose -15/4*y + 3/2 + 3/2*y**d = 0. Calculate y.
1/2, 2
Factor 344/5*s**3 + 12972/5*s**2 + 2/5*s**4 - 31304*s + 82810.
2*(s - 5)**2*(s + 91)**2/5
Factor 36686*x**2 + 155*x - 84*x**3 - 36694*x**2 + 181*x + 2*x**4.
2*x*(x - 42)*(x - 2)*(x + 2)
Let w(y) be the first derivative of -y**3/9 - 335*y**2/2 + 1006*y/3 - 10478. Factor w(z).
-(z - 1)*(z + 1006)/3
Let s be (12/(-150)*-2)/(58/870). Factor -s*h**3 + 0 - 3/5*h**4 - 12/5*h**2 + 0*h.
-3*h**2*(h + 2)**2/5
Let r(q) be the third derivative of 1/12*q**4 + 1/420*q**7 + 0*q + 3/40*q**5 + 17*q**2 - 1/40*q**6 - q**3 + 0. Factor r(z).
(z - 3)*(z - 2)**2*(z + 1)/2
Let b(h) be the first derivative of h**6/9 - 32*h**5/15 - 155*h**4/6 - 340*h**3/9 + 704*h**2/3 + 1472*h/3 - 899. Determine p so that b(p) = 0.
-4, -1, 2, 23
Factor -605*k**2 - 980*k - 593*k - 1445 - 297*k.
-5*(11*k + 17)**2
Solve 1/3*n**5 + 8*n**2 - 34/3*n**3 + 0 + 3*n**4 + 0*n = 0 for n.
-12, 0, 1, 2
Let x(m) = m**2 + 18*m + 7. Let v be x(-17). Let c be -8 - (-10 + v) - 9. What is t in -5/4*t**c + 0*t**2 + 0*t + 5/4*t**4 + 0 = 0?
0, 1
Let q(w) be the third derivative of w**5/30 - 79*w**4/12 + 1054*w**3/3 + 4417*w**2 + 2*w. Factor q(k).
2*(k - 62)*(k - 17)
Let h = 247/9700 - 3/194. Let p(y) be the third derivative of 16*y**2 + h*y**5 - 1/350*y**7 + 1/200*y**6 + 0*y**3 + 0*y - 1/40*y**4 + 0. Solve p(a) = 0.
-1, 0, 1
Let z = 37 - 37. Suppose 0 = -3*p - h + 35, z*p - h + 59 = 5*p. Find s, given that 8*s**3 - p*s**4 + 10 + 11 - 21 - 56*s**5 = 0.
-1/2, 0, 2/7
Solve -1/8*y**4 - 901/8*y**3 + 0 - 905/2*y + 452*y**2 = 0.
-905, 0, 2
Suppose -2*y + 16 = 10*q - 6*q, -3*q + 13 = 2*y. Factor -64 + 522*n**2 + 563*n**y - 14*n**3 - 256*n - 1201*n**2.
-2*(n + 4)**2*(7*n + 2)
Let p be -2*(-5)/(-30)*-72. Find b, given that 38*b - 77*b + 4*b**2 + 6*b**3 - p*b + 29*b**2 = 0.
-7, 0, 3/2
Let g(i) = -2*i**4 + i**3 - 5*i - 1. Let d(x) = 11*x**4 + 118*x**3 - 249*x**2 + 150*x + 5. Let n(y) = -d(y) - 5*g(y). Factor n(l).
-l*(l - 1)**2*(l + 125)
Suppose 79*n - 74*n + 10 = 5*j, -5*n = 4*j - 26. Suppose 4*w - 2*q + 147 = 921, 3*q - 759 = -4*w. Factor 2*l - w*l**2 + 192*l**2 + 0*l - n*l**3.
-2*l*(l - 1)*(l + 1)
Find c such that 1172184/5*c**2 + 128/5 - 21216/5*c - 21587722/5*c**3 = 0.
4/221
Let h(y) be the third derivative of -7*y - 6*y**2 + 17/36*y**4 + 0 - 289/180*y**5 - 1/18*y**3. Factor h(g).
-(17*g - 1)**2/3
Let h(p) be the first derivative of 5*p**6/6 + 7*p**5 + 35*p**4/3 - 40*p**3/3 + 90*p + 212. Let t(f) be the first derivative of h(f). Let t(u) = 0. What is u?
-4, -2, 0, 2/5
Suppose -14 - 615/2*i**2 + 155/4*i**4 - 239*i + 2087/4*i**3 = 0. What is i?
-14, -2/5, -2/31, 1
Let s be 12/10 + 42/70*48. Let q(y) be the first derivative of -s*y**2 - 40*y + 150*y**3 + 14 + 875/4*y**4. What is l in q(l) = 0?
-2/5, 2/7
Suppose 0 = 30*a - 38*a + 48. Let w be (a + 0)/(630/60). Let -30/7*t - 22/7*t**3 + w + 48/7*t**2 = 0. What is t?
2/11, 1
Let a(g) be the first derivative of 5*g**3/3 - 15*g**2 - 1235*g - 3653. Factor a(t).
5*(t - 19)*(t + 13)
Let t(j) be the third derivative of j**5/300 + 1457*j**4/120 + 728*j**3/15 - 3698*j**2. Suppose t(z) = 0. What is z?
-1456, -1
Let g(o) be the second derivative of o**5/110 + 388*o**4/33 + 150544*o**3/33 - 1638*o. Factor g