- 1. Suppose -4*u = 0, 5*d - 13 = 2*u + 2. Suppose 0 = -3*q + 9 - d. Let i(m) = 2*m**2 - m - 1. Let p(n) = q*i(n) - 3*y(n). Factor p(s).
(s - 1)**2
Let s(b) be the first derivative of 4/3*b**2 - 1/3*b**4 + 0*b - 19 + 4/9*b**3. Find t such that s(t) = 0.
-1, 0, 2
Suppose 0 - 1/5*y**5 + 2*y**3 + 8/5*y**2 + 1/5*y**4 + 0*y = 0. Calculate y.
-2, -1, 0, 4
Factor 12*v**3 + 25*v**2 + 11*v**3 + 5*v**2 - 18*v**3 + 11*v + 14*v.
5*v*(v + 1)*(v + 5)
Suppose -5/3*i**2 - 80/3 - 50/3*i = 0. What is i?
-8, -2
Let h(n) be the third derivative of 12*n**2 + 0 + 1/30*n**5 + 0*n**4 + 0*n**3 - 1/105*n**7 - 1/168*n**8 + 0*n + 1/60*n**6. Let h(x) = 0. What is x?
-1, 0, 1
Let i(f) = -f**3 + 7*f**2 - 12*f + 15. Let q be i(5). Let z(d) = -2*d**3 - 2*d - 1. Let b be z(-1). Solve 4*w**2 + 2*w**4 - 2*w**3 - q*w**2 - b*w**2 = 0 for w.
-1, 0, 2
Let o(s) = 217*s + 48. Let y be o(4). Factor -4*a**2 - y + 311 - a**2 + 110*a.
-5*(a - 11)**2
Let d(o) be the third derivative of o**8/168 + 4*o**7/105 + o**6/10 + 2*o**5/15 + o**4/12 + 126*o**2. Factor d(p).
2*p*(p + 1)**4
Let n(r) be the first derivative of r**6/1440 - r**5/120 - 5*r**4/96 + 2*r**3/3 + 14. Let b(t) be the third derivative of n(t). Determine f so that b(f) = 0.
-1, 5
Factor -98/13*i**2 - 4608/13 + 1344/13*i.
-2*(7*i - 48)**2/13
Factor 14/5*w**4 + 0*w**2 - 16/5*w**3 + 0 + 0*w + 2/5*w**5.
2*w**3*(w - 1)*(w + 8)/5
Let y = -13 - -140. Let w = -127 + y. Factor 6/5*i**3 - 4/5*i + w - 2/5*i**2.
2*i*(i - 1)*(3*i + 2)/5
Factor -37*x + 21*x + 97*x - 5*x**3 - 44*x**2 + x**3 - 112 + 79*x.
-4*(x - 2)*(x - 1)*(x + 14)
Factor -324*b - 4*b**3 + 3*b**3 + 2 - 2*b**2 + 325*b.
-(b - 1)*(b + 1)*(b + 2)
Find l, given that -l**2 - 22/5*l - 16/5 + 1/5*l**3 = 0.
-2, -1, 8
Suppose -23*q = -26*q + 6. Factor -4 - 783*o + 25*o**q + 781*o + 4.
o*(25*o - 2)
Let b(a) be the first derivative of -a**4 + 16*a**3/3 - 3. Factor b(j).
-4*j**2*(j - 4)
Let l = 20 + -4. Let -s**2 + s - 13 + l - 3*s = 0. What is s?
-3, 1
Let z = -1143 + 1145. Suppose 9/4*i - 3/2 - 3/4*i**z = 0. Calculate i.
1, 2
Let j(f) be the first derivative of -f**5/20 - 3*f**4/16 - f**3/12 + 3*f**2/8 + f/2 + 75. Factor j(h).
-(h - 1)*(h + 1)**2*(h + 2)/4
Let f(y) be the first derivative of 10 - 10/3*y**3 - y**5 + 0*y**2 - 15/4*y**4 + 0*y. Find j such that f(j) = 0.
-2, -1, 0
Let m(b) = 25*b**3 + 2770*b**2 - 40*b + 40. Let r(u) = -2*u**3 - 213*u**2 + 3*u - 3. Let z(o) = -3*m(o) - 40*r(o). Let z(v) = 0. Calculate v.
-42, 0
Solve 4*k**2 - 12*k**4 + 16*k**3 + 2*k**5 + 46*k - 39*k - 25*k + 8 = 0.
-1, 1, 4
Let q = 50 + -46. Suppose 5*c + 2*m - 11 = 0, 3*c + 3*m - 11 = q*m. Let 1/3*s + 0 - 1/3*s**c + 0*s**2 = 0. Calculate s.
-1, 0, 1
Factor -76/5*a**2 + 2/5*a**3 - 1296/5 + 792/5*a.
2*(a - 18)**2*(a - 2)/5
Let h(a) = 3*a**2 - a + 2. Let k be h(1). Factor 18*f + 2 - k*f - 35*f**2 + 8 + 11*f.
-5*(f - 1)*(7*f + 2)
Let y(r) be the first derivative of r**5/5 + r**2/2 + r - 12. Let k(j) = 5*j**5 + 5*j**4 - 5*j**3 + 5*j + 5. Let s(d) = k(d) - 5*y(d). What is f in s(f) = 0?
-1, 0, 1
Let v(x) be the second derivative of -1/24*x**4 + 0 + 7/6*x**3 - 13*x - 49/4*x**2. Find m, given that v(m) = 0.
7
Let v = -54635621/42 + 1300695. Let d = -905/6 - v. Factor -32/7*g**2 - 2/7 - d*g.
-2*(4*g + 1)**2/7
Let j(o) = -2*o**2 - 44*o + 62. Suppose 32 = 106*a - 110*a. Let n(c) = -c**2 - 15*c + 21. Let m(q) = a*n(q) + 3*j(q). Determine b, given that m(b) = 0.
3
Let y(z) be the second derivative of 5/24*z**4 - 5/4*z**3 + 13*z + 5/2*z**2 + 0. Suppose y(s) = 0. What is s?
1, 2
Factor -21 + 32*p**2 - 4*p**4 + 40 + 8*p**3 - 72*p + 17.
-4*(p - 3)*(p - 1)**2*(p + 3)
Let d = 33 + -54. Let w be (-332)/(-14) - 6/d. Factor 0 - 12*k**3 + 104*k**2 - w + 52*k + 40*k**3.
4*(k + 1)*(k + 3)*(7*k - 2)
Suppose 0 = -21*k + 6*k + 263 - 188. Factor -1/7*g**3 - 3/7*g**4 + 11/7*g**2 + 1/7*g**k + 4/7 - 12/7*g.
(g - 2)*(g - 1)**3*(g + 2)/7
Let c(j) = -7*j**2 + 3*j - 7. Let q be c(-4). Let o = -914/7 - q. Solve -6/7*h + 0 - o*h**3 + 9/7*h**2 = 0 for h.
0, 1, 2
Let t(v) = -v**3 - v**2 - 1. Let k(s) = -39*s**2 + 1 + 16 - 7*s**3 + 1 + 22*s**2. Let w(l) = -k(l) + 2*t(l). Factor w(a).
5*(a - 1)*(a + 2)**2
Let b(f) be the second derivative of 0 + 1/27*f**4 + 0*f**2 - 1/27*f**3 - 1/90*f**5 - 4*f. Find v such that b(v) = 0.
0, 1
Let d(r) be the third derivative of 1/24*r**4 - 1/96*r**8 - 1/120*r**5 - 19/420*r**7 + 0*r + 0*r**3 + 0 - 1/16*r**6 - 12*r**2. Suppose d(k) = 0. Calculate k.
-1, 0, 2/7
Let w be (-10)/(-6) - 87/18 - -4. Factor 2/3*s - 1/6*s**2 + w.
-(s - 5)*(s + 1)/6
Let u(i) be the first derivative of i**5/15 - i**4/2 - i**3/9 + i**2 - 22. Find r, given that u(r) = 0.
-1, 0, 1, 6
Let z(h) be the third derivative of h**8/112 + h**7/7 + 3*h**6/10 - 18*h**5/5 + 6*h**2 - 20*h. Solve z(q) = 0.
-6, 0, 2
Let l be 153 + -1*(1 - 1)/(-1). Let g be l/270 + 1/(-6). What is b in 1/5 - g*b - 3/5*b**2 = 0?
-1, 1/3
Let m(j) be the third derivative of j**8/33600 - j**6/1200 + j**5/300 - 11*j**4/24 - 8*j**2. Let p(b) be the second derivative of m(b). Factor p(h).
(h - 1)**2*(h + 2)/5
Suppose -6*g = -5*g - 2. Suppose 1 = g*f - 9. Factor -6*z**f - 2*z**3 - 9*z**4 + 3*z**5 - 4*z**3.
-3*z**3*(z + 1)*(z + 2)
Suppose -28*i = -86 + 30. Find l such that 6/11 - 6/11*l**i + 0*l = 0.
-1, 1
Let x be 2/(-8) + (-1650)/(-8). Determine l so that 4 + 10*l**3 + x*l - 192*l + 3*l**4 + 18*l**2 - l**4 = 0.
-2, -1
Let b be (-12)/(-5) - (-2)/(-5). Suppose -7*k + 19 = -2*k + 3*v, 0 = 3*k - 4*v + 6. Find h such that -k*h + 2/3*h**b + 0 = 0.
0, 3
Let v(a) = a - 1. Let t(y) = 14 - 12*y - y**2 + 22*y - 18*y. Let q(j) = -t(j) - 6*v(j). Factor q(k).
(k - 2)*(k + 4)
Let q = 3931 + -3929. Factor 2/3*z**3 - 4/3*z**q + 0 + 2/3*z.
2*z*(z - 1)**2/3
Suppose -4*u + 2 = -18. Suppose -u*j = -0*j - 15. Factor 3*x**5 - 5*x**3 + 2*x**3 + j*x - 3*x**3.
3*x*(x - 1)**2*(x + 1)**2
Suppose 8*a + 20 = 3*a. Let s(f) = f**2 + 4*f + 4. Let b be s(a). Suppose 0*n**4 - 4*n**b + 5*n**4 - 3*n**2 + 2*n**4 = 0. Calculate n.
-1, 0, 1
Let v = 3/371 - -5927/1113. Factor 0 + v*z + 0*z**2 - 4/3*z**3.
-4*z*(z - 2)*(z + 2)/3
Let v(k) be the first derivative of k**4/6 - 46*k**3/9 + 72. Solve v(a) = 0.
0, 23
Let t(k) be the first derivative of -k**3/7 - 6*k**2/7 + 15*k/7 - 53. Determine z so that t(z) = 0.
-5, 1
Let f(a) = -4*a**5 - 4*a**4 + 6*a**3 + a**2 - 8*a - 3. Let x(s) = 11*s**5 + 11*s**4 - 18*s**3 - 2*s**2 + 23*s + 7. Let n(r) = 8*f(r) + 3*x(r). Factor n(i).
(i - 1)**3*(i + 1)*(i + 3)
Let h(g) be the third derivative of g**9/151200 - g**8/50400 - g**5/12 + 3*g**2. Let s(b) be the third derivative of h(b). Solve s(z) = 0.
0, 1
Let s(f) = -34*f + 296. Let u be s(8). Factor -3/2*h**2 - u + 12*h.
-3*(h - 4)**2/2
Factor 4/5*s - 1/5*s**3 + 4/5*s**2 + 0 - 1/5*s**4.
-s*(s - 2)*(s + 1)*(s + 2)/5
Let l be (-1)/(-3) - (-22)/6. Suppose -4*f + 8 = l*n, n - 6*n = 2*f - 1. What is a in -a**4 + 0*a**4 + 6*a**f + 4*a**4 + 5*a**2 - 2*a**2 = 0?
-1, 0
Let r = 101 + -63. Factor -r + 5*q**2 + 19 + 9 + 5*q.
5*(q - 1)*(q + 2)
Suppose -7*q + 4*q + 3*x = 18, 2*x - 12 = 0. Find k such that 4/7*k**3 + 4/7*k**4 - 4/7*k**2 - 4/7*k**5 + q*k + 0 = 0.
-1, 0, 1
Factor 10*b + 3*b**2 - 6 + 2*b**2 - 16 - 18.
5*(b - 2)*(b + 4)
Let t = -294 + 297. Let b(q) be the third derivative of -1/60*q**6 + 3*q**2 + 0 + 5/36*q**4 + 2/9*q**t + 0*q - 2/45*q**5. Find h such that b(h) = 0.
-2, -1/3, 1
Suppose 8*i = 6*i + 8. Suppose 3*x = i*n - 4, n = x - 0 + 1. Factor -6/17*u**3 + 6/17*u**2 + x + 2/17*u**4 - 2/17*u.
2*u*(u - 1)**3/17
Factor -396*g**2 - 11*g**4 + 7*g**4 + 76*g**3 - 281*g + 605*g.
-4*g*(g - 9)**2*(g - 1)
Suppose 0 = -g + 5*s + 111, 2*g + 4*s = 5*g - 355. Let n be 22/g - 60/(-33). Factor 2/5 - 2/5*d**n - 2/5*d + 2/5*d**3.
2*(d - 1)**2*(d + 1)/5
Determine g so that -2/3*g**5 + 0 - 26/3*g**3 - 8/3*g - 4*g**4 - 8*g**2 = 0.
-2, -1, 0
Let q be (3 - -1) + (0 - -1). Suppose 38*y - 35*y - 24 = 0. Solve -9*u - 4*u**2 + q*u**4 - u**4 + u + y*u**3 = 0 for u.
-2, -1, 0, 1
Find y, given that 138/5*y - 3/5*y**2 + 0 = 0.
0, 46
Let n(p) be the third derivative of p**6/660 + p**5/330 - p**4/66 + 71*p**2. Factor n(y).
2*y*(y - 1)*(y + 2)/11
Let w(i) be the third derivative of -i**8/168 - 17*i**7/105 + i**6/15 + 34*i**5/15 - 188*i**2. Let w(c) = 0. Calculate c.
-17, -2, 0, 2
Solve -249*c**4 + 6*c**5 - 25*c**5 - 18714*c**3 + 376*c**4 + 353*c**4 - 38880*c**2 - 19683*c + 16*c**5