r a(t).
(t - 32)*(t + 38)**2
Let n = 1429 + -1424. Suppose 0 = p - 4*j + 12, 3*j - 4 = 3*p + n. Factor 3/2*i**4 - 3/2*i**2 + 3*i + p - 3*i**3.
3*i*(i - 2)*(i - 1)*(i + 1)/2
Factor 3068/7*f + 2/7*f**2 - 6144/7.
2*(f - 2)*(f + 1536)/7
Factor -4*h**5 + 226549*h**3 + 3*h**5 - 226651*h**3 + 0*h**5 - 103*h**4.
-h**3*(h + 1)*(h + 102)
Let f be 6/(-12) + 63/18. Factor 15*s**2 + f*s**2 - 4 - 4*s**2 - 6*s**2 - 14*s.
2*(s - 2)*(4*s + 1)
Suppose -40*y = -2183 + 2063. Let n(q) be the third derivative of 1/3*q**y + 5/6*q**5 + 5/6*q**4 + 0 + 16*q**2 + 0*q. Solve n(m) = 0 for m.
-1/5
Let z(x) be the first derivative of -x**6/360 + x**5/24 + 7*x**4/12 + x**3 - 5*x + 156. Let o(y) be the third derivative of z(y). Suppose o(b) = 0. What is b?
-2, 7
What is l in 2/11*l**2 + 0 + 282/11*l = 0?
-141, 0
Let m(h) = 195*h**4 - 2675*h**3 + 3643*h**2 + 40269*h. Let l(c) = 97*c**4 - 1337*c**3 + 1825*c**2 + 20127*c. Let g(x) = 5*l(x) - 3*m(x). Factor g(j).
-4*j*(j + 3)*(5*j - 41)**2
Let r(j) be the second derivative of -25*j**4 + 200*j**3/3 - 24*j**2 + 19*j + 171. Factor r(w).
-4*(5*w - 6)*(15*w - 2)
Suppose -11*k + 327 = -25. What is g in 12*g**5 - 48*g - 31*g**2 + 64*g**4 + 108*g**3 - 22*g**2 - k + 93*g**2 = 0?
-2, -1, 2/3
Let l(o) be the first derivative of -1/8*o**3 - 3/16*o**2 - 17 + 9/4*o. Solve l(b) = 0.
-3, 2
Suppose -3*o - 48 + 54 = 0. Factor -7702*w**o + 153*w - 70 + 7705*w**2 + 220.
3*(w + 1)*(w + 50)
Let x(l) = -l**2 - 21*l - 100. Let h be x(-8). Suppose 12 - a**2 + 2*a**h + 10*a**2 + 12*a - 5*a**4 - 6*a**3 - 24 = 0. Calculate a.
-2, 1
Let d(p) = 10*p**2 + 4*p - 6. Let m(c) = -3*c**2 - c + 2. Suppose -2*h = -16*h - 224. Let f(g) = h*m(g) - 5*d(g). Factor f(s).
-2*(s + 1)**2
Suppose -1 - 55 = -28*y. Let g be (-205)/82 + ((-30)/(-4) - y). Suppose -20/3*a - 5/6*a**g - 40/3 + 35/6*a**2 = 0. What is a?
-1, 4
Factor 8*q**3 + 713 + 317*q**2 - 798*q**2 + 998 + 7320*q + 89 + 963*q**2.
2*(q + 30)**2*(4*q + 1)
Let s(x) = x**3 + 2*x**2 + 7*x + 34. Suppose 6*j - 7*j = 3. Let a be s(j). Factor 0 + 10/7*h**2 - 2/7*h**a + 2/7*h**5 - 4/7*h - 6/7*h**3.
2*h*(h - 1)**3*(h + 2)/7
Suppose -56*z**3 + 89036/15*z**2 + 2/15*z**4 + 87362/15 - 11704*z = 0. What is z?
1, 209
Let n(w) = 0*w + 7*w - 5 + 6*w**2 - 1 + 1. Let u(m) be the first derivative of m**3/3 + m**2/2 - m - 70. Let y(g) = n(g) - 5*u(g). Solve y(i) = 0.
-2, 0
Suppose -85*l = -115*l. Let f(z) be the third derivative of -1/15*z**5 + 0 - z**2 + l*z - 2/3*z**4 - 8/3*z**3. Factor f(k).
-4*(k + 2)**2
Let f = -55 - -57. Let 1205 + 0*g**2 - 230*g + 5*g**f + 428 + 1012 = 0. Calculate g.
23
Suppose 5*k - 41 = -46, 3*v = -3*k + 15. Let a(b) be the first derivative of 1/7*b**4 - 2/7*b - 2/35*b**5 + 9 - 1/21*b**v - 1/7*b**2 + 4/21*b**3. Factor a(p).
-2*(p - 1)**2*(p + 1)**3/7
Let i = 1286 + -506. Factor -i*x**4 + 784*x**4 + 15*x**3 + 13*x**3.
4*x**3*(x + 7)
Let v(r) = -r**3 - 49*r**2 - 51*r + 2025. Let i be v(-47). Let m(c) be the second derivative of c + 5/4*c**3 + 3/2*c**2 + 3/40*c**5 + 1/2*c**i + 4. Factor m(p).
3*(p + 1)**2*(p + 2)/2
Let x(w) be the first derivative of 3*w**5/5 + 30*w**4 + 514*w**3 + 2880*w**2 - 7425*w - 12238. Solve x(n) = 0 for n.
-15, -11, 1
Let i = -1192824234/19 + 62762670. Let c = i + 17558. Factor c - 28/19*x + 2/19*x**2.
2*(x - 7)**2/19
Factor 13/9*c**4 - 1/9*c**5 + 0*c + 0*c**2 + 10/3*c**3 + 0.
-c**3*(c - 15)*(c + 2)/9
Let w(z) be the second derivative of -z**5/160 + z**4/64 - z**2 + 4*z + 4. Let l(u) be the first derivative of w(u). Factor l(q).
-3*q*(q - 1)/8
Suppose 5*t - 834 - 616 = 0. Let x be (-29)/t*(-50)/4. Suppose -5/2*z + 0 - 5/4*z**2 + x*z**3 = 0. What is z?
-1, 0, 2
Let w(z) be the first derivative of -2/9*z**2 + 1/9*z**4 + 2/45*z**5 + 45 - 2/27*z**3 + 0*z. Let w(f) = 0. What is f?
-2, -1, 0, 1
Suppose -10*n + 4*v - 26 = -11*n, v = 4. Factor -52*c - 5*c**2 + 31*c + 36*c - n.
-5*(c - 2)*(c - 1)
Let j = 967419 + -2902256/3. Factor j*i**2 - 4/3*i**3 + 0 + 0*i.
-i**2*(4*i - 1)/3
Let w(l) = -7*l + 71. Let c be w(11). Let y be ((-52)/741)/(1*2/c). Determine h, given that -y*h**2 - 2/19*h + 0 = 0.
-1/2, 0
Let d(l) be the second derivative of l**5/60 + 4*l**4 + 384*l**3 + 18432*l**2 - 3908*l. Let d(i) = 0. Calculate i.
-48
Let o(d) be the first derivative of d**4/20 - 7*d**3/15 - 21*d**2/5 + 216*d/5 - 13778. Factor o(g).
(g - 9)*(g - 4)*(g + 6)/5
Let z(k) be the first derivative of -36/5*k**2 - 24 + 44/5*k**3 - 9/25*k**5 - 1/2*k**6 + 63/10*k**4 + 0*k. Let z(m) = 0. Calculate m.
-2, 0, 2/5, 3
Factor 2/11*p**2 + 456/11 - 8*p.
2*(p - 38)*(p - 6)/11
Let u(k) = 15*k + 7*k**3 - 14 + 82*k**2 + 90*k**2 - 180*k**2. Let h(r) = 6*r**3 - 8*r**2 + 14*r - 12. Let o(d) = 5*h(d) - 4*u(d). What is n in o(n) = 0?
1, 2
Factor 876/7 + 2/7*w**2 + 298/7*w.
2*(w + 3)*(w + 146)/7
Let w(f) be the third derivative of -7*f**5/15 + 71*f**4/4 - 15*f**3 - 104*f**2 + 9*f - 2. Let w(o) = 0. Calculate o.
3/14, 15
Let t(v) = -37*v**2 + 119*v - 147. Let o(s) = -17*s**2 + 61*s - 74. Let u(m) = 13*o(m) - 6*t(m). Solve u(z) = 0.
-80, 1
Let d(k) = 3*k**2 + k - 1. Let i be d(2). Let g = 19312 - 19308. Solve 5*a + g*a - i*a + a**2 + 9*a = 0.
-5, 0
Let p be (-171 - -108)*1/(-2) - (-21)/98. Let -6/7*v**2 - 216/7 - p*v = 0. What is v?
-36, -1
Let p(d) = 6*d**2 + 76*d + 1062. Let r(g) = -17*g**2 - 232*g - 3185. Let i(h) = -11*p(h) - 4*r(h). Suppose i(n) = 0. What is n?
-23
Let u(s) = s**2 - 412*s + 421. Let x(l) = -405*l + 420. Let r(f) = -3*u(f) + 2*x(f). Factor r(m).
-3*(m - 141)*(m - 1)
Let j(u) = -17*u**3 + 1751*u**2 - 3941*u + 984. Let l(m) = 16*m**3 - 1752*m**2 + 3942*m - 984. Let s(o) = 2*j(o) + 3*l(o). Suppose s(n) = 0. What is n?
2/7, 2, 123
Suppose -4646 = -29*f + 6*f. Let -84 + f*i + 220*i - 669*i + 211*i + 3*i**2 = 0. What is i?
-2, 14
Let q = -346 - -304. Let y be (-147)/q*8/35. Factor -y*n**2 + n + 1/5*n**3 - 2/5.
(n - 2)*(n - 1)**2/5
Let u(s) be the third derivative of s**6/360 + 3*s**5/80 + s**4/12 + 31*s**3/6 + 30*s**2. Let k(j) be the first derivative of u(j). Factor k(a).
(a + 4)*(2*a + 1)/2
Let f(y) be the first derivative of -1/22*y**4 + 52/33*y**3 + 205 + 0*y - 24/11*y**2 - 2/55*y**5. What is p in f(p) = 0?
-6, 0, 1, 4
Solve 112 - 2/3*a**2 - 44/3*a = 0 for a.
-28, 6
Let p(y) be the first derivative of -y**7/70 - 7*y**6/120 - y**5/12 - y**4/24 - 21*y**2 + 42. Let v(l) be the second derivative of p(l). Factor v(h).
-h*(h + 1)**2*(3*h + 1)
Let a(r) be the third derivative of -2*r**7/105 + r**6 - 51*r**5/5 + 110*r**4/3 - 64*r**3 - 4484*r**2 - 1. Let a(x) = 0. Calculate x.
1, 4, 24
Determine j so that -3999/8*j**3 - 36015/4*j + 261/8*j**4 - 3/8*j**5 - 76293/8*j**2 + 0 = 0.
-10, -1, 0, 49
Solve 1 + 7 + 8 - 15*u**2 + 65*u**3 - 70*u**3 - 1 + 5*u = 0.
-3, -1, 1
Let k = 397 - 379. Factor -18 + 33*q**3 - 14*q**3 + k*q**2 - 8*q**3 + 2*q - 13*q**3.
-2*(q - 9)*(q - 1)*(q + 1)
Suppose q + 5 = -1. Let y be -4 - (-6)/2 - 15/q. Suppose l**2 + 1/2*l**3 - y*l + 0 = 0. What is l?
-3, 0, 1
Let t(f) = f**3 - 5*f**2 - 4*f - 6. Let h be t(6). Suppose -65*n = -63*n - h. Factor -4/5*c**n + 8/5*c - 8/5 - 2/5*c**4 + 6/5*c**2.
-2*(c - 1)**2*(c + 2)**2/5
Factor 316 - 76*f**2 - 32*f + 30*f**2 - 92 + 48*f**2 - 84*f.
2*(f - 56)*(f - 2)
Let s(c) be the first derivative of -4*c**3/9 + 118*c**2/3 - 752*c + 1397. Factor s(b).
-4*(b - 47)*(b - 12)/3
Let k be (4/((-80)/65))/((-49)/(-2800)*-5). Factor 0 + k*a**4 + 0*a - 25*a**5 + 18/7*a**2 - 123/7*a**3.
-a**2*(5*a - 3)**2*(7*a - 2)/7
Let h(k) = 67*k + 873. Let j be h(-13). Let a(n) be the second derivative of 4/3*n**3 + 1/24*n**4 + 0 + 6*n + 16*n**j. Factor a(d).
(d + 8)**2/2
Suppose 21*i = -316 + 6784. Let d be (-4)/22 + -1 + 716/i. Factor 2/7*h - d*h**2 + 0 + 12/7*h**3 - 8/7*h**4 + 2/7*h**5.
2*h*(h - 1)**4/7
What is x in 39/4*x**3 + 1/2*x**5 + 35/4*x**2 + 17/4*x**4 + 11/4*x + 0 = 0?
-11/2, -1, 0
Factor 1/8*f**2 - 73/8 + 9*f.
(f - 1)*(f + 73)/8
Let v(a) be the third derivative of -2*a**7/105 + a**6/2 - 24*a**5/5 + 18*a**4 - 4619*a**2. Suppose v(h) = 0. Calculate h.
0, 3, 6
Let d(r) be the second derivative of -r**5/4 - 515*r**4/12 + 5*r**3/6 + 515*r**2/2 + 3*r - 155. Solve d(m) = 0.
-103, -1, 1
Let q = 192559/130032 - -3/4816. Let g(b) be the third derivative of 1/9*b**6 + 0*b + 64/27*b**3 + 16*b**2 + 1/105*b**7 - q*b**4 + 0 + 26/135*b**5. Factor g(c).
2*(c + 4)**2*(3*c - 2)**2/9
Let x(g) be the first derivati