ative of q**5/24 + 5*q**4/9 - 20*q**3/9 - 160*q**2/3 - 2165*q. Factor g(y).
5*(y - 4)*(y + 4)*(y + 8)/6
Suppose -68693*d - 3*a - 2518 = -68698*d, 2118 = 4*d + 5*a. Factor d + 64/3*b + 2/9*b**2.
2*(b + 48)**2/9
Let b(d) be the first derivative of 4*d**5/5 + 68*d**4 - 1444*d**3/3 + 584*d**2 - 4512. Factor b(j).
4*j*(j - 4)*(j - 1)*(j + 73)
Factor -102*j - 16*j**2 - 11*j**2 + 9*j**2 - 424 + 19*j**2.
(j - 106)*(j + 4)
Let d(o) be the third derivative of -9*o**6/40 - o**5/30 + 9*o**4/2 + 4*o**3/3 + 999*o**2. Suppose d(z) = 0. What is z?
-2, -2/27, 2
Let m(p) = -p**3 - 632*p**2 - 16843*p + 17411. Let s(b) = 315*b**2 + 8421*b - 8697. Let c(g) = 3*m(g) + 5*s(g). Factor c(u).
-3*(u - 1)*(u + 54)**2
Let y(g) be the third derivative of g**5/300 + 52*g**4/3 + 108160*g**3/3 + 2631*g**2. Solve y(s) = 0.
-1040
Let m(a) be the first derivative of -30/11*a**4 - 2/55*a**5 + 0*a + 177 - 8000/11*a**2 - 800/11*a**3. Factor m(x).
-2*x*(x + 20)**3/11
Let h be -7*112 - (-77)/11. Let d = -772 - h. Solve -1/3*u**3 - 1/6 + 1/3*u**2 - 1/6*u**4 + 1/6*u + 1/6*u**d = 0.
-1, 1
Let s be 308/847*(-627)/(-912). Let j(r) = r. Let d be j(3). Factor -x**d + s*x**4 + 3/2*x**2 + 1/4 - x.
(x - 1)**4/4
Suppose -5*n - 10 = -4*b - 59, 3*n = -3*b - 3. Let h be -1 - (-3)/(-2)*b. Solve -h*m**3 + 69 + 70 + 4*m**2 - 145 + 8*m + 2*m**4 = 0 for m.
-1, 1, 3
Let l(r) = r**4 + 67*r**3 + 135*r**2 - 25*r - 143. Let s(k) = -k**4 - 64*k**3 - 134*k**2 + 28*k + 141. Let a(m) = 6*l(m) + 7*s(m). Find t such that a(t) = 0.
-43, -3, -1, 1
Let w(h) be the first derivative of -8*h**2 - 4/9*h**3 - 13 - 1/90*h**5 + 0*h + 1/9*h**4. Let c(i) be the second derivative of w(i). What is g in c(g) = 0?
2
Let u(n) be the first derivative of -n**5/35 + 5*n**4/4 - 200*n**3/21 - 1000*n**2/7 + 4463. Let u(q) = 0. What is q?
-5, 0, 20
Suppose 1512 = 28*i - 560. Suppose -36*t = t - i. Factor 0*w**3 + 5/2*w + 0 + 5*w**4 - 5/2*w**5 - 5*w**t.
-5*w*(w - 1)**3*(w + 1)/2
Let 189/4*g**2 + 0 + 0*g + 183/4*g**3 - 9/4*g**4 - 3/4*g**5 = 0. What is g?
-9, -1, 0, 7
Find a, given that -1755828*a - 12/5*a**3 + 20524/5*a**2 + 584820 = 0.
1/3, 855
Let m be (80/10 + -20)*2/(-8). Factor 60*o**m + 4*o**4 + 12*o**2 + 15*o**2 - 9*o**4 - 4*o**4 - 42*o.
-3*o*(o - 7)*(o + 1)*(3*o - 2)
Suppose 0 = -4984*h + 5124*h. Let n be (-4)/14 - 6/(-21). Factor n*u + 0 - 2/13*u**3 + h*u**2 - 2/13*u**4.
-2*u**3*(u + 1)/13
Let p(h) be the first derivative of -1/18*h**4 - 14*h - 14 - 4/3*h**3 - 12*h**2. Let l(d) be the first derivative of p(d). Factor l(a).
-2*(a + 6)**2/3
Let h = 143/2 - 70. Suppose 3*z + 3*i = 129, -158*i = -4*z - 156*i + 58. Factor -h*w**2 + z*w - 96.
-3*(w - 8)**2/2
Let z be 12/(-18)*21/(-1). Factor -3 + 3 - 1557*g**4 + 1559*g**4 + z*g**3.
2*g**3*(g + 7)
Suppose -3*s + 115 = 79. Solve 104*l**4 - 9*l + s*l**3 - l**2 - 3*l**5 - 197*l**4 - 5*l**2 + 99*l**4 = 0 for l.
-1, 0, 1, 3
Let o(x) = x**3 + 7*x**2 + 7*x + 1. Let r be o(-5). Find u, given that -252*u + 73*u**3 - 22*u**3 + 3*u**5 + 216 + 7*u**2 - 8*u**4 - r*u**4 + 35*u**2 = 0.
-2, 2, 3
Let w be (24/20)/((-6)/(-50) - 0). Suppose w*i - 62 = -32. What is s in 16/3*s**i + 0 - 8/5*s**2 + 0*s + 14/15*s**4 = 0?
-6, 0, 2/7
Find i such that 928/9*i**2 - 536/9 - 226/3*i + 94/3*i**3 + 4/9*i**4 = 0.
-67, -4, -1/2, 1
Suppose 3*b + 3*i = -3, -2*i = -4*b - 0*i + 26. Suppose -r + b = r. Determine j so that 2*j**2 + r - 10*j + 15 - 5 = 0.
2, 3
Suppose 3*n + 3*y - 3 = 0, -3*y + 0*y + 3 = 4*n. Suppose n = -2*d - 0*d + 10. Solve -g**4 - 4*g**2 - 2*g**3 + d*g**4 + 3*g**5 - g**5 = 0 for g.
-2, -1, 0, 1
Factor 214326 - 1134*q + 3/2*q**2.
3*(q - 378)**2/2
Let o(l) be the third derivative of -l**9/60480 + l**8/5040 - l**7/1260 + l**5/15 - 25*l**3/6 - 83*l**2. Let c(y) be the third derivative of o(y). Factor c(z).
-z*(z - 2)**2
Let z(g) be the first derivative of g**4/2 + 664*g**3/3 + 27556*g**2 + 1131. Suppose z(k) = 0. Calculate k.
-166, 0
Suppose 2*s + 3*o = 0, 20*o - 22*o = 4*s - 8. Find u, given that 12 - 2*u**4 + 14*u**5 + 25*u**5 + 26*u - 2*u**4 - 12*u**s + 21*u**5 - 58*u**5 + 8*u**2 = 0.
-1, 2, 3
Let y(m) be the second derivative of m**6/72 - 5*m**5/24 - 14*m**3/3 - 5*m. Let u(r) be the second derivative of y(r). Suppose u(i) = 0. What is i?
0, 5
Find z, given that 1/5*z**4 + 3*z**2 + 0 - 9/5*z**3 - 7/5*z = 0.
0, 1, 7
Let k be -3 + 329/(-81) + 7. Let f = 49/81 - k. Factor -4/3*b - 2/3*b**4 + 0 + 4/3*b**3 + f*b**2.
-2*b*(b - 2)*(b - 1)*(b + 1)/3
Suppose 0 - 2/5*a**3 + 298/5*a + 296/5*a**2 = 0. Calculate a.
-1, 0, 149
Let j(u) = -5*u**4 + u**3 - 6*u**2 + 8. Let y(q) = -18*q**4 - 17*q**4 + 2 + 34*q**4 - 2*q**3 + q**3. Let t(l) = -j(l) + 4*y(l). Let t(x) = 0. What is x?
0, 2, 3
Let r be 244/182 - (-2730)/(-3549). Factor 120/7*f**2 + 6*f**3 + r*f**4 + 0 + 50/7*f.
2*f*(f + 5)**2*(2*f + 1)/7
Let u = 371/565 + -258/565. Factor u*x**2 - 9/5*x + 14/5.
(x - 7)*(x - 2)/5
Let l(h) be the first derivative of h**8/672 - 2*h**7/105 + 13*h**6/240 - h**5/20 + h**2/2 + 10*h + 103. Let u(w) be the second derivative of l(w). Factor u(r).
r**2*(r - 6)*(r - 1)**2/2
Let n(z) be the second derivative of -2/3*z**3 + 2/15*z**6 - 8*z + z**4 - 3/5*z**5 + 0 + 0*z**2. Factor n(q).
4*q*(q - 1)**3
Find i such that -236*i**3 - 6190*i**2 + 12373*i**2 - 6191*i**2 = 0.
-2/59, 0
Suppose -q = -2*k + 15, 0 = -4*k - 1417*q + 1414*q - 25. Let g = 3/2 + -29/22. Factor -14/11*u + g*u**3 - 8/11 - 4/11*u**k.
2*(u - 4)*(u + 1)**2/11
Let k(u) be the third derivative of -u**5/240 + u**4/6 + 99*u**3/8 + 1933*u**2. Factor k(l).
-(l - 27)*(l + 11)/4
Let z(m) be the third derivative of 1/240*m**6 - 1/12*m**4 + 1/3*m**3 - 1/120*m**5 + 2*m + 0 + 29*m**2. What is t in z(t) = 0?
-2, 1, 2
Suppose 3*z = -4*p + 3612, -42*p + 15 = -37*p. Let u = 4801/4 - z. Find t such that 0 - 3/4*t**3 + u*t**4 - 5/4*t - 9/4*t**2 = 0.
-1, 0, 5
Suppose -85 = -11*x - 19. Suppose w - 6 = x. Find u such that 7 - 7 + w*u**3 + 15*u**2 + 3*u**4 + 6*u = 0.
-2, -1, 0
Let o = 1913 - 1910. Let w(i) be the third derivative of 0*i + 9/2*i**o + 4*i**2 + 3/4*i**4 + 0 + 1/20*i**5. Factor w(t).
3*(t + 3)**2
Let y(w) be the first derivative of 0*w - 1/6*w**4 - 19 - 4/15*w**5 - 4*w**2 + 1/10*w**6 + 4/3*w**3. Let o(a) be the second derivative of y(a). Factor o(j).
4*(j - 1)**2*(3*j + 2)
Determine n so that -31 + 2256*n**3 + 230*n**3 + 62*n**3 - 5400*n**2 + 1440*n - 97 + 4202*n**3 = 0.
4/15
Let n(w) be the second derivative of w**5/35 + 2*w**4/21 - 8*w**3 - 720*w**2/7 - 1625*w. Factor n(o).
4*(o - 10)*(o + 6)**2/7
Let t(k) be the first derivative of 5*k**4/8 + 3245*k**3/6 + 6475*k**2/4 + 3235*k/2 + 1607. Find s, given that t(s) = 0.
-647, -1
Let m(s) be the first derivative of -75*s**4/8 - 87*s**3/2 - 129*s**2/2 - 36*s - 1659. Determine p, given that m(p) = 0.
-2, -1, -12/25
Suppose 220 = 122*m - 29 - 117. Suppose 2/13*v**m - 8/13*v - 2/13*v**2 + 8/13 = 0. What is v?
-2, 1, 2
Factor -228 + 14/5*s**2 - 3986/5*s.
2*(s - 285)*(7*s + 2)/5
Let l(d) be the second derivative of 3*d**5/5 + 61*d**4/9 - 820*d**3/9 + 176*d**2/3 - 2878*d. Determine i, given that l(i) = 0.
-11, 2/9, 4
Suppose -2*r + 7 = -3. Factor 24*m**2 - 15*m**5 + 16*m + 3*m - 32*m**3 - 24*m**4 + 9*m + 19*m**r.
4*m*(m - 7)*(m - 1)*(m + 1)**2
What is o in 1764*o + 685*o**2 + 59*o**3 - 61*o**2 + 2*o**3 + o**4 = 0?
-49, -6, 0
Let r(o) be the second derivative of -5/24*o**4 + 0 + 13/6*o**3 + 31*o + 1/12*o**5 + 0*o**2 - 1/72*o**6. Let v(s) be the second derivative of r(s). Factor v(y).
-5*(y - 1)**2
Let j(v) be the first derivative of 5*v**4/4 - 10*v**3 - 75*v**2/2 - 40*v + 732. Solve j(n) = 0.
-1, 8
Let v(o) be the third derivative of o**8/588 - o**7/147 - 2*o**6/105 + 17*o**5/210 - o**4/14 - 2296*o**2. Let v(x) = 0. Calculate x.
-2, 0, 1/2, 1, 3
Solve 33/4*p**3 + 0 - 63*p**2 + p**4 - 65/4*p = 0.
-13, -1/4, 0, 5
Suppose -7*d = 4 - 32. Factor 20734*l - d - 20680*l - 2*l**2 + 4.
-2*l*(l - 27)
Suppose -1364*t + 398*t = -3395 + 497. Factor 3/2*p**2 + 3 + 3/2*p**t - 11/2*p - 1/2*p**4.
-(p - 3)*(p - 1)**2*(p + 2)/2
Factor -392*l - 2/3*l**4 + 0 + 238/3*l**2 + 4/3*l**3.
-2*l*(l - 7)**2*(l + 12)/3
Let j(t) = -37*t + 67. Let k be j(2). Let z(g) = -29*g**2 - 31*g + 24. Let o(l) = -33*l**2 - 32*l + 23. Let i(v) = k*z(v) + 6*o(v). Factor i(x).
5*(x - 1)*(x + 6)
Let p(i) be the third derivative of -i**7/1155 - i**6/330 + 4*i**5/55 + 2848*i**2. Factor p(v).
-2*v*