1
Let w(i) be the third derivative of -i**8/336 - i**7/42 + 3*i**6/20 + 29*i**5/30 - 145*i**4/24 + 25*i**3/2 + 368*i**2 + 1. Factor w(j).
-(j - 3)*(j - 1)**2*(j + 5)**2
Factor 75*f - 3/4*f**2 - 1875.
-3*(f - 50)**2/4
Let k(h) be the third derivative of -7*h**5/570 + 2753*h**4/228 - 262*h**3/19 - 67*h**2 + h - 4. What is w in k(w) = 0?
2/7, 393
Factor -291*a + 607*a + 2*a**2 + 372*a.
2*a*(a + 344)
Let x = 1190 + -281. Solve x - 3*m + 15*m**2 - 905 - 10*m + m**4 - 7*m**3 = 0.
1, 4
Let k(w) be the second derivative of -w**4/4 + 1430*w**3 - 8577*w**2/2 - 4030*w. Suppose k(c) = 0. What is c?
1, 2859
Let o(c) be the second derivative of 1406/27*c**3 + 361/9*c**2 + 0 + 2/45*c**5 - 8*c - 151/54*c**4. Factor o(q).
2*(q - 19)**2*(4*q + 1)/9
Let l(m) be the first derivative of -1/3*m**3 + 0*m - 7/2*m**2 - 19 + 7/4*m**4 + 1/5*m**5. Factor l(a).
a*(a - 1)*(a + 1)*(a + 7)
Let l be 2 + 66/(-27) - 17608/(-36). Let m = l + -2929/6. Factor -m*b**2 - 7/2*b - 5.
-(b + 2)*(b + 5)/2
Let s(y) = -19502*y - 19500. Let b be s(-1). Factor 3/4*r - 1/2 - 1/4*r**b.
-(r - 2)*(r - 1)/4
Determine h, given that 3972*h**3 - 3975*h**3 + 20*h**2 - 612*h - 185*h**2 = 0.
-51, -4, 0
Let w(b) = 2*b - 18. Let i be w(9). Factor 4*h**4 - 2888*h + i*h**4 + 24*h**3 - 96*h**2 + 2992*h - 36.
4*(h - 1)**3*(h + 9)
Solve 2/3*m**3 + 32*m - 128/3 - 8*m**2 = 0 for m.
4
Suppose 2*a + 1592 = -2*g, 332 = 3*g - 3*a + 2732. Let f = g + 798. Solve 3/2*y + f - 3/4*y**3 + 3/4*y**2 = 0 for y.
-1, 0, 2
Let g(h) = 7*h**2 - 44*h + 75. Let u(f) = 8*f**2 - 44*f + 76. Let s = 105 + -101. Let t(k) = s*g(k) - 3*u(k). Factor t(z).
4*(z - 9)*(z - 2)
Let v(n) be the second derivative of 531*n**5/20 + 89*n**4 + 181*n**3/2 + 3*n**2 + 2767*n. Suppose v(r) = 0. What is r?
-1, -2/177
Find c such that 4/3*c**2 + 36 + 112/3*c = 0.
-27, -1
Let m(a) be the second derivative of -2*a**7/21 - 4*a**6/3 - 6*a**5/5 + 32*a**4/3 + 94*a**3/3 + 36*a**2 + 2*a + 28. Factor m(o).
-4*(o - 2)*(o + 1)**3*(o + 9)
Suppose 2*c - 52 = -84. Let h be (c/85)/((-19)/95). Factor -h*u - 10/17*u**2 - 8/17 - 2/17*u**3.
-2*(u + 1)*(u + 2)**2/17
Suppose 6 = 4*q - 5*s, -5*s + 3*s + 24 = 5*q. Let m be 0/(-14)*(2/q - 0). Determine y so that m - 16/3*y**5 - 8*y**3 + 12*y**4 + 0*y + 4/3*y**2 = 0.
0, 1/4, 1
Suppose 0 = -151*g - 134*g + 103*g + 546. Find j such that -59319/4 - 4563/4*j - 1/4*j**g - 117/4*j**2 = 0.
-39
Let i be ((-4956)/105)/((-4)/10). Let u = -116 + i. Factor -a**3 + 9*a**2 - 5*a**2 - 8*a**u.
-a**2*(a + 4)
Let h = -2764 - -2766. Let c(d) be the second derivative of -1/36*d**4 + 1/120*d**5 - 20*d + 0*d**3 + 0*d**h + 0. Factor c(t).
t**2*(t - 2)/6
Let a(u) be the third derivative of -64*u**2 - 25*u**3 - 47/45*u**5 - 20/3*u**4 - 4/45*u**6 + 0*u + 0 - 1/315*u**7. Let a(g) = 0. Calculate g.
-5, -3
Let j = 50797/4 - 152071/12. Determine q so that -2/3*q**4 + 8000/3*q + j*q**3 - 400*q**2 - 20000/3 = 0.
10
Let w be (8 + (5 - 14))*0. Let b(f) be the first derivative of w*f**3 + 2/5*f**4 + 5 + 0*f**2 + 0*f + 2/25*f**5. Factor b(q).
2*q**3*(q + 4)/5
Solve 2*a**4 - 1/5*a**5 + 42/5 + 43/5*a - 18/5*a**3 - 28/5*a**2 = 0 for a.
-1, 2, 3, 7
Let l(j) = j + 1. Let y = 62 + -92. Let z(d) = 11*d**2 - 24*d - 35. Let w(k) = -k**2 - k. Let a(p) = -6*w(p) - z(p). Let x(t) = y*l(t) + a(t). Factor x(o).
-5*(o - 1)*(o + 1)
Let z(c) = -16*c**2 + 714. Let s(d) = -39*d**2 - 2*d + 1425. Let l(t) = 2*s(t) - 5*z(t). Let l(h) = 0. Calculate h.
-18, 20
Determine q, given that 70 + 24*q + 72 - 210 + 3*q**3 + 18*q**2 + 68 = 0.
-4, -2, 0
Let z(d) be the third derivative of -d**5/12 - 59*d**4/24 - 39*d**3 - 16*d**2 + 1. Let l(q) = q**2 + 12*q + 47. Let g(i) = -22*l(i) - 4*z(i). Factor g(w).
-2*(w + 7)**2
Let s = 373 + -370. Let d(i) be the first derivative of 1/4*i**2 - 2 - 1/8*i**4 - 1/3*i**s + i. Find p, given that d(p) = 0.
-2, -1, 1
Suppose 96 = -14*t + 6*t. Let f be (t/504*-9)/((-4)/(-14)). Find n such that 3*n**2 - 3/4*n**4 + 0 - 9/2*n**3 + f*n**5 + 6*n = 0.
-2, -1, 0, 2
Let a = -129 - -133. Let -22*p**4 + 51*p**2 + 30*p - 24*p**4 + 24*p**3 + 79*p**a - 30*p**4 = 0. What is p?
-5, -2, -1, 0
Suppose -2*u - 15 + 5 = 0. Let y(f) = f**3 + 4*f**2 - 7*f - 6. Let r be y(u). Factor -2*k**2 + 74*k**3 + r - k**4 - 80*k**3 + 6*k - k**4.
-2*(k - 1)*(k + 1)**2*(k + 2)
Let v(r) be the first derivative of r**4/3 + 8*r**3/9 - 2*r**2/3 - 8*r/3 - 1638. What is o in v(o) = 0?
-2, -1, 1
Let x(a) be the second derivative of a**6/6 - 25*a**5 - 85*a**4/2 + 250*a**3/3 + 505*a**2/2 - 10758*a. Factor x(u).
5*(u - 101)*(u - 1)*(u + 1)**2
Let z be -1 + 6 - (-4 + -5 + 12). Factor z*c**3 - 2*c**2 - 96*c - 2*c**2 + 96*c.
2*c**2*(c - 2)
Let l(x) be the third derivative of -x**8/84 - 2*x**7/21 + 9*x**6/10 + 17*x**5/15 - 31*x**4/3 - 32*x**3 - 11*x**2 + 2*x + 6. What is k in l(k) = 0?
-8, -1, 2, 3
Suppose 99 = v + 5*t, -5*t = 4*v - 9*t - 300. Factor -3*c**5 - 84*c**4 + 4*c**5 + v*c**4 - 3*c**2 + 7*c**3.
c**2*(c - 3)*(c - 1)**2
Let g = 27 - 25. Let y(o) = -5*o**3 - 5*o**2 - 30*o. Let m(w) = -w**3 - w**2 - 8*w. Let k(x) = g*y(x) - 9*m(x). Factor k(p).
-p*(p - 3)*(p + 4)
Let w(a) be the first derivative of a**7/5040 - a**6/144 + 11*a**5/180 + 313*a**3/3 + 327. Let v(f) be the third derivative of w(f). Factor v(m).
m*(m - 11)*(m - 4)/6
Suppose -33*z + 38*z = 5*w + 210, -2*w = 2*z - 100. Suppose 2*y**2 + 2*y - 4*y**4 + z*y**3 + 2*y**4 + 10*y**2 - 50*y**3 - 6 - 4*y**4 + 2*y**5 = 0. What is y?
-1, 1, 3
Let r be 2/(5 + -6 + 2). Let z(g) be the first derivative of 26 - 5*g - 5/6*g**3 + 15/4*g**r. Factor z(n).
-5*(n - 2)*(n - 1)/2
Let v(b) = 3*b**3 - 21*b**2 + 27*b. Let i = 3058 + -3050. Let w = -1 + -2. Let y(g) = 9*g**3 - 62*g**2 + 81*g. Let m(l) = i*v(l) + w*y(l). Factor m(p).
-3*p*(p - 3)**2
Let w = 65 - 65. Suppose -y + 8 = -r, -4*y - r - r + 8 = w. Determine v so that -3*v - v + 19*v**y - 7*v**5 - 4*v + 6*v**3 - 28*v**2 = 0.
-1, -2/7, 0, 2
Factor -26/7*y + 68/7 - 6*y**2.
-2*(y - 1)*(21*y + 34)/7
Suppose -260*n - 6 = -256*n - 2*d, -5*n = -5*d + 15. Find m, given that 0 - 1/3*m + n*m**2 - 1/3*m**5 + 0*m**4 + 2/3*m**3 = 0.
-1, 0, 1
Let a(z) be the third derivative of -2/15*z**5 - 1/30*z**6 - 1/6*z**4 + 0 - 50*z**2 + 0*z + 0*z**3. Factor a(w).
-4*w*(w + 1)**2
Let a = 112846496975/1578 + -71512348. Let h = 2/789 + a. Suppose h*v**2 + 1 - 5/2*v**4 + 13/2*v - 1/2*v**3 = 0. What is v?
-1, -1/5, 2
Determine x so that 4/7*x**2 + 380/7*x + 1104/7 = 0.
-92, -3
Let q(f) be the second derivative of 3*f**5/35 - 1767*f**4/28 + 13923*f**3 + 146523*f**2/14 - 1976*f. Find a such that q(a) = 0.
-1/4, 221
Suppose -38 - 12 = -25*q. Let y(w) be the third derivative of -1/80*w**5 + 0*w + 0 + 1/4*w**3 - 10*w**q + 1/32*w**4. Factor y(g).
-3*(g - 2)*(g + 1)/4
Let o(j) = -8*j**2 + 346*j - 3528. Let q be 24*(-3)/48*-8. Let i(t) = 20*t**2 - 864*t + 8820. Let z(f) = q*o(f) + 5*i(f). Factor z(p).
4*(p - 21)**2
Let x(d) be the first derivative of 28*d**5/5 + 2*d**4 - 28*d**3/3 - 4*d**2 - 1062. Suppose x(q) = 0. Calculate q.
-1, -2/7, 0, 1
Let k(c) be the first derivative of c**4/14 + 46*c**3/21 + 8*c**2 - 280*c - 4524. Factor k(t).
2*(t - 5)*(t + 14)**2/7
Let s(g) be the first derivative of -g**5/10 - 3*g**4/4 - 11*g**3/6 - 3*g**2/2 - 854. Let s(n) = 0. Calculate n.
-3, -2, -1, 0
Let o(b) = -78*b**2 + 156*b - 35904. Let x(g) = 7*g**2 - 14*g + 3264. Let r(u) = -10*o(u) - 111*x(u). Determine h so that r(h) = 0.
-32, 34
Factor 0 + 0*p**2 - 2/17*p + 2/17*p**3.
2*p*(p - 1)*(p + 1)/17
Let k = -17 - -21. Let n(x) = -9 + 5 - x**2 + 0 - 18*x - 17. Let i(y) = 3*y**2 + 36*y + 42. Let q(f) = k*i(f) + 9*n(f). Factor q(p).
3*(p - 7)*(p + 1)
Let o(t) = -3*t**2 - 5*t**2 + 4*t**2 + 3*t**2 + 13*t - 28. Let j be o(9). Solve -4 + 9*w**2 - j - 7*w**3 + 2*w**3 + 2*w**3 = 0 for w.
-1, 2
Let f be (0 + 1)/(345/2185). Suppose f + 7/2*o - 28/3*o**2 - 1/2*o**3 = 0. What is o?
-19, -2/3, 1
Let c = -428 - -431. Factor -272*g**2 + 213*g - 63*g + 2500*g**c + 266*g + 16 + 3172*g**2.
4*(g + 1)*(25*g + 2)**2
Let o(c) be the first derivative of -c**3/9 + 5*c**2/6 + 14*c/3 - 5186. Suppose o(s) = 0. What is s?
-2, 7
Suppose 5*r + 4*l = -1465, -4*r + 5*l - 1168 = 45. Let c = -2669/9 - r. Suppose 0 - 8/9*j + c*j**3 - 4/9*j**2 = 0. Calculate j.
-1, 0, 2
Let -54*g**2 + 6843 - 6843 + 26*g + 78*g + g**3 = 0. Calculate g.
0, 2, 52
Let i(g) be the second derivative of -1/10*g**6 + 9/4*g**4