30 + 21*n**4/4 + 4*n**2 + 35. Let a(l) be the second derivative of k(l). Factor a(y).
-2*y**2*(y - 2)
Let s = 998909 - 62929913/63. Let b = 322/9 - s. Determine d, given that 24/7*d**3 - 32/7*d - 220/7*d**4 + 16*d**2 + 0 - b*d**5 = 0.
-2, -1, 0, 2/5
Let o(m) be the third derivative of 1/15*m**5 + 24*m**3 + 2*m**4 + 0*m - 11*m**2 + 0. Solve o(s) = 0.
-6
Factor -6272000 + 67200*z + 2/7*z**3 - 240*z**2.
2*(z - 280)**3/7
Factor -728*l - 1/5*l**4 - 8281/5 - 582/5*l**2 - 8*l**3.
-(l + 7)**2*(l + 13)**2/5
Let o(j) be the third derivative of 1/3*j**3 - 17/60*j**5 + 0 + 11*j + 5/8*j**4 - 3*j**2. Factor o(v).
-(v - 1)*(17*v + 2)
Let g(k) = -5*k**3 - k**2 + 3*k**3 + 77 - 76. Let o(x) = -5*x**4 - 20*x**3 - 40*x**2 - 20*x - 5. Let m(t) = -5*g(t) - o(t). Factor m(q).
5*q*(q + 1)**2*(q + 4)
Let o(b) = b**3 + 8*b**2 - 8*b + 22. Let q be o(-9). Suppose -3*i = -q + 4. Factor 4 + 2*x - x**2 + i*x**2 - 4*x**2 + 0*x**2.
-2*(x - 2)*(x + 1)
Let t(j) be the third derivative of -1/40*j**6 + 0 + 1/280*j**7 + 0*j - 11/80*j**5 - 3/16*j**4 + 0*j**3 - 91*j**2. Let t(v) = 0. What is v?
-1, 0, 6
Let f(y) be the first derivative of 6*y**3/5 + 968*y**2 - 2152*y/5 - 34. Factor f(n).
2*(n + 538)*(9*n - 2)/5
Factor -40*b**3 + 215*b**2 + 3875 - 1764 - 5*b**4 - 1991 - 290*b.
-5*(b - 2)*(b - 1)**2*(b + 12)
Let j(n) be the third derivative of -45*n**2 - 392/3*n**3 + 0 + 0*n - 14/3*n**4 - 1/15*n**5. Suppose j(d) = 0. Calculate d.
-14
Let t(c) be the first derivative of 4*c**5/5 + 19*c**4 + 64*c**3/3 - 72*c**2 + 6419. Factor t(f).
4*f*(f - 1)*(f + 2)*(f + 18)
Factor 1176 - 8*m**4 + 156*m**2 + 5*m**4 - 105*m**3 - 471*m + 2259*m + 984.
-3*(m - 5)*(m + 2)**2*(m + 36)
Let v be (3/(-4))/((-3)/72*9). Solve 170*x**4 - 252*x**3 + 206*x**4 - 24*x**v - 450*x**5 + 334*x**4 + 16*x = 0 for x.
-2/9, 0, 2/5, 1
Let s(g) be the third derivative of 2*g**7/105 - 23*g**6/15 - 19*g**5/3 - 8*g**4 + 106*g**2 + g + 2. Factor s(j).
4*j*(j - 48)*(j + 1)**2
Let i(y) be the second derivative of -y**4/18 + 10*y**3/9 + 8*y**2 + 282*y. Suppose i(o) = 0. What is o?
-2, 12
Let s(n) be the first derivative of 1/2*n**3 + 128 + 1/2*n - 1/8*n**4 - 3/4*n**2. Solve s(w) = 0.
1
Let s(a) be the second derivative of a**4/4 - 37*a**3 + 639*a**2/2 - 4*a - 101. Let s(x) = 0. What is x?
3, 71
Let i(j) be the second derivative of -j**5/60 - 5*j**4/12 - 8*j**3/3 - 13*j**2/2 - 2*j + 12. Let l(h) be the first derivative of i(h). Factor l(d).
-(d + 2)*(d + 8)
Let r be ((-56)/(-2100))/((243/120 - 2)*1). Let z(c) be the third derivative of 0*c - 1/150*c**5 + 2/15*c**4 + 19*c**2 + 0 - r*c**3. Factor z(p).
-2*(p - 4)**2/5
Let h(f) be the first derivative of -5/4*f**4 + 153 - 35/3*f**3 + 20*f**2 + 0*f. Factor h(c).
-5*c*(c - 1)*(c + 8)
Let i(q) be the second derivative of -3*q**5/140 - 5*q**4/7 - 33*q**3/14 + 81*q**2/7 - 2*q + 1774. Factor i(d).
-3*(d - 1)*(d + 3)*(d + 18)/7
Suppose -t = -5*k + 102, -2*t = k - 4*k + 64. Suppose 3*s = -k*s + 92. Find a, given that -18/7*a - 32/7*a**2 - 12/7*a**s - 2/7*a**5 - 4/7 - 4*a**3 = 0.
-2, -1
Let i(j) be the third derivative of -227*j**2 + 0*j - 37/390*j**5 + 0*j**3 + 0 + 1/60*j**6 - 1/26*j**4. Factor i(l).
2*l*(l - 3)*(13*l + 2)/13
Let l(n) = n**4 - 2*n**3 + 2*n - 1. Let q(v) = -v**5 - 20*v**4 - 19*v**3 - 31*v**2 - 24*v + 7. Let h(j) = -28*l(j) - 4*q(j). Suppose h(g) = 0. What is g?
-10, -1, 0
Suppose 1 = -5*k + 4*a, -5*k + 2*a = -a - 3. Suppose 8 = 2*c - y - 4, 3*c = -5*y - 8. Determine t so that 9/4*t**2 + 3/2*t**3 - 3/4*t**c + k - 6*t = 0.
-2, 1, 2
Let x(w) be the third derivative of -w**5/240 - 219*w**4/16 - 143883*w**3/8 + 7*w**2 - 10. Factor x(n).
-(n + 657)**2/4
Let f(r) be the first derivative of 3125*r**6/12 + 125*r**5/2 + 25*r**4/4 + r**3/3 + 73*r**2/2 + r + 3. Let w(g) be the second derivative of f(g). Factor w(v).
2*(25*v + 1)**3
Let p(x) be the third derivative of -x**7/210 - x**6/60 + 157*x**5/60 - 77*x**4/12 + 224*x**2 - 3*x + 2. Factor p(c).
-c*(c - 11)*(c - 1)*(c + 14)
Suppose 621*r - 641 + 16 = 617. Let x(f) be the second derivative of 0*f**r - 1/18*f**4 + 0 - 13/9*f**3 - 35*f. Solve x(v) = 0.
-13, 0
Let b be (3/(-6))/(1*(-1)/12). Suppose -86 = -b*q - 50. Factor 9/2*u**3 + 0 + 0*u - 3/2*u**2 + 0*u**4 - q*u**5.
-3*u**2*(u + 1)*(2*u - 1)**2/2
Suppose 88 - 192 = -8*w. Solve 732*g**3 - 6*g**5 + w*g**2 - 3*g**2 - 10*g**4 - 722*g**3 - 4*g = 0.
-2, -1, 0, 1/3, 1
Factor 665*d**3 - 1663 + 1955*d - 5*d**4 + 1784 - 771 - 1965*d**2.
-5*(d - 130)*(d - 1)**3
Factor 5*m**4 + 193*m + 1065*m**2 + 5872*m**3 - 1383*m - 6012*m**3 - 7840.
5*(m - 16)*(m - 7)**2*(m + 2)
Suppose -3*j + 61 = 4*i, -2*i - 41 = -3*j - i. What is u in -10*u**3 - 15*u**4 + 40*u**3 - 32*u**3 + 20*u + 5*u**5 - 23*u**3 + j*u**2 = 0?
-1, 0, 1, 4
Let g be (12/70)/(2406/8020). Find y, given that 0 + 6/7*y - 2/7*y**3 + g*y**2 = 0.
-1, 0, 3
Let t(b) = b**2 - 237*b - 4415. Let y(l) = -2*l**2 - 9*l + 1. Let q(z) = -t(z) + y(z). Factor q(p).
-3*(p - 92)*(p + 16)
Let s = 5 + -3. Suppose 7*a - 4 = 5*a, 0 = 3*y + 3*a - 63. Factor 14*x**4 + 0*x**2 - y*x**4 + 8*x**s - 5 + 2*x**2.
-5*(x - 1)**2*(x + 1)**2
Let z be (9 - 4)*(-834)/(-695). Let a(y) be the first derivative of z - 3/16*y**4 - 1/8*y**2 + 0*y - 1/20*y**5 - 1/4*y**3. Factor a(d).
-d*(d + 1)**3/4
What is p in -195 + 20*p**4 + 309*p**5 + 762*p**3 + 777*p - 312*p**5 - 202*p**4 - p**4 - 1158*p**2 = 0?
-65, 1
Let i be (20/(-14) - -1)*(4020/(-120) + 30). Let z - 1/2 + i*z**2 = 0. What is z?
-1, 1/3
Let w(v) = 29*v + 2149. Let i be w(-74). Let b(u) be the first derivative of 0*u**5 - 4/9*u + 2/9*u**4 - 1/27*u**6 - 1/3*u**2 + 4/27*u**i - 24. Solve b(d) = 0.
-1, 1, 2
Let g be -5 + (93/2)/((-18)/(-24)). Factor -52*r**3 - 24*r**5 + 27*r**4 - g*r**3 + 106*r**3.
-3*r**3*(r - 1)*(8*r - 1)
Let g(t) = -2233*t**2 - 33492*t + 47. Let r be g(-15). Factor 4/13*c**r - 6/13 - 2/13*c.
2*(c + 1)*(2*c - 3)/13
Let r = -47135/4 + 47201/4. Factor -r - 15*m + 3/2*m**2.
3*(m - 11)*(m + 1)/2
Let a(j) = 5*j**2 - 41*j - 24. Let n(m) = 496*m**2 - 494*m**2 - 4*m - 8 - 10*m. Let v(b) = 4*a(b) - 11*n(b). Suppose v(i) = 0. What is i?
-4, -1
Let j(r) be the second derivative of -r**7/630 + 7*r**6/180 - 2*r**5/5 + 50*r**4/3 - 126*r. Let d(u) be the third derivative of j(u). Solve d(q) = 0 for q.
3, 4
Let z(q) be the second derivative of 1/6*q**6 + 5*q - 1/10*q**5 + 0*q**3 + 0 + 0*q**4 + 1/6*q**7 + 0*q**2. Factor z(h).
h**3*(h + 1)*(7*h - 2)
Let v(m) be the second derivative of m**6/6 + 47*m**5/4 + 515*m**4/2 + 3850*m**3/3 + 2420*m**2 + 15*m - 6. What is o in v(o) = 0?
-22, -2, -1
Factor 9*a + 165/7 + 6/7*a**2.
3*(a + 5)*(2*a + 11)/7
Let k(x) be the second derivative of -x**7/21 + 59*x**6/15 - 899*x**5/10 + 841*x**4/6 - 669*x. Factor k(a).
-2*a**2*(a - 29)**2*(a - 1)
Let v = 1259 - 831. Let t = v - 428. Factor -1/6*w**4 + 0*w + 0 + 1/6*w**2 + t*w**3.
-w**2*(w - 1)*(w + 1)/6
Suppose 19*m - 17*m + 8 = 2*s, -4*m = s - 4. Suppose -2*x - s*l = 2, l + 0*l = -2. Let 0 + 0*a + 0*a**2 + 0*a**4 - 1/11*a**5 + 1/11*a**x = 0. Calculate a.
-1, 0, 1
Find x, given that 3*x**3 + 4 - 16/3*x - 1/3*x**5 + 1/3*x**4 - 5/3*x**2 = 0.
-2, 1, 3
Suppose 1/3*u**4 + 46/3*u**2 + 0 + 13/3*u**3 + 16*u = 0. What is u?
-8, -3, -2, 0
Let r = 49390/74103 - -4/24701. Find v such that 2*v**3 - 4/3*v**2 - 16/3 + r*v**4 - 8*v = 0.
-2, -1, 2
Let q be (146349/3735)/7 - 2. Let i = q - -1/415. Factor -3/5*k**2 + i*k - 3/5 - 72/5*k**3 - 48/5*k**4.
-3*(k + 1)**2*(4*k - 1)**2/5
Let g(k) = 49*k - 31*k**2 - 6*k**2 + 2 + 58 - 15*k**3. Let v(q) = -5*q**3 - 13*q**2 + 16*q + 20. Let c(h) = -4*g(h) + 11*v(h). Let c(j) = 0. Calculate j.
-2, -1, 2
Let k(j) = 858*j**2 - 897*j + 930. Let z(m) = -127*m**2 + 128*m - 133. Let s(o) = -4*k(o) - 27*z(o). Find r, given that s(r) = 0.
1, 43
Let i = 1633 + -1630. Let j(r) = r**2 - 2*r + 7. Let y be j(6). Solve -3*o + i*o**3 + y*o**2 - 34*o**2 + 3*o - 3*o + 3 = 0 for o.
-1, 1
Let v(z) = 15*z**2 - 642*z + 960. Let f(h) = -h**2 + 40*h - 60. Let q(s) = 33*f(s) + 2*v(s). Let q(c) = 0. What is c?
2, 10
Let s = -34 - -34. Suppose s = -b + 2*b - 3. Factor 11 + d**b + 20*d + 3*d**3 - 19 - 12*d**2 - 4*d**2.
4*(d - 2)*(d - 1)**2
Suppose -258*o = 58*o. Let h(i) be the third derivative of -1/24*i**6 - 1/12*i**5 + o*i + 0 - 5/2*i**3 + 25/24*i**4 + 5*i**2. Factor h(z).
-5*(z - 1)**2*(z + 3)
Solve -169*r**2 + 1275*r - 87*r - 596 - 4*r**3 - 419*r**2 = 0 