1
Let j(f) = 201*f + 8447. Let s be j(-42). Find w such that 964/5*w**3 + 344*w**2 - 1360*w + 112/5*w**4 + 800 + 4/5*w**s = 0.
-10, 1
Factor -2459*p - 2*p**3 - 823*p - 3910*p - 83*p**2 - 117*p**2 - 13456 - 36*p**2.
-2*(p + 2)*(p + 58)**2
Let a = -1143245 + 1143249. Suppose 24*v - 10/3*v**3 + a*v**4 - 32/3 - 40/3*v**2 - 2/3*v**5 = 0. Calculate v.
-2, 1, 2, 4
Let z(x) be the first derivative of 8/3*x**3 + 1/4*x**4 + 8*x**2 + 0*x - 47. Suppose z(p) = 0. Calculate p.
-4, 0
Let a = -124746 - -124750. Let 4/7*w**3 + 0*w + 0 + 0*w**2 + 10/7*w**5 - 2*w**a = 0. Calculate w.
0, 2/5, 1
Let s(f) be the third derivative of -961*f**5/240 + 31*f**4/8 - 3*f**3/2 + 9*f**2 - 13*f. Solve s(o) = 0.
6/31
Factor -2635*q + 11521*q + 4704561 - 4548*q + q**2.
(q + 2169)**2
Let l(p) be the third derivative of p**7/1080 - p**6/144 + p**5/180 - p**4/8 + p**3/3 + 49*p**2. Let g(b) be the second derivative of l(b). Factor g(q).
(q - 2)*(7*q - 1)/3
Suppose -3*x + 13*i = 12*i - 6, 5*x = i + 12. Factor 5*m**2 - 64*m - 74*m + 76*m - x*m**2.
2*m*(m - 31)
Factor 0 + 1/4*v**4 + 0*v + 3*v**2 - 7/4*v**3.
v**2*(v - 4)*(v - 3)/4
Let g(r) = -r**3 + 8*r**2 + 10*r - 85. Let j be g(5). Suppose -12*k = -j*k + 84. Determine z so that -1/4*z**4 - 4*z + 0*z**2 + z**k + 4 = 0.
-2, 2
Suppose -2*w - 3*w = 5*l + 110, -5*l = 2*w + 35. Let x be ((-48)/(-60))/((-10)/w). What is v in 2/11*v**3 + 10/11*v**x + 8/11 + 16/11*v = 0?
-2, -1
Let s = -2802 - -84061/30. Let b(o) be the third derivative of 0 + 0*o**3 + 1/6*o**4 + 2/105*o**7 - s*o**6 + 0*o - 1/15*o**5 - 8*o**2. Factor b(z).
4*z*(z - 1)**2*(z + 1)
Suppose 14*g = 242 - 214. Let z(u) be the third derivative of -1/80*u**5 + 0*u + 2*u**2 - g*u**3 + 0 - 1/4*u**4. Solve z(v) = 0.
-4
Let g(m) be the first derivative of -2*m**5/5 - 7*m**4/2 - 10*m**3/3 + 7*m**2 + 12*m + 1477. Factor g(h).
-2*(h - 1)*(h + 1)**2*(h + 6)
Suppose -4*x = -4*c - 5*x - 58, -5*c = -3*x + 81. Let v = c - -35. Suppose -v*q**4 - 16*q**4 + 3*q - 3*q**5 + 30*q**4 + 6*q**2 = 0. Calculate q.
-1, 0, 1
Let q(x) be the second derivative of -x**4/12 - 5*x**3/7 - 16*x**2/7 + 2*x + 6. Factor q(a).
-(a + 2)*(7*a + 16)/7
Determine m, given that -1/6*m**5 - 324 + 373/2*m**2 - 7/6*m**4 + 131/6*m**3 + 117*m = 0.
-9, -2, 1, 12
Let u(y) be the first derivative of 3*y**5/5 + 9*y**4/4 - 135*y**3 + 1875*y**2/2 - 2250*y + 6917. What is c in u(c) = 0?
-15, 2, 5
Let x(v) be the second derivative of -262*v**6/45 - 133*v**5/15 - 2*v**4/9 + 696*v. Factor x(p).
-4*p**2*(p + 1)*(131*p + 2)/3
Let p(b) be the third derivative of -b**5/60 + b**4/12 + 22*b**2. Let k(y) = 5*y**2 + 46*y. Let h(v) = -k(v) - 3*p(v). Factor h(x).
-2*x*(x + 26)
Let k(j) be the second derivative of j**6/1260 - 17*j**3 - 304*j. Let p(n) be the second derivative of k(n). Factor p(d).
2*d**2/7
Let r(s) be the first derivative of 0*s - 3*s**3 + 0*s**2 + 1/1620*s**6 + 1/108*s**4 - 1/270*s**5 + 6. Let b(d) be the third derivative of r(d). Factor b(h).
2*(h - 1)**2/9
Let c(r) be the second derivative of -19*r + 11/3*r**2 + 2/3*r**4 + 1/60*r**5 + 0 + 5/2*r**3. Factor c(k).
(k + 1)**2*(k + 22)/3
Let j(v) = 37*v**2 + 3539*v - 7009. Let o(a) = 26*a**2 + 2362*a - 4673. Let f(t) = 5*j(t) - 7*o(t). Determine d so that f(d) = 0.
-389, 2
Let a = 1/16077 - -5354/80385. Let p(k) be the third derivative of -4/3*k**3 + 1/60*k**6 + 0 + 0*k - 7/12*k**4 - a*k**5 - 17*k**2. Factor p(h).
2*(h - 4)*(h + 1)**2
Suppose 18*b - 13 = -3*j + 19*b, 0 = -3*b - 3. Let t(i) be the first derivative of -1/20*i**5 + 21/16*i**j + 0*i - 33/4*i**3 - 121/8*i**2 + 30. Factor t(m).
-m*(m - 11)**2*(m + 1)/4
Let r(t) be the third derivative of -1/660*t**6 + 0*t + 0*t**4 + 0 - 1/385*t**7 + 1/110*t**5 - 59*t**2 + 1/1848*t**8 + 0*t**3. Solve r(x) = 0 for x.
-1, 0, 1, 3
Factor 0 + 3/2*f**3 + 90*f - 51/2*f**2.
3*f*(f - 12)*(f - 5)/2
Let s(y) be the first derivative of 1/12*y**4 - 3/2*y + 1/30*y**5 - 186 - 3/2*y**2 - 4/9*y**3. Factor s(c).
(c - 3)*(c + 1)**2*(c + 3)/6
Let b(d) be the third derivative of 4*d**5/105 - 29*d**4/84 - 55*d**3/21 - 6518*d**2. Factor b(z).
2*(z - 5)*(8*z + 11)/7
Find s such that 56/3 - 10/9*s - 2/9*s**2 = 0.
-12, 7
Let v(u) be the third derivative of 10 + 13/1050*u**7 + 3/10*u**3 + 29/150*u**5 + 7/100*u**6 + 37/120*u**4 + 1/1680*u**8 + 14*u**2 + 0*u. Factor v(i).
(i + 1)**4*(i + 9)/5
Let o(s) be the third derivative of -s**8/168 + s**7/105 + s**6/60 - s**5/30 + 70*s**2. Solve o(u) = 0.
-1, 0, 1
Factor -4/7*i**4 - 492*i**2 + 0*i + 3448/7*i**3 + 0.
-4*i**2*(i - 861)*(i - 1)/7
Suppose -229 = -20*r + 51. Let k be (r/(-13) + 1)/((-124)/248). What is p in 0*p + k - 2/13*p**2 = 0?
-1, 1
Let d(v) be the second derivative of v**6/195 + 29*v**5/65 + 28*v**4/13 + 166*v**3/39 + 55*v**2/13 + 733*v. Factor d(p).
2*(p + 1)**3*(p + 55)/13
Let z(f) be the second derivative of 5*f**4/36 - 71*f**3/18 - 119*f**2/3 + f + 1536. Factor z(i).
(i - 17)*(5*i + 14)/3
Factor 0 + 4/15*c**3 - 2/3*c**2 - 4/5*c + 2/15*c**4.
2*c*(c - 2)*(c + 1)*(c + 3)/15
Let l(q) = -35*q**2 - 418*q + 28. Let c be l(-12). Find v such that -11/2*v**3 - 26*v - 12 - 1/2*v**c - 19*v**2 = 0.
-6, -2, -1
Let t(k) = -4*k + 120. Let l be t(20). Let r be -6*(-4)/((-36)/(-237)). Find q such that -l*q**3 - 38*q**2 - 80*q + 5*q**4 + r*q**2 - 80*q + 80 = 0.
2
Let u(s) be the third derivative of s**8/784 - 31*s**7/490 + 307*s**6/280 - 151*s**5/20 + 26*s**4 - 338*s**3/7 + 23*s**2 - 15. What is h in u(h) = 0?
1, 2, 13
Let d(k) = 3*k**3 - 699*k**2 + 4149*k - 6057. Let c(q) = -q**3 + 176*q**2 - 1037*q + 1514. Let r(o) = -9*c(o) - 2*d(o). Find j, given that r(j) = 0.
3, 56
Let s(i) be the second derivative of i**4/72 - 13*i**3 + 4563*i**2 + 388*i. Factor s(y).
(y - 234)**2/6
Factor 271*d + 883*d - 4*d**3 + 60*d**2 - 448*d + 788*d + 306*d.
-4*d*(d - 30)*(d + 15)
Let m(p) be the second derivative of -p**6/30 + 23*p**5/10 - 143*p**4/3 + 484*p**3/3 + 1788*p. Factor m(i).
-i*(i - 22)**2*(i - 2)
Find p, given that 48/5*p**2 + 4/5*p**4 + 0 + 8/5*p - 18*p**3 + 6*p**5 = 0.
-2, -2/15, 0, 1
Let h(m) = 4*m**3 + 3712*m**2 - 3700*m - 16. Let n(c) = 2*c**3 + 1591*c**2 - 1586*c - 7. Let q(p) = 7*h(p) - 16*n(p). Factor q(x).
-4*x*(x - 131)*(x - 1)
Let o be (-18)/(-42)*-1*442/(-51). Factor 2/7*w**2 - 4 + o*w.
2*(w - 1)*(w + 14)/7
Let c be 6941/2310 + 10 - 13. Let h(s) be the third derivative of 0*s**3 + 1/84*s**4 + 0 + 13*s**2 + c*s**5 + 0*s. Factor h(l).
2*l*(l + 1)/7
Let f(g) = 8*g**2 - 2*g - 27. Let v be f(-16). Let z = v - 2048. Suppose -q**2 + 1/4*q**z - q**4 + 1/4*q + 0 + 3/2*q**3 = 0. Calculate q.
0, 1
Suppose 4*y + 3*d - 15 = 0, -2*y - 3*d + 18 = 3*y. Suppose -6*a + 32 = 2*j - a, -y*a = -5*j + 80. Factor -j*m + 8*m**2 + 4*m**4 + 0*m**2 + 16*m**3 - 6 - 6.
4*(m - 1)*(m + 1)**2*(m + 3)
Let z(d) = 903*d**3 - 8892*d**2 - 1220*d - 37. Let o(f) = -f**3 + 4*f**2 + 8*f - 1. Let h(w) = 3*o(w) + z(w). What is r in h(r) = 0?
-1/15, 10
Let f be 4147/462 - (-649)/(-354). Determine s, given that 58/7*s**3 + f*s - 16*s**2 + 4/7 = 0.
-2/29, 1
Factor -249*g**2 - 32136/5*g + 8112/5 - 12/5*g**3.
-3*(g + 52)**2*(4*g - 1)/5
Let r(c) be the first derivative of 0*c + 3/50*c**5 + 0*c**2 + 37 + 1/600*c**6 + 9/10*c**4 - 10/3*c**3. Let l(w) be the third derivative of r(w). Factor l(k).
3*(k + 6)**2/5
Let x = -137/20 - -83/12. Let r(z) be the first derivative of 8 - 3/5*z + 2/5*z**2 - x*z**3. Suppose r(j) = 0. Calculate j.
1, 3
Let f(z) = z**3 + 47*z**2 - 207*z + 16. Let n be f(4). Factor -686/11*i + 294/11*i**2 + 0 + 2/11*i**n - 42/11*i**3.
2*i*(i - 7)**3/11
Let g(q) = -120*q**2 - 145*q + 45. Let l(m) = 9*m**2 + 3*m + 1. Let t(j) = g(j) + 15*l(j). Factor t(r).
5*(r - 6)*(3*r - 2)
Let v be 15 + -1 + 1 - 189720/13175. Factor -v + s - 2/5*s**2.
-(s - 1)*(2*s - 3)/5
Factor -2/11*a**2 - 33456200/11 + 16360/11*a.
-2*(a - 4090)**2/11
Let q be (7 - 13)*40/(-30). Let m(f) be the third derivative of 0*f + 0 + 1/240*f**5 + 0*f**3 + q*f**2 + 1/48*f**4. Factor m(x).
x*(x + 2)/4
Let m be (4 + 74/(-14))*(-7)/(-2) - (-848308)/167272. Determine j, given that -2/7*j**2 + m + 2/7*j = 0.
-1, 2
Factor -126071*z - 3198*z**2 + 2*z**3 + 0*z**3 - 302838874 + 1830605*z.
2*(z - 533)**3
Let g(z) be the third derivative of -z**6/60 - 58*z**5/15 + 235*z**4/12 - 118*z**3/3 + z**2 + 709*z. Suppose g(d) = 0. What is d?
-118, 1
Let z(x) be the first derivative of x**5/15 + x**4/2 - 19*x**3/9 - 4