r**6 + 1/42*r**7 - 10/3*r**4 + 36*r**2 + 0*r + 0*r**3 + 0 + 5/3*r**5. Find c such that q(c) = 0.
0, 2, 4
Let p = 9965294/2179905 + -2/311415. Factor -20/7*q**2 - 16/7 + 4/7*q**3 + p*q.
4*(q - 2)**2*(q - 1)/7
Let f(q) be the first derivative of 1/40*q**5 - 1/16*q**2 - 1/24*q**3 + 0*q + 1/32*q**4 + 91. Factor f(d).
d*(d - 1)*(d + 1)**2/8
Let u(o) be the first derivative of 3*o**5/5 + 633*o**4/4 - 213*o**3 - 633*o**2/2 + 636*o + 794. Factor u(h).
3*(h - 1)**2*(h + 1)*(h + 212)
Let f(m) be the third derivative of -m**5/90 - 181*m**4/27 + 484*m**3/27 - 338*m**2. What is c in f(c) = 0?
-242, 2/3
Let x = 50 + -64. Let b be (x - -4)*1/(-2). Factor b*a - 1 + 4*a**2 - 1 + 10 + 7*a.
4*(a + 1)*(a + 2)
Let r(y) = -2*y**2 + 17*y - 4. Suppose 0 = -4*p - p + 40. Let h be r(p). Factor 11*g**3 + 4*g**h - 2*g + 2*g - 17*g**3 + 2*g**5.
2*g**3*(g - 1)*(g + 3)
Find z, given that 382/5*z + 76*z**2 + 0 - 2/5*z**3 = 0.
-1, 0, 191
Let w be 1/((-6)/16)*57/(-38). Suppose -3*s**2 - 54*s - 35 - w - 57 = 0. Calculate s.
-16, -2
Suppose 2*f + 0*f - 6 = 0. Suppose 0 = -f*d + d + 52. Factor -7*y**3 - d*y + 22*y**3 + 5*y**4 + 6*y.
5*y*(y - 1)*(y + 2)**2
Let a(f) be the second derivative of f**7/6720 - f**5/960 - 65*f**3/6 + 89*f. Let u(l) be the second derivative of a(l). Solve u(d) = 0.
-1, 0, 1
Let b(v) be the first derivative of -7*v**4/2 - 43*v**3/3 - 22*v**2 - 15*v - 132. Factor b(p).
-(p + 1)**2*(14*p + 15)
Let z = 704 + -575. Factor 131 - 11*b**4 - z*b**2 + b**4 - 155 + 3*b**5 - 17*b**4 + 87*b**3 + 90*b.
3*(b - 4)*(b - 2)*(b - 1)**3
Determine g, given that 6*g**3 - 749*g**2 + 215*g + 1000 - 15*g**3 + g**4 + 639*g**2 + 243*g + 442*g = 0.
-10, -1, 10
Suppose 149*q + 1478 + 538 = 821*q. Factor -18/5*f**q - 3/5*f - 12/5*f**4 + 0 - 12/5*f**2 - 3/5*f**5.
-3*f*(f + 1)**4/5
Let g(o) = 6*o - 86. Let u be g(14). Let p be 12/(-3) + ((-14)/u)/1. Solve -5/4*z + 1/4 - 3/4*z**p + 7/4*z**2 = 0.
1/3, 1
Determine j, given that -48/7*j - 96*j**3 - 348/7*j**2 - 21*j**4 + 0 = 0.
-4, -2/7, 0
Let m(n) be the third derivative of 0 + 0*n + 1/16*n**4 + 7/18*n**3 + 1/360*n**5 - 161*n**2. What is y in m(y) = 0?
-7, -2
Let f(n) = 9*n**2 + 13*n + 18. Let c be f(-2). Suppose 8*j**3 - 26*j**3 + 2*j**3 - c*j**5 - 64*j**4 = 0. Calculate j.
-2, -2/7, 0
Suppose 94*t + 118 - 86 - 32 = 0. Factor -l**4 - 1/2*l**3 + 0 + t*l + l**2 + 1/2*l**5.
l**2*(l - 2)*(l - 1)*(l + 1)/2
Let 176/13*a**2 + 28/13 + 124/13*a**3 + 36/13*a**4 + 2/13*a**5 + 114/13*a = 0. What is a?
-14, -1
Let n(m) be the third derivative of -m**5/105 - 271*m**4/84 + 136*m**3/21 + 334*m**2. Factor n(v).
-2*(v + 136)*(2*v - 1)/7
Let o be -4 + -10 + (-10 - (-12 + -14)). Factor 2/5*w**o - 6/5*w**4 - 11/5*w**3 + 0*w + 0.
-w**2*(w + 2)*(6*w - 1)/5
Factor -50*r**2 + 5*r**3 + 230*r - 20*r + 135*r**2.
5*r*(r + 3)*(r + 14)
Let f(i) be the first derivative of i**5 + 65*i**4/2 + 545*i**3/3 - 1950*i**2 + 4500*i - 13341. Factor f(n).
5*(n - 2)**2*(n + 15)**2
Let m(v) be the third derivative of v**8/168 + 79*v**7/735 + 137*v**6/210 + 54*v**5/35 + 6*v**4/7 + 1645*v**2. Determine b so that m(b) = 0.
-6, -3, -2, -2/7, 0
Let p(j) be the first derivative of j**3/8 - 1833*j**2/8 + 1119963*j/8 + 4503. Suppose p(s) = 0. Calculate s.
611
Factor -100/3*q**3 + 0 - 224*q**2 + 0*q - 2/3*q**4.
-2*q**2*(q + 8)*(q + 42)/3
Let c(f) = 5*f**2 - 1697*f + 3332. Let i(u) = u**2 - 9*u. Let p(x) = -c(x) + 3*i(x). Solve p(o) = 0 for o.
2, 833
Let k(m) = 7*m**2 - 4*m - 33. Let d be k(7). Let j = d + -282. Factor 9/7*c**4 + 0*c**2 + 0*c + 3/7*c**5 + j + 6/7*c**3.
3*c**3*(c + 1)*(c + 2)/7
Factor -84*n**2 - 33*n + 287*n + 99 + 8*n + 113*n.
-3*(4*n + 1)*(7*n - 33)
Let i = -309/2 + 155. Let p = 8639 + -8636. Factor i*c**2 + 0 + 0*c + 2*c**4 + 5/2*c**p.
c**2*(c + 1)*(4*c + 1)/2
Let v(s) be the third derivative of -s**5/300 - 19*s**4/10 - 45*s**3/2 + 4*s**2 + 5*s + 23. Factor v(o).
-(o + 3)*(o + 225)/5
Let x(r) = -r**3 - 60*r**2 - 377*r - 316. Let o be x(-53). Find b, given that 3*b**o - 6/5*b**3 - 8/5*b - 1/5*b**4 + 0 = 0.
-8, 0, 1
Suppose 3*r + 2*s - 106 = 0, 2*r - 17 = 4*s + 27. What is a in -4*a**2 - 15*a - 64 - r*a - 21*a = 0?
-16, -1
Let n(w) be the first derivative of 5*w**6/6 - 3*w**5 + 20*w**3/3 + 1120. Factor n(u).
5*u**2*(u - 2)**2*(u + 1)
Let -98/5*u**2 - 1932*u - 47610 = 0. What is u?
-345/7
Let c be 1/(6*9/(-324)). Let d be (-6)/(2*(c - -5)). Find j such that 3/4*j**4 - 6*j + 0 - 3*j**2 + 3/2*j**d = 0.
-2, 0, 2
Let t = 1499 + -1497. Let v(n) be the first derivative of -2/7*n - 2/7*n**t + 6 - 2/21*n**3. Factor v(u).
-2*(u + 1)**2/7
Let a be 99/345 - (4/(-26) + 144/598). Let o(m) be the second derivative of 0*m**2 + 0 + 0*m**3 + 23*m + 2/3*m**4 - a*m**5. Factor o(i).
-4*i**2*(i - 2)
Let f(v) be the second derivative of 3*v**5/20 - 679*v**4/4 + 4047*v**3/2 - 18171*v**2/2 + 12979*v. Factor f(c).
3*(c - 673)*(c - 3)**2
Let u(m) be the first derivative of -m**7/1176 + m**6/360 + m**5/105 - m**4/42 + 56*m**3/3 - 84. Let t(c) be the third derivative of u(c). Factor t(p).
-(p - 2)*(p + 1)*(5*p - 2)/7
Find k, given that -1/6*k**4 + 4*k**3 - 39/2*k**2 - 12 + 83/3*k = 0.
1, 4, 18
Factor 3/5*i**3 + 5292/5 - 249/5*i**2 + 1008*i.
3*(i - 42)**2*(i + 1)/5
Let t(h) = 2*h**2 + 3*h. Let o be t(-4). Let a be o/6*(-20)/(-150). Factor -a*w**2 - 2/9 + 2/3*w.
-2*(w - 1)*(2*w - 1)/9
Suppose 0 = -43*h + 45*h. Let m be 123/(-27) - (-5 + h). Suppose 0*y + 0 + m*y**2 + 2/9*y**3 = 0. What is y?
-2, 0
Let r = 2629 + -2627. Let c(t) be the second derivative of -r*t + 0 + 2/5*t**2 + 1/50*t**5 + 1/15*t**3 - 1/5*t**4 + 2/75*t**6. Suppose c(l) = 0. Calculate l.
-2, -1/2, 1
Let d(c) be the second derivative of c**7/210 + c**6/90 - c**5/30 - c**4/6 - 5*c**3/6 - c**2 - 82*c. Let w(a) be the second derivative of d(a). Factor w(t).
4*(t - 1)*(t + 1)**2
Suppose -13*u - 12*u = -100. Factor -3*a**2 + 24 + 15*a + 9*a + a - u*a.
-3*(a - 8)*(a + 1)
Let c(m) be the first derivative of -13*m**3/9 - 10*m**2 - 47*m/3 + 5513. Solve c(f) = 0.
-47/13, -1
Factor 936/5 + 176/5*r**2 + 804/5*r + 4/5*r**3.
4*(r + 2)*(r + 3)*(r + 39)/5
Let z = 79 - -20. Let i be z/21 - (-10)/35. Factor 0*p - 3/5*p**i + 0 + 9/5*p**3 + 0*p**4 + 6/5*p**2.
-3*p**2*(p - 2)*(p + 1)**2/5
Let h(v) be the second derivative of v**5/60 + v**4/24 - v**3 - 27*v**2 + 49*v + 3. Let b(a) be the first derivative of h(a). Factor b(w).
(w - 2)*(w + 3)
Let w(k) = -834*k - 13342. Let b be w(-16). Determine z, given that -23/3*z - 2/3 - 7*z**b = 0.
-1, -2/21
Factor -2*h**3 + 8*h**3 - 942*h**2 - 369*h + 369*h - 3*h**3.
3*h**2*(h - 314)
Let d be (-6 - -5) + 724/716. Let w = 372/1253 - d. Factor 0*b**2 + 0*b - 1/7*b**4 + 0 - w*b**3.
-b**3*(b + 2)/7
Let y be (6 + 2 - 11)*(-8)/15. Let n(b) be the first derivative of -7 - y*b**2 + 32/5*b + 2/15*b**3. Determine z, given that n(z) = 0.
4
Factor 384*p + 73728 + 1/2*p**2.
(p + 384)**2/2
Let m(s) = s**4 + s**3 + s**2 - 2*s - 2. Let a(d) = -d**5 - d**4 + 5*d**3 + 9*d**2 - 8*d - 8. Let w(p) = -a(p) + 4*m(p). Find i such that w(i) = 0.
-5, -1, 0, 1
Let l(t) = -9*t**2 + 83*t + 180. Let n(v) = 30*v**2 + 49*v - 88*v - 115*v - 96*v + 167 - 710. Let k(s) = 7*l(s) + 2*n(s). Let k(a) = 0. What is a?
-2, 29
Let v = -2/58025 + -65046019/174075. Let i = v - -374. Factor -2/3*z - 1/3*z**2 - i.
-(z + 1)**2/3
Determine m, given that 178*m**4 + 0 - 138*m**2 - 34*m + 21/2*m**5 - 33/2*m**3 = 0.
-17, -2/3, -2/7, 0, 1
Let s(p) be the second derivative of 2*p**5/5 + p**4/12 - p**3/6 + 6*p**2 - p + 191. Let u(k) = k**3 - k**2 + 4*k. Let x(c) = s(c) - 5*u(c). Factor x(j).
3*(j - 1)**2*(j + 4)
Let l(p) be the first derivative of p**6/6 - 9*p**5 + 327*p**4/4 + 3961*p**3/3 + 4836*p**2 + 6084*p + 995. Factor l(t).
(t - 26)**2*(t + 1)*(t + 3)**2
Let m(r) be the first derivative of -2/3*r**4 + 0*r - 11/3*r**2 + 10*r**3 + 10. Factor m(f).
-2*f*(f - 11)*(4*f - 1)/3
Let n(v) be the third derivative of 0*v**3 - 1/18*v**4 + 0*v + 1/270*v**5 - 125*v**2 + 1/540*v**6 + 0. Find k such that n(k) = 0.
-3, 0, 2
Let z(l) = l**3 + 7*l**2 + 50*l + 256. Let v be z(-5). Let j = 19 - 11. Factor v - j*b + 2/7*b**2.
2*(b - 14)**2/7
Let l = 2640 - 2634. Let v(r) be the third derivative of 0*r + 2/15*r**4 + 2/525*r**7 + 1/30*r**l + 0*r**3 + 0 + 8/75*r**5 - 11*r**2. Factor v(u).
4*u*(u + 1)*(u + 2)**2/5
Let v be 5 + -6 + (-8394)/18. Let b = -462 - v. Suppose 0*t + 0 + 20/3*t**3 + 4/3*t