42*o**2 - 268*o + 522. Let g(u) = 8*u**2 - 54*u + 104. Let l(a) = 11*g(a) - 2*j(a). Factor l(h).
2*(h - 2)*(2*h - 25)
Let v(f) be the first derivative of -f**4/46 + 18*f**3/23 + 58*f**2/23 - 2905. Let v(p) = 0. What is p?
-2, 0, 29
Let f = -937408 - -937410. Factor -4/5*c - 2/5*c**f + 16/5.
-2*(c - 2)*(c + 4)/5
Let f(a) be the second derivative of 170*a + 11/7*a**2 + 3/14*a**4 - a**3 + 0 + 1/70*a**5. Suppose f(k) = 0. What is k?
-11, 1
Let b(t) be the second derivative of -67*t + 18*t**2 - 1/2*t**4 + 11/2*t**3 - 3/20*t**5 + 0. Factor b(s).
-3*(s - 3)*(s + 1)*(s + 4)
Let y(j) = 3*j**2 - 24*j + 48. Let a(f) = -6*f**2 + 48*f - 96. Suppose 0*h + 200 = 4*h. Let m be 5*(-5)/h*-6. Let u(z) = m*a(z) + 7*y(z). Solve u(i) = 0.
4
Let o(i) be the first derivative of -i**3/9 + 2251*i**2/3 - 5067001*i/3 - 6427. Let o(p) = 0. Calculate p.
2251
Let l(p) be the second derivative of 7*p**4 - 44/5*p**6 + 87/20*p**5 + 0 - 32*p + 0*p**2 + 2*p**3 - 24/7*p**7. Find u, given that l(u) = 0.
-2, -1/4, 0, 2/3
Let n(w) = 2*w**3 + 2*w**2 + 4*w - 6. Let l be n(1). What is t in 5*t + 8 + 2 - t**3 + 3*t**2 - 13*t**l - 4*t = 0?
-10, -1, 1
Let s(v) = -v**3 + 13*v**2 + 30*v + 2. Let z be s(15). Suppose -2 + 5 - 140*f**4 - 3*f**z - 138*f**4 - 3*f**2 + 281*f**4 = 0. Calculate f.
-1, 1
Let s(r) = -76*r**2 - 4528*r + 1290544. Let z(j) = -5*j**2 + j + 3. Let w(q) = s(q) - 16*z(q). Factor w(g).
4*(g - 568)**2
Determine k so that 84*k**2 + 160*k + 478*k**2 - 2*k**3 + 315*k + 89*k = 0.
-1, 0, 282
Let s(p) be the third derivative of -p**7/630 + p**6/60 + 4*p**5/15 + 37*p**4/36 + 11*p**3/6 + 3955*p**2. Factor s(b).
-(b - 11)*(b + 1)**2*(b + 3)/3
Suppose f + 102 = -16*f. Let h(r) = 20*r**3 + 36*r**2 - 28*r + 5. Let j(l) = 11*l**3 + 19*l**2 - 14*l + 2. Let c(d) = f*h(d) + 11*j(d). Factor c(a).
(a - 4)*(a - 2)*(a - 1)
Suppose -46293 = 2*d - 46323. Let q(w) be the second derivative of 1/15*w**4 + 0*w**2 + 8/15*w**3 + 0 + d*w. Factor q(z).
4*z*(z + 4)/5
Factor -22*a**2 + 5232 + 8*a**2 - 4*a**3 - 90*a**2 - 256*a + 0*a**3 + 912.
-4*(a - 6)*(a + 16)**2
Suppose 19 = 5*q + x + x, -4*x + 8 = 0. Suppose q*y + 0*b = b + 3, 3*b - 13 = -2*y. Factor -162 + 353*z + 3*z**2 - 5*z**y - 317*z.
-2*(z - 9)**2
Let w = -87 - -107. Suppose -w = -16*k + 11*k. Determine a, given that -1198*a**2 - 6*a**3 - 2*a**5 + 1206*a**2 + 8*a - 8*a**4 + 4 - k = 0.
-2, -1, 0, 1
Let k(n) be the second derivative of n**5/15 - 5*n**4/6 + 4*n**3 - 95*n**2 - 92*n. Let h(y) be the first derivative of k(y). Factor h(z).
4*(z - 3)*(z - 2)
Let h(t) be the first derivative of 180*t - 5/4*t**4 - 39 - 55/3*t**3 - 60*t**2. Suppose h(q) = 0. Calculate q.
-6, 1
Let f(n) be the second derivative of 5776*n**6/15 + 4997*n**5/5 - 1664*n**4/3 - 430*n**3/3 - 12*n**2 + 1209*n. Find d, given that f(d) = 0.
-2, -1/19, 3/8
Let h = -45884/35 + 6546/5. Let t = -4/7 - h. Factor 1/5*f**3 + 0*f + t*f**2 + 0.
f**2*(f + 6)/5
Suppose -17*x + 20*x = 15. Let 20*k**3 + 14*k**x - 319*k**2 + 22*k**5 + 48*k**4 + 319*k**2 - 4*k**3 = 0. Calculate k.
-2/3, 0
Let o = 1 + -10. Let d be ((-3)/o)/(2/6). Find u such that 12*u**4 + u**2 + 8*u**3 - 6*u**3 - d - 8*u**5 + 6*u - 12*u**2 = 0.
-1, 1/2, 1
Let c(v) be the second derivative of -3*v**5/160 - 25*v**4/16 - 187*v**3/16 - 207*v**2/8 - 2399*v. Find m, given that c(m) = 0.
-46, -3, -1
Suppose -t = -4*o + 24, 8 + 105 = -4*t - o. Let f be (-12)/(-168) - (-2)/t. Suppose f + 1/4*c**5 - 1/4*c**3 + 0*c - 1/4*c**2 + 1/4*c**4 = 0. Calculate c.
-1, 0, 1
Let x be (-52*(-156)/40)/(7/(-35)). Let m = -1012 - x. Factor 0 - 3/5*s**m - 1/5*s**5 + s**3 + 0*s - 1/5*s**4.
-s**2*(s - 1)**2*(s + 3)/5
Suppose 5*x = 0, -11*v + 5*x + 21 = -10*v. Let o(q) = -25*q + 528. Let h be o(v). Suppose -2/3 - 3*u**2 + 5/3*u**h + 7/3*u - 1/3*u**4 = 0. Calculate u.
1, 2
Let i(v) = -4*v**3 - 292*v**2 + 1136*v - 1728. Let x(l) = l**3 + 96*l**2 - 379*l + 576. Let m(u) = -5*i(u) - 16*x(u). Find b such that m(b) = 0.
3, 4, 12
Suppose 0 = -3*w - 7*w + 20. Factor i**w - i**5 + 26*i**4 - 28*i**4 + i + i**2.
-i*(i - 1)*(i + 1)**3
Let j(q) be the second derivative of 3*q**5/25 + 109*q**4/15 + 384*q**3/5 + 72*q**2 + 642*q - 2. What is w in j(w) = 0?
-30, -6, -1/3
Let y(g) be the second derivative of g**6/105 - 3*g**5/7 + 277*g**4/42 - 176*g**3/7 - 2420*g**2/7 + 4556*g. Determine t, given that y(t) = 0.
-2, 10, 11
Let c(r) = -6*r - 226. Suppose 0 = 113*p - 89*p + 912. Let w be c(p). Factor -12/11*g**3 - 16/11*g**w + 0*g**4 + 0 + 2/11*g**5 - 6/11*g.
2*g*(g - 3)*(g + 1)**3/11
Factor -2167*f**2 - 1002*f**2 - 71850*f**3 - 4893*f - 4319*f**2 + 69534*f**3 - 156*f**4 - 2019*f - 3*f**5.
-3*f*(f + 2)**2*(f + 24)**2
Let w(c) = -c**2 + c - 1. Let s(g) = -6*g**2 + 3*g - 1. Let m(y) = s(y) - w(y). Let n(o) = -o**2 + 2*o. Let r(p) = m(p) - 4*n(p). Suppose r(z) = 0. Calculate z.
-6, 0
Let h = 34697/9 + -3855. Let j(c) be the second derivative of 42*c + 1/12*c**4 + 1/6*c**2 + 0 - h*c**3. Determine d, given that j(d) = 0.
1/3, 1
Let d(l) be the second derivative of l**4/3 + 6*l**3 + 55*l - 7. Determine z, given that d(z) = 0.
-9, 0
Let u(i) be the second derivative of -i**7/42 - 19*i**6/30 - 19*i**5/5 - 7*i**4 + 706*i. Factor u(x).
-x**2*(x + 2)*(x + 3)*(x + 14)
Determine x, given that 100*x**2 + 8153*x + 7*x**5 - 4153*x - 5 - 10*x**4 + 5 - 315*x**3 - 2*x**5 = 0.
-5, 0, 4, 8
Suppose -6*z - 9 = -21. Suppose -2*g = -j + z*j - 5, -20 = -3*g - 4*j. Determine b so that 0 - 1/2*b**4 + 0*b**2 + 1/4*b**5 + 1/4*b**3 + g*b = 0.
0, 1
Let v(a) be the second derivative of 1/8*a**4 + 3/40*a**5 - 3/2*a**3 + 0 + 0*a**2 - 63*a. What is u in v(u) = 0?
-3, 0, 2
Let n(d) be the first derivative of -7*d**3 + 7/5*d**5 + 111 + 10*d**2 - 4*d - 1/2*d**4. Factor n(x).
(x - 1)**2*(x + 2)*(7*x - 2)
Suppose 11*a - 81 = 7. Suppose 18*b - a*b - 40 = 0. Find x such that -2*x**3 - 2/3*x + 2/3*x**b + 2*x**2 + 0 = 0.
0, 1
Let s = -9837/23 + 108345/253. Let s*j**5 - 2*j**4 + 2*j**2 + 0 - 12/11*j + 6/11*j**3 = 0. Calculate j.
-1, 0, 2/3, 1, 3
Let q(o) be the third derivative of o**8/168 + 4*o**7/7 + 419*o**6/30 - 62*o**5 + 961*o**4/12 - 43*o**2 - 3*o. Factor q(p).
2*p*(p - 1)**2*(p + 31)**2
Suppose -2*h = -4*k + 12, 4*h = h. Factor 1/7*y**k + 1701*y - 27*y**2 - 35721.
(y - 63)**3/7
Let u(r) be the third derivative of -1/120*r**5 + 0*r + 39 + 4/3*r**3 + r**2 + 5/16*r**4. Solve u(x) = 0.
-1, 16
Let b(g) be the first derivative of g**4/2 - 64*g**3 - 97*g**2 + 384. Factor b(u).
2*u*(u - 97)*(u + 1)
Let y be (0 + -12)*1 - (-253 - -238). Find h such that 3/2 - 1/2*h - 3/2*h**2 + 1/2*h**y = 0.
-1, 1, 3
Let d(w) be the second derivative of 0*w**2 - 271*w - 1/36*w**4 + 0*w**3 - 1/126*w**7 + 0 + 1/90*w**6 + 1/60*w**5. What is q in d(q) = 0?
-1, 0, 1
Let g(n) = -17*n**4 - 44*n**3 + 210*n**2 + 15. Let k(p) = -27*p**4 - 67*p**3 + 314*p**2 + 24. Let c(y) = -8*g(y) + 5*k(y). Factor c(z).
z**2*(z - 5)*(z + 22)
Let y be 1/(3/(-30)) + 21 + -9. Let c(v) be the third derivative of 1/540*v**6 + v**y + 0*v + 8/27*v**3 + 1/9*v**4 + 1/45*v**5 + 0. Factor c(n).
2*(n + 2)**3/9
Let o(y) = -41553*y + 290877. Let l be o(7). Factor 0 - l*g**2 + 14/5*g**3 + 4/5*g.
2*g*(g - 2)*(7*g - 1)/5
Let i(k) = -24*k**3 + 96*k**2 - 1200*k + 1028. Let m(j) = -j**3 - 4*j**2 - j + 1. Let s(c) = i(c) - 20*m(c). Factor s(h).
-4*(h - 36)*(h - 7)*(h - 1)
Let c(q) = 7*q**5 - 14*q**4 + 10*q**3 + 48*q**2 - 73*q + 38. Let a(y) = 2*y**5 - y**4 + y**3 - y**2 + y + 2. Let n(s) = 4*a(s) - c(s). Factor n(h).
(h - 1)**3*(h + 3)*(h + 10)
Factor 1054 + 18*w**2 - 96*w**2 - 334 + 110*w**3 - 145*w**3 - 50*w - 557*w**2.
-5*(w - 1)*(w + 18)*(7*w + 8)
Let t = -21 - -23. Factor -9 + 18 + 4*f**3 + 30*f - 71*f**t + 48*f**2.
(f - 3)**2*(4*f + 1)
Suppose 5*x = -12*x + 102. Let v(y) be the third derivative of 0*y - 9/100*y**5 - 1/30*y**3 + 9/200*y**x + 7*y**2 + 0 + 3/40*y**4. Factor v(l).
(3*l - 1)**3/5
Suppose 5*i = 4*h + 51, 5265 - 5246 = 5*i + 4*h. Let 79/4*z**2 + i*z**4 - 2 + 33*z**3 - 3/2*z = 0. What is z?
-4, -1/2, 2/7
Let s(x) = -x**2 - 5*x + 3. Let n be s(0). Factor 0*p**n + 6*p - 6485*p**2 + 6494*p**2 + 3*p**3.
3*p*(p + 1)*(p + 2)
Solve 477/8*c**2 + 1 - 24*c**4 + 22*c**3 - 63/4*c = 0 for c.
-4/3, 1/8, 2
Let k be (-20)/38 + (-470466)/(-126255). Solve -9/5*v**2 + k*v + 4/5 = 0.
-2/9, 2
Let x be (-22)/((-16)/4 - 0 - -2). What is d in 69*d + 60*d**2 + 0*d**4 + 64 - 4*d + 14*d**3 + d**4 + x