?
-251, 0, 3
Let d be 1*57/(-15) - (-25)/(-125) - -7. Let f(j) be the first derivative of -1/21*j**d + 19 + 1/7*j**2 + 0*j - 1/28*j**4. Find a, given that f(a) = 0.
-2, 0, 1
Let f be 75 + 4/(-4) - (-5 + 8). Let b = f - 495/7. Factor -b*h**2 + 2*h - 12/7.
-2*(h - 6)*(h - 1)/7
Let g(s) be the first derivative of -s**5/330 + s**4/66 + 28*s**2 + 27. Let i(w) be the second derivative of g(w). Factor i(p).
-2*p*(p - 2)/11
Determine a so that -995*a**3 + 46 - 16 - 53*a + 1006*a**3 + 12*a**2 = 0.
-3, 10/11, 1
Let c be (415/(-498))/((-5)/(-3)) + ((-1000)/112 - -10). Suppose -c*k**3 + 12/7*k + 0*k**2 + 8/7 = 0. Calculate k.
-1, 2
Let p be (-1216)/38*-1 + -29. Factor 0 - i + 1/8*i**p - 7/8*i**2.
i*(i - 8)*(i + 1)/8
Let y(n) = -33*n - 297. Let a be y(-9). Let q(m) = -2*m**3 - 2*m**2 - m + 3. Let w be q(a). What is v in 0*v**2 - 2*v + 0 + 1/2*v**w = 0?
-2, 0, 2
Let b = -4 - -184. Suppose b*x - 161*x = 57. Factor 6/5*k**2 - 6/5 + 3/5*k - 3/5*k**x.
-3*(k - 2)*(k - 1)*(k + 1)/5
Factor -2/3*q**2 + 40*q + 2072/3.
-2*(q - 74)*(q + 14)/3
Let l(s) be the first derivative of 2*s**5/45 - 29*s**4/18 - 70*s**3/3 - 111*s**2 - 228*s - 1330. Solve l(r) = 0 for r.
-3, 38
Let j(h) be the second derivative of -h**4/3 - 232*h**3/3 - 1526*h**2 + 4995*h. Find z, given that j(z) = 0.
-109, -7
Suppose 381/7*h - 150/7 - 45*h**2 + 87/7*h**3 - 3/7*h**4 = 0. What is h?
1, 2, 25
Let l(d) = -d**2 + 25*d + 10. Let u be l(25). Factor -35*s**4 - 8*s + u*s**3 + 33*s**4 + 1 - 12*s**2 + 15.
-2*(s - 2)**3*(s + 1)
Let b(u) = 58*u**3 - 955*u**2 + 1635*u - 336. Let w(v) = -115*v**3 + 1910*v**2 - 3270*v + 665. Let l(z) = 5*b(z) + 2*w(z). Factor l(n).
5*(n - 14)*(3*n - 5)*(4*n - 1)
Suppose -1097 + 1111 = t. Suppose -4 = -4*h + 2*m, -15*h - 5*m = -17*h - t. Factor 9*l**2 + 432 - 108*l - 1/4*l**h.
-(l - 12)**3/4
Let n(l) be the second derivative of -l**4/16 + 5*l**3/2 + 207*l**2/8 + 233*l. Factor n(z).
-3*(z - 23)*(z + 3)/4
Let v = -27 - -31. Determine o, given that -8*o**5 - 14*o**4 + v*o**5 - 20*o**3 - 4*o**4 + 200*o**2 - 14*o**4 = 0.
-5, 0, 2
Suppose -344 = -5*t - 364. Let v be (-1 + (-32)/(-28))/(t/(-14)). Suppose v*h**3 + 0 + 0*h - h**2 = 0. What is h?
0, 2
Let f(b) be the first derivative of -b**4/28 + 10*b**3/21 - 310. Solve f(m) = 0 for m.
0, 10
Suppose f**3 - 32*f**4 - 384 + 36*f**4 - 160*f**2 + 464*f + 0*f**4 + 3*f**3 = 0. Calculate f.
-8, 2, 3
Let j(x) be the first derivative of 8/15*x**3 + 0*x + 12 - 1/10*x**4 - 3/5*x**2. Factor j(z).
-2*z*(z - 3)*(z - 1)/5
Let c = 166321 - 166305. Factor 1/2*u**2 + 9*u + c.
(u + 2)*(u + 16)/2
Determine k so that 6992744 - 6988104 + 298*k**2 - 657*k - k**3 - 1679*k = 0.
4, 290
Let u(b) be the third derivative of 14*b**2 + 0 + 1/48*b**5 + 375/8*b**3 + 0*b + 25/16*b**4. Factor u(h).
5*(h + 15)**2/4
Let z(a) = 12*a + 38. Let t be z(-3). Let u(l) = 3*l**2 + 3*l - 2. Let k be u(1). What is r in -51*r**4 - 8*r - k + t*r - 6*r + 18*r**5 + 42*r**3 + 7 = 0?
-1/2, 1/3, 1
Let r = -253 - -258. Solve -26*u**3 - 180*u**2 - 162*u - 66*u**3 - 22*u**4 + u**5 - 8*u**5 - 54 + 5*u**r = 0.
-3, -1
Let m = 109 - 102. Let u(v) = -1757*v**3 + 721*v**2 + 24*v - 31. Let y(c) = 1171*c**3 - 481*c**2 - 16*c + 21. Let h(z) = m*y(z) + 5*u(z). Solve h(d) = 0 for d.
-1/6, 2/7
Let n(u) be the first derivative of u**7/210 - 2*u**6/45 + u**5/10 - 2*u**3/3 - 7*u + 34. Let w(j) be the third derivative of n(j). Solve w(a) = 0 for a.
0, 1, 3
Let b be (-16)/(-8) - (-1152)/(-594). Let m(p) be the second derivative of 0*p**4 + 1/165*p**6 - 1/11*p**2 + 1/55*p**5 - b*p**3 + 15*p + 0. Factor m(u).
2*(u - 1)*(u + 1)**3/11
Suppose 18/5 + 1/5*q**4 - 19/5*q**2 - 17/5*q + 17/5*q**3 = 0. What is q?
-18, -1, 1
Suppose f = -4*b + 222 - 2, f = -3*b + 217. Determine i, given that -15 - 13*i + 31*i - 211*i**2 + f*i**2 = 0.
1, 5
Suppose 7 = -2*w + 13. Factor 169 - 213*i - 25*i**w + 76 + 35*i + 355*i**2 - 1117*i.
-5*(i - 7)**2*(5*i - 1)
Let o be ((-4)/(-10) + 0)/(9 + 124/(-20)). Factor -5/7*s**3 + 6/7*s**2 - 8/7 + o*s**4 + 4/7*s.
(s - 2)**3*(s + 1)/7
Factor -10552*x**3 - 3449952*x - 804*x**4 + 28*x**5 - 574*x**3 - 32*x**5 - 21875*x**3 - 1306800*x**2 - 21647*x**3.
-4*x*(x + 3)*(x + 66)**3
Suppose 3*c - n = -48 + 50, 2*n = 41 - 33. Factor 0*l**c + 0*l + 0 - 12/5*l**4 + 3/5*l**5 + 12/5*l**3.
3*l**3*(l - 2)**2/5
Let f be (-9)/(-15)*-1 + 1076/36. Let p = f - 242/9. Factor -4/5*x**3 - 28/5*x + 4*x**2 + p.
-4*(x - 3)*(x - 1)**2/5
Let s(c) be the first derivative of 3/4*c**4 + 115 - 8*c**3 + 0*c + 21/2*c**2. Find i such that s(i) = 0.
0, 1, 7
Let j = 578 - 116. Suppose j = -2*d + 468. Factor 0*n**4 + 4/5*n**5 - 8/5*n**d + 0 + 4/5*n + 0*n**2.
4*n*(n - 1)**2*(n + 1)**2/5
Let i(l) = -7*l + 2. Let f(b) = -9*b + 3. Let t(m) = -2*f(m) + 3*i(m). Let q(u) = -u**2 - 22*u + 3. Let k(g) = -3*q(g) + 24*t(g). Factor k(p).
3*(p - 3)*(p + 1)
Let d be 100450/(-196) + 10/4. Let k be (-4)/(-10) - 204/d. Factor 7/10*r - 2/5 + 1/5*r**2 + 1/5*r**4 + 1/10*r**5 - k*r**3.
(r - 1)**3*(r + 1)*(r + 4)/10
Let p(h) be the third derivative of -h**8/10080 + h**7/210 - 9*h**5/10 + 2*h**2 - 45*h. Let u(t) be the third derivative of p(t). Factor u(x).
-2*x*(x - 12)
Factor 0 - 1/2*x**2 - 27/2*x.
-x*(x + 27)/2
Suppose -107*o = -158*o. Let i(x) be the first derivative of 0*x**5 + o*x + 12 + 5/24*x**6 - 5/16*x**4 + 0*x**3 + 0*x**2. Factor i(t).
5*t**3*(t - 1)*(t + 1)/4
Let j(s) = -s**2 + s. Suppose 3*w - 5*f - 14 = 0, 74*w - 4*f - 14 = 73*w. Let i(b) = 8 + 2*b - 5*b + b. Let d(z) = w*j(z) - i(z). Factor d(p).
2*(p - 2)*(p + 2)
Let a = 588 + -613. Let g = a - -25. Solve -3/4*o**5 + 3/2*o**2 + 0*o + g - 3/2*o**4 + 3/4*o**3 = 0 for o.
-2, -1, 0, 1
Let x(l) be the first derivative of -85 + 0*l**2 + 0*l + 0*l**3 - 1/8*l**5 - 1/12*l**6 - 1/32*l**4. Let x(d) = 0. Calculate d.
-1, -1/4, 0
Suppose 3*m = 74 - 68. Solve 244*o - 244*o + o**m = 0.
0
Let h(j) be the first derivative of 5*j**3/3 + 355*j**2/2 + 3990*j + 7548. Factor h(s).
5*(s + 14)*(s + 57)
Let p be 19/76 + (-129)/860. Suppose -p - 2/5*d**4 - 3/10*d + 1/2*d**2 + 3/10*d**3 = 0. Calculate d.
-1, -1/4, 1
Suppose -584/3*y - 85264/3 - 1/3*y**2 = 0. Calculate y.
-292
Let o(w) = 4*w**4 - 8*w**3 + 2*w**2 + 128*w + 148. Let p(q) = -3*q**4 + 5*q**3 - q**2 - 85*q - 98. Let t(u) = -5*o(u) - 7*p(u). What is i in t(i) = 0?
-3, -2, 3
Factor 33/4*l**2 + 11/2*l**3 + 1/4*l**4 - 34*l + 20.
(l - 1)**2*(l + 4)*(l + 20)/4
Factor 832/9*c - 16/3*c**3 + 256/3 + 4/9*c**4 + 4/3*c**2.
4*(c - 8)**2*(c + 1)*(c + 3)/9
Let x(g) be the second derivative of -g**6/90 - 34*g**5/15 - 578*g**4/3 - 5*g**3/2 + 26*g - 2. Let b(v) be the second derivative of x(v). Factor b(f).
-4*(f + 34)**2
Let x = 955 + -943. Suppose x*i - 10*i + 5*q + 20 = 0, 2*i = -q - 4. Factor -5/3*k**2 + 0*k - 25/6*k**3 + i.
-5*k**2*(5*k + 2)/6
Suppose 4*s - 87 = -975. Let z = s + 226. What is g in 0 + 9/2*g**3 + 0*g + 0*g**z - 3/2*g**5 - 3*g**2 = 0?
-2, 0, 1
Let h(z) be the third derivative of -z**6/840 - 51*z**5/140 - 2601*z**4/56 + 16*z**3/3 - 6*z**2 + 4*z. Let k(i) be the first derivative of h(i). Factor k(u).
-3*(u + 51)**2/7
Let n(s) = s**2 + 5. Let h(l) be the second derivative of 1/6*l**3 - 1/2*l**4 - 13*l**2 + 0 + 17*l. Let y(d) = 6*h(d) + 33*n(d). Determine g so that y(g) = 0.
-1, 3
Let t(x) be the third derivative of 25*x**2 + 1/24*x**6 + 0*x + 7/12*x**5 - 5/24*x**4 - 35/6*x**3 + 2. Suppose t(h) = 0. What is h?
-7, -1, 1
Let r(o) = -o**3 - 15*o**2 + 6*o - 158. Let s be r(-16). Suppose 4*q - 6 = f, -s*f + 0*f - 6 = -5*q. Determine p so that -2/3 - 2*p**q - 2*p - 2/3*p**3 = 0.
-1
Let d = 349973/204155 + 1/29165. Determine b, given that 3/7*b**2 + d*b + 0 = 0.
-4, 0
Determine r so that 1/5*r**2 + 136/5*r + 268/5 = 0.
-134, -2
Suppose -2917*s + 2153 + 5165 = 1484. Factor 24/13 - 2/13*f**s - 22/13*f.
-2*(f - 1)*(f + 12)/13
Suppose 3 + 3 = 3*c. Factor v**2 + 48*v**3 + 5*v**c - 33*v**3 - 12*v**3.
3*v**2*(v + 2)
Let t(d) be the first derivative of -d**7/105 - 2*d**6/15 - 8*d**5/15 - 75*d**2/2 - 100. Let j(y) be the second derivative of t(y). Factor j(o).
-2*o**2*(o + 4)**2
Let u = -2/7961 - -71669/79610. Let f(i) be the second derivative of 0 + 1/60*i**4 + 15*i + 1/5*i**3 + u*i**2. Factor f(b).
(b + 3)**2/5
Factor -168/5*j + 4/5*j**3 + 64 - 156/5*j**2.
4*(j - 40)*(j - 1)*(j + 2)/5
Let 3200/3 - 320*v + 14*v**2 - 1/6*v**3 = 0. Calculate v.
4, 40
Let x(r) be the third