 What is j?
-1/4, 169
Let f(n) be the second derivative of 1/360*n**6 + 0*n**2 - n**3 - 1/120*n**5 + 3*n - 1/12*n**4 + 0. Let i(m) be the second derivative of f(m). Factor i(b).
(b - 2)*(b + 1)
Let w(m) be the second derivative of -m**6/195 - 28*m**5/65 - 127*m**4/78 + 7320*m**3/13 + 22032*m**2/13 - 62*m - 15. Find f such that w(f) = 0.
-36, -1, 17
Let j be -9 - (-108)/(-24)*(-3 - (-5 - -4)). What is h in j - 10/9*h**4 + 2/9*h**5 + 2/9*h**3 + 14/3*h**2 - 4*h = 0?
-2, 0, 1, 3
Factor -58/3*k**2 + 0 + 0*k + 59/3*k**3 - 1/3*k**4.
-k**2*(k - 58)*(k - 1)/3
Let x(i) = i**2 + 7*i + 31. Let j be x(-4). Suppose -33*c**3 + 56*c - 6*c**2 + 16 + 2*c**2 + j*c**3 = 0. What is c?
-2, -2/7, 2
Let o(y) be the second derivative of 0*y**2 - 33*y + 21/20*y**5 + 0*y**3 + 1/2*y**6 + 3/4*y**4 - 2 + 1/14*y**7. Factor o(b).
3*b**2*(b + 1)**2*(b + 3)
Suppose -13*r + 357 - 2736 = 0. Let f = r + 186. Let 44/5*x + 8/5*x**2 - x**f + 16/5 = 0. Calculate x.
-2, -2/5, 4
Let d(o) be the second derivative of o**4/15 + 2*o**3/3 + 12*o**2/5 + 592*o. Let d(h) = 0. What is h?
-3, -2
Let t = 584 + -61903/106. Let s = 26/53 + t. Suppose s*p**2 - 1/4*p**3 - 1/4*p + 0 = 0. Calculate p.
0, 1
Let p(n) = -n**3 + 9*n**2 - 11*n - 15. Let d be p(7). Factor 2*x**3 + 4*x**3 - 3*x**3 - 10*x - 2*x**3 + d*x.
x*(x - 2)*(x + 2)
Let h(w) be the second derivative of 0 - 1/4*w**4 + 2*w**2 - 48*w + 0*w**3 + 1/20*w**5. Factor h(f).
(f - 2)**2*(f + 1)
Let s be (-3)/(2/5*(-825)/(-308)) - (-5 - -1). Factor -22/15*n**2 - s*n + 4/15.
-2*(n + 1)*(11*n - 2)/15
Let t(g) = -1 + 10*g - 9*g + 2 + g**2. Suppose -h - 18 = -24. Let w(d) = -d**3 + 3*d**2 - 10*d + 2. Let s(a) = h*t(a) + 3*w(a). Suppose s(l) = 0. What is l?
1, 2
Suppose 5*s - 6*s + 2 = -4*z, 0 = -2*z - 2*s + 4. Let g(a) be the second derivative of 0*a**2 + 0*a**3 - 20*a - 1/24*a**4 + 0*a**5 + z + 1/60*a**6. Factor g(m).
m**2*(m - 1)*(m + 1)/2
Let y be (2/(-5))/(3/(-15)). Suppose -5*a - 45 = -5*r, r - 3*r + y = 2*a. Determine x so that -5*x**2 + 2 + r - 4 - 4*x + 6*x**2 = 0.
1, 3
Determine w so that -80*w**2 - 6/7*w**5 + 264/7*w - 642/7*w**3 + 0 - 160/7*w**4 = 0.
-22, -3, -2, 0, 1/3
Let s be (919 + -919)/(3/2*4/(-3)). Factor 8*f + 18*f**2 + 9/2*f**4 + 14*f**3 + 1/2*f**5 + s.
f*(f + 1)*(f + 2)**2*(f + 4)/2
Let u be 0/((-22)/(20 + -18)). Let z(l) be the first derivative of 1/4*l**4 + u*l**3 + 2*l - 3/2*l**2 + 11. Factor z(f).
(f - 1)**2*(f + 2)
Let c(o) = o**3 - 55*o**2 + 78*o - 126. Let n be c(54). Let q be (4/(-33))/((-39)/n). Solve 7/11*u**2 + q*u - 12/11 = 0 for u.
-6, 2/7
Let i(l) be the first derivative of -107*l**3/3 - 374*l**2 + 7*l - 3702. Factor i(j).
-(j + 7)*(107*j - 1)
Suppose 1269*a + 31 = 1247*a + 97. Let c(q) be the second derivative of 1/85*q**6 - 28*q + 0 - 1/17*q**5 - 4/51*q**4 + 0*q**a + 0*q**2. Factor c(u).
2*u**2*(u - 4)*(3*u + 2)/17
Let x(t) be the first derivative of -51/5*t**2 + 867/5*t + 1/5*t**3 - 243. Suppose x(q) = 0. Calculate q.
17
Let h = 4216 - 2609705/619. Let j = 621/1238 + h. Factor 3/2 + j*b**4 - b + b**3 - 2*b**2.
(b - 1)**2*(b + 1)*(b + 3)/2
Let l(u) be the third derivative of -3*u**8/112 - 2*u**7/7 + 12*u**6/5 + 36*u**5 + 54*u**4 - 871*u**2. Determine r, given that l(r) = 0.
-6, -2/3, 0, 6
Let g(p) be the third derivative of -1/45*p**3 + 1/90*p**4 - 100*p**2 + 0 - 1/450*p**5 - p. Let g(t) = 0. Calculate t.
1
Let j = -13 - -63. Let v = 53 - j. Factor 1630 + 6*q**v - 2*q**5 - 1630 + 4*q - 10*q**2 + 2*q**4.
-2*q*(q - 1)**3*(q + 2)
Let f(k) be the first derivative of -1/3*k**3 + 108 + 28*k + 27/2*k**2. Factor f(i).
-(i - 28)*(i + 1)
Let s(j) = 3*j**3 + 698*j**2 + 38980*j - 80740. Let u(k) = 3*k**3 + 700*k**2 + 38981*k - 80741. Let r(l) = 5*s(l) - 4*u(l). Factor r(y).
3*(y - 2)*(y + 116)**2
Let q(r) be the third derivative of -r**5/20 + 18*r**4 + 146*r**3 - r**2 - 35. Factor q(l).
-3*(l - 146)*(l + 2)
Suppose 0 = -9*y + 5*y. Let n(l) = 27*l + 4. Let f be n(y). Determine g, given that 0*g**2 - 1/6*g**3 - 1/6*g**f + 0*g + 0 = 0.
-1, 0
Let z = -739 + 739. Let p(t) be the third derivative of 1/80*t**5 + z*t + 1/2*t**3 - 5/32*t**4 - 9*t**2 + 0. Determine d so that p(d) = 0.
1, 4
Determine k so that -289/4*k**2 - 2916 + 918*k = 0.
108/17
Let l(m) be the second derivative of 6 + 1/8*m**4 + 9*m - 3/4*m**3 + 3/2*m**2. Factor l(o).
3*(o - 2)*(o - 1)/2
Let d = 90 + -45. Suppose -3*p + 4*r + 30 = 0, 0 = -0*p + 5*p - 5*r - d. Factor 8*w**2 - 7 + 1 + 3*w**3 + 4*w + p.
w*(w + 2)*(3*w + 2)
Let -30/13*t**3 + 22/13*t**4 + 0*t + 6/13*t**5 - 126/13*t**2 + 0 = 0. What is t?
-3, 0, 7/3
Let k = -378 - -387. Factor -k*f**2 + 306*f**3 + 30 - f**2 + 24*f - 311*f**3 + f.
-5*(f - 2)*(f + 1)*(f + 3)
Let i(z) be the third derivative of -z**6/24 - 19*z**5/12 - 35*z**4/2 + 2*z**2 + 297. Factor i(m).
-5*m*(m + 7)*(m + 12)
Let v(k) be the first derivative of 5*k**4/12 + 5*k**3/2 - 45*k**2 - 272*k + 271. Let b(z) be the first derivative of v(z). Find y such that b(y) = 0.
-6, 3
Let b be (-9)/(9 + 276/(-23)). Let w(o) be the third derivative of -b*o**3 - 18*o**2 + 1/8*o**4 + 0 + 1/40*o**6 + 1/5*o**5 + 0*o. Factor w(x).
3*(x - 1)*(x + 2)*(x + 3)
Let b be 18*(1 - (30/(-12) - -3)). Suppose 7*s + 5*u + 26 = b*s, 0 = 4*s + 4*u - 80. Determine n, given that 12 - s*n - 3/2*n**3 + 9*n**2 = 0.
2
Suppose 0 = -164*q - 3545 + 4037. Let o = -6 + 8. Factor 14/9*k**o + 2/9 + 10/9*k + 2/3*k**q.
2*(k + 1)**2*(3*k + 1)/9
Let p(d) = -14*d - 639. Let c be p(-28). Let f = -245 - c. What is o in -1/2*o**4 - f + 6*o + 3*o**3 - 13/2*o**2 = 0?
1, 2
Let q(t) = -3*t**3 + t**2 - 4*t + 1. Let r(m) = -6*m**4 + 54*m**3 - 7*m**2 - 95*m - 91. Let k(u) = 7*q(u) + r(u). Solve k(j) = 0 for j.
-1, 7/2, 4
Factor 1042 + 15*k**2 - 17*k**2 - 88*k - 1362.
-2*(k + 4)*(k + 40)
Let l = -4118 + 5997. Let t = 7517/4 - l. Factor -t*y**2 + 1/2*y + 0.
-y*(y - 2)/4
Let g be ((-1)/((-50)/(-920)))/((-4)/30). Suppose 0 = g*m - 97*m - 328. Find l such that -m - 12*l - 9/2*l**5 + 15/2*l**2 - 3/2*l**4 + 29/2*l**3 = 0.
-1, 4/3
Let s(c) = 25*c**3 - 1712*c**2 - 9570*c + 11. Let k(h) = 5*h**3 - 344*h**2 - 1915*h + 2. Let b(m) = -11*k(m) + 2*s(m). Factor b(u).
-5*u*(u - 77)*(u + 5)
Suppose f - 12*c - 4 = -13*c, 0 = -5*f - 2*c + 20. Factor -p + 312*p**3 + p - 10*p**2 - 5*p**f - 297*p**3.
-5*p**2*(p - 2)*(p - 1)
Let d be 20*3*9/(-6 + 42). Let u(m) = m**2 - 4*m - 163. Let t be u(d). Factor 3*r**t + 2*r + 1/2 + 1/2*r**4 + 2*r**3.
(r + 1)**4/2
Let r be (-26)/(-15) - (70/75)/7. Suppose 4*s - c - 853 + 842 = 0, -3 = -3*s - c. Factor 12/5*a**s + 36/5*a - 16/5*a**3 + r.
-4*(a - 2)*(a + 1)*(4*a + 1)/5
Let u(i) be the third derivative of i**6/780 + 1471*i**5/130 + 2163841*i**4/52 + 3183010111*i**3/39 + 711*i**2. Determine v, given that u(v) = 0.
-1471
Factor 0 + 27/4*x**2 + 33/2*x - 3/4*x**3.
-3*x*(x - 11)*(x + 2)/4
Let h(q) = q**3 - 9*q**2 - 17*q - 31. Let u be h(11). Let k be 2 - (u/36)/((-21)/(-54)). Factor -8/7*b + 0 - k*b**2.
-2*b*(b + 4)/7
Let n(d) be the third derivative of -d**7/70 + d**6/40 + 7*d**5/10 - 3*d**4 + 468*d**2. Let n(p) = 0. What is p?
-4, 0, 2, 3
Factor 552/5*k + 0 - 2/5*k**3 + 110*k**2.
-2*k*(k - 276)*(k + 1)/5
Suppose 1161 = -5*j - 1424. Let p = -515 - j. Factor 3/4*d**p - 9/2 - 15/4*d.
3*(d - 6)*(d + 1)/4
Let q(n) be the first derivative of 5*n**4/8 + 595*n**3/6 - 455*n**2 + 610*n - 1673. Suppose q(v) = 0. Calculate v.
-122, 1, 2
Let x be 20/(-10) + (3 - -17)/4. Suppose 81*a - 16*a**5 + 3 + 211*a**2 + x + 340*a**5 + 999*a**3 + 1053*a**4 + 206*a**2 = 0. What is a?
-2, -1/3, -1/4
Suppose -62*y - 5*t - 13 = -58*y, 2*y + 9 = -3*t. Let x(b) be the second derivative of 0 + 0*b**y - 16*b + 3/16*b**2 - 1/32*b**4. Suppose x(g) = 0. Calculate g.
-1, 1
Let a be 6/(-76)*8/(-3). Let i be (330/(-25) - -13)*(-1 + 1). Factor 10/19*r**3 + i - a*r**2 + 0*r.
2*r**2*(5*r - 2)/19
Let g(t) be the second derivative of -125*t + 67*t**5 - 4000/3*t**3 + 0 + 800/3*t**4 - 5000*t**2 + 29/6*t**6 + 5/42*t**7. Suppose g(d) = 0. What is d?
-10, -1, 2
Let n(d) = -3*d + 50. Let z be n(14). Suppose -z = -12*x + 16. Factor -1/2*v**x - 3*v - 9/2.
-(v + 3)**2/2
Let 396/5*d + 416/5*d**2 - 4 = 0. What is d?
-1, 5/104
Solve 112*d**3 - 12*d**3 + 2*d**4 + 17*d**2 + 2*d**4 - 17*d**2 = 0 for d.
-25, 0
Suppose 0 = -37*k + 3414 - 3414. Let i(q) be the third derivative of 0*q**3 - 8*q**2 + 0*q + k - 1/90*q**5 + 0*q**4. What is x in i(x) = 0?
0
Let 