w + 1)/15
Let w = 5/7 + -113/168. Let u(z) be the second derivative of -w*z**4 - 5*z + 0*z**3 + 0*z**2 + 1/60*z**6 + 0*z**5 + 0. Factor u(o).
o**2*(o - 1)*(o + 1)/2
Solve -4*w**2 + 13*w**4 - 21*w**3 + 0*w**5 + 3*w**5 - 4*w**5 - 3*w**4 + 28*w = 0 for w.
-1, 0, 2, 7
Let h(z) be the first derivative of 1/4*z**3 + 1/16*z**4 + 6 + 3/8*z**2 + 1/4*z. What is o in h(o) = 0?
-1
Let h(o) be the second derivative of o**7/840 - o**5/40 + 5*o**4/6 + 6*o. Let d(w) be the third derivative of h(w). Solve d(c) = 0.
-1, 1
Let n = 36 - 31. Let -4*p**3 - p**3 - n*p**2 - 10*p**2 = 0. What is p?
-3, 0
Let w(g) be the first derivative of -g**5 - 5*g**4/2 + 65*g**3/3 - 25*g**2 - 364. Solve w(a) = 0.
-5, 0, 1, 2
Factor 1/3*h**2 + 82*h + 5043.
(h + 123)**2/3
Let d = -2 - -5. Suppose -25*s + 23*s + 4 = -t, -3*s + 16 = t. Solve 0 + 6*c - t*c**2 + 2/3*c**d = 0 for c.
0, 3
Let m = 1741 - 1741. Factor 1/6*d**5 + 0 + m*d + 0*d**2 + 0*d**3 - 1/3*d**4.
d**4*(d - 2)/6
Let v(l) = -l**5 - l**3 - l**2 - l. Let u(d) = -9*d**5 - 110*d**4 - 315*d**3 - 395*d**2 - 155*d + 32. Let o(n) = u(n) + 5*v(n). Find b such that o(b) = 0.
-2, 1/7
Let j(x) be the first derivative of x**6/4 - 3*x**5/2 + 3*x**4/2 + 8*x**3 - 24*x**2 + 24*x + 49. Factor j(k).
3*(k - 2)**3*(k - 1)*(k + 2)/2
Factor 86/15*a**4 + 4/15*a - 2*a**5 + 6/5*a**2 - 26/5*a**3 + 0.
-2*a*(a - 1)**3*(15*a + 2)/15
Let i be (-1 - -2) + (-1)/2*-10. Let v(z) = 19*z**2 + 43*z - 49. Let s(a) = -3*a**2 - 7*a + 8. Let o(k) = i*v(k) + 39*s(k). Factor o(y).
-3*(y - 1)*(y + 6)
Let i = 60 + -55. Factor 20*u**2 - 216 - 15*u + 216 - i*u**3.
-5*u*(u - 3)*(u - 1)
Let g = -37 - -61. Suppose 3*n = -n + g. Determine i, given that -2*i + 8*i + 4*i**2 + n*i = 0.
-3, 0
Let b(c) = c**3 + c + 2. Let x(p) = -5*p**3 - 7*p**2 + 24*p - 28. Let z(g) = -4*b(g) - x(g). Factor z(q).
(q - 2)*(q - 1)*(q + 10)
Let -29 - 19 - 24*a + 20*a**2 - 8*a + 4*a**3 = 0. What is a?
-6, -1, 2
Let c be (132/616)/(46/8 + -5). Factor -c - 1/7*n**2 - 3/7*n.
-(n + 1)*(n + 2)/7
Factor -2/5*k**2 - 162/5 + 36/5*k.
-2*(k - 9)**2/5
Factor 2/7*n**3 - 72/7*n**2 - 256/7 + 264/7*n.
2*(n - 32)*(n - 2)**2/7
Suppose 0*y - 2/3*y**2 + 2/9*y**3 + 8/9 = 0. What is y?
-1, 2
Suppose -4/5*f**3 + 356/5*f - 276/5 - 76/5*f**2 = 0. What is f?
-23, 1, 3
Let -29 - 53 - 2 - 21 - 55*z + 10*z**2 = 0. What is z?
-3/2, 7
Let o = 12 - 9. Let f be (-2)/(-9) + -10*(-64)/36. Factor -6*m**2 - f*m - 2/3*m**o - 18.
-2*(m + 3)**3/3
Let v = -6 - -4. Let i = v + 8. Factor 10*b - b - i*b**2 + 2*b**3 - 5*b**3.
-3*b*(b - 1)*(b + 3)
Let t(l) be the second derivative of l**7/4620 + l**6/990 - 5*l**3/6 + 29*l. Let q(b) be the second derivative of t(b). Find p such that q(p) = 0.
-2, 0
Let i(j) = j**3 + 34*j**2 + 37*j + 4. Let q(d) = -33*d**2 - 36*d - 3. Let p(l) = 3*i(l) + 4*q(l). Suppose p(a) = 0. Calculate a.
-1, 0, 11
Let v(h) be the third derivative of -h**6/280 - 3*h**5/140 - 34*h**2 - 1. Factor v(o).
-3*o**2*(o + 3)/7
What is x in 2*x**2 + 203 - 18*x - 85 - 90 = 0?
2, 7
Let t(s) be the second derivative of 0 - 1/36*s**4 - 32/3*s**2 - 8/9*s**3 - 30*s. Factor t(c).
-(c + 8)**2/3
Let x(z) be the second derivative of 1/18*z**3 - 12*z - 1/60*z**5 + 1/90*z**6 + 0 + 0*z**2 - 1/36*z**4. Factor x(j).
j*(j - 1)**2*(j + 1)/3
Let w(h) = -7*h**4 + 69*h**3 - 926*h**2 + 4320*h - 3451. Let q(f) = -f**4 - f**3 + 2*f**2 + 1. Let p(r) = 5*q(r) - w(r). Find y, given that p(y) = 0.
1, 12
Let g(a) = a**4 + 15*a**3 + 43*a**2 + 29*a - 12. Let p(d) = -9*d**4 - 120*d**3 - 345*d**2 - 234*d + 99. Let c(m) = 33*g(m) + 4*p(m). Solve c(l) = 0 for l.
-1, 0, 7
Factor 0 - 3/2*z**2 + 15/2*z**4 + 3*z**5 - 3/2*z + 9/2*z**3.
3*z*(z + 1)**3*(2*z - 1)/2
Let 0 - 360*n**2 - 2019/5*n**3 - 60*n**4 - 12/5*n**5 - 432/5*n = 0. Calculate n.
-12, -1/2, 0
Let b(h) be the second derivative of 0*h**2 - h**3 - 1/180*h**6 + 0*h**4 + 0 - 3*h - 1/60*h**5. Let i(s) be the second derivative of b(s). Factor i(l).
-2*l*(l + 1)
Let q be (0 + -2)*2*35/(-28). Let l(y) = -8*y**3 + 8*y**2 + 11*y. Let a(h) = -7*h**3 + 7*h**2 + 10*h. Let d(f) = q*a(f) - 4*l(f). Let d(g) = 0. Calculate g.
-1, 0, 2
Let z be 1/6*(249 + -121). Factor -32/3 - 16/3*w**3 - z*w - 16*w**2 - 2/3*w**4.
-2*(w + 2)**4/3
Let x(t) be the second derivative of -6*t + 0*t**2 - 1/30*t**3 - 1/30*t**4 - 1/100*t**5 + 0. Solve x(h) = 0.
-1, 0
Let m = -8 - 4. Let o be 27/(-84) + m/(-16). Factor 0*l + 0*l**3 - 3/7*l**4 + 0 + o*l**2.
-3*l**2*(l - 1)*(l + 1)/7
Let b = 36 + -31. Factor -8*a - 12*a + 0*a**3 + 20*a**2 - b*a**3.
-5*a*(a - 2)**2
Suppose 5*r - 2*r - 9 = 0. Let f be (2 + (-20)/15)*r. What is v in -6*v - 3*v**f - v - 3*v - 2*v = 0?
-4, 0
Let q be (22/(-330)*12)/((-8)/5). Factor 0*z + 0 - 3/2*z**2 - q*z**3 + 2*z**4.
z**2*(z - 1)*(4*z + 3)/2
Let d be 115/30 + (-26)/(-12) + -2. Let w(b) be the first derivative of 0*b + d - 1/12*b**3 + 1/4*b**2. Factor w(n).
-n*(n - 2)/4
Let y(w) = 7*w**2 - 11*w + 13. Let l(m) = 3*m**2 - 5*m + 6. Let f(b) = 3*b - 5. Let x be f(3). Let o(j) = x*y(j) - 9*l(j). Find c such that o(c) = 0.
-2, 1
Let l(w) = -2*w - 8. Let i be l(-9). Let -10*q**4 - 5 + 20*q**2 - i*q**3 - 5 + 30*q**5 - 25*q**5 + 5*q = 0. Calculate q.
-1, 1, 2
Let h(w) be the third derivative of -w**6/900 + w**5/75 - w**4/20 - 7*w**3/6 - 10*w**2. Let n(m) be the first derivative of h(m). What is i in n(i) = 0?
1, 3
Let d be 160/(-336) - 128/(-112). Factor 0 + 4*n**2 + 14/3*n - d*n**3.
-2*n*(n - 7)*(n + 1)/3
Let i = -1 - -26. What is j in -20*j**2 + i*j + 2 + 3 - 10 = 0?
1/4, 1
Let k = 69 + -82. Let f be 2/22*(-11 - k). Factor -2/11*n**3 + 0 - f*n**2 + 2/11*n**4 + 2/11*n.
2*n*(n - 1)**2*(n + 1)/11
Solve -87/5*y**2 + 0 - 21/5*y**4 - 81/5*y**3 + 3/5*y**5 - 6*y = 0.
-1, 0, 10
Let h(s) be the third derivative of -s**6/80 + s**4/4 + s**2 - 32. Factor h(f).
-3*f*(f - 2)*(f + 2)/2
Let k(n) = -3*n**2 - 15*n + 10. Let c(p) = -p**2 - 15*p + 10. Let q(h) = 4*c(h) - 3*k(h). Suppose q(z) = 0. Calculate z.
1, 2
Factor -2/7*m**2 + 16/7*m + 24.
-2*(m - 14)*(m + 6)/7
Let t(i) be the third derivative of i**5/60 - 5*i**4/12 + 10*i**3/3 - 8*i**2. Let q be t(8). Solve -2 - 5 + q + z - 5*z - z**2 = 0.
-3, -1
Let t(f) be the first derivative of -f**3/6 - 3*f**2/4 + 14*f - 376. Factor t(c).
-(c - 4)*(c + 7)/2
Let k(j) be the first derivative of 2*j**3/9 - 4*j**2/3 + 2*j - 103. Determine v so that k(v) = 0.
1, 3
Let i(d) be the first derivative of -3 + 1/75*d**6 + 4/25*d**2 - 8/25*d**3 + 0*d - 12/125*d**5 + 13/50*d**4. Find p such that i(p) = 0.
0, 1, 2
Let -24*y**3 - 744*y - 1124*y**2 - 4*y**3 + 16*y**3 = 0. Calculate y.
-93, -2/3, 0
Let f(k) = -5*k**2 - 294*k - 4506. Let l(u) = -70*u**2 - 4115*u - 63085. Let q(w) = -85*f(w) + 6*l(w). Factor q(i).
5*(i + 30)**2
Let g(a) be the first derivative of -1/14*a**4 + 0*a - 5 + 2/21*a**3 + 2/7*a**2. Factor g(m).
-2*m*(m - 2)*(m + 1)/7
Let a(x) be the second derivative of -x**6/120 - 19*x**5/80 - 45*x**4/16 - 425*x**3/24 - 125*x**2/2 - 173*x. Factor a(m).
-(m + 4)*(m + 5)**3/4
Let o = 15 + 17. Let u be 5/(20/8)*(-9)/(-6). Factor o*f**2 + 2*f - 22*f**u + 52*f**4 - 4 - 46*f**3 - 3*f**5 - 11*f**5.
-2*(f - 1)**4*(7*f + 2)
Let 4/5*c + 2/5*c**2 + 0 - 6/5*c**3 + 2/5*c**5 - 2/5*c**4 = 0. What is c?
-1, 0, 1, 2
Factor 0 + 296/7*j**2 - 8/7*j - 2738/7*j**3.
-2*j*(37*j - 2)**2/7
Let m(i) = 17*i**4 + 55*i**3 - 27*i**2 - 155*i + 134. Let u(k) = 6*k**4 + 18*k**3 - 9*k**2 - 51*k + 45. Let a(y) = -3*m(y) + 8*u(y). Factor a(c).
-3*(c - 1)**2*(c + 2)*(c + 7)
Let j(c) be the second derivative of c**4/9 - 128*c**3/9 - 130*c**2/3 - 2*c + 50. Determine m so that j(m) = 0.
-1, 65
Let h(f) be the third derivative of f**5/450 + 8*f**4/45 + 256*f**3/45 - 7*f**2 + 4. Solve h(t) = 0.
-16
Let g(j) be the second derivative of 105/2*j**4 - 5 + 4*j - 270*j**3 - 19/4*j**5 + 540*j**2 + 1/6*j**6. Factor g(w).
5*(w - 6)**3*(w - 1)
Let t(o) be the third derivative of o**8/84 - 2*o**7/75 - o**6/25 + 2*o**5/15 + o**4/30 - 2*o**3/5 - 4*o**2 - 4*o. Determine q so that t(q) = 0.
-1, -3/5, 1
Let n be 276 - (-10)/(7 + -5). Let v = -277 + n. Factor -2/5*a**v - 6/5*a**3 - 6/5*a**2 + 0 - 2/5*a.
-2*a*(a + 1)**3/5
Let p(m) be the second derivative of -m**4/8 + 21*m**3/2 - 252*m. Factor p(c).
-3*c*(c - 42)/2
Let q(z) = 5*z**4 + 16*z**3 + 43*z**2 + 35*z. Let j(u) = 9*u**4 + 32*u**3 + 85*u**2 + 69*u. Let b(n) = 3*j(n) - 5*q(n). Factor b(f).
2*f*(f + 2)**2*(f + 4)
Let 