(j).
3*(j - 2)*(j + 1)
Solve 10/7*u - 2/7*u**2 + 48/7 = 0 for u.
-3, 8
Suppose -126 = -39*z - 49*z + 402. Factor -27 - 1/3*a**2 + z*a.
-(a - 9)**2/3
Let w(d) be the first derivative of 2*d**6 + 12*d**5 + 99/4*d**4 + 0*d + 6*d**2 - 48 + 20*d**3. Determine i so that w(i) = 0.
-2, -1/2, 0
Let s be (-2 + 14/10)*580/(-1392). Factor s*g**2 + 1 - g.
(g - 2)**2/4
Let w(c) be the second derivative of c**7/2520 - c**6/180 + c**5/40 + 11*c**4/12 - 4*c. Let u(p) be the third derivative of w(p). Suppose u(g) = 0. What is g?
1, 3
Let f(o) be the second derivative of o**7/21420 + o**6/6120 - o**5/170 - 25*o**4/12 - 7*o. Let q(c) be the third derivative of f(c). Find u such that q(u) = 0.
-3, 2
Let n(o) = 8*o**4 + 372*o**3 + 23067*o**2 + 476647*o. Let b(g) = 18*g**4 + 744*g**3 + 46135*g**2 + 953291*g. Let a(c) = 3*b(c) - 7*n(c). Factor a(j).
-2*j*(j + 62)**3
Suppose -62 = -3*a - 53. Factor -65 - 21*h - a*h**2 - 43 + 78.
-3*(h + 2)*(h + 5)
Let u(v) = -2*v**4 - 6*v**3 - 14*v**2 - 13*v - 4. Let f(w) = -w**4 - w**2 - w. Let q be (10 - 12)/(4/(-6)*1). Let h(g) = q*f(g) - 3*u(g). Factor h(d).
3*(d + 1)**2*(d + 2)**2
Let d(c) be the third derivative of -c**5/150 + 7*c**4/30 + 74*c**2 + 1. Factor d(t).
-2*t*(t - 14)/5
Let r = 1539959/1428105 - -103/21315. Let t = r - -4/67. Solve -4/7 - t*x + 0*x**2 + 8/7*x**3 + 4/7*x**4 = 0 for x.
-1, 1
Let t(o) be the second derivative of 9*o**7/280 - 3*o**6/40 + 3*o**5/40 - o**4/24 + o**3/2 + 12*o. Let f(l) be the second derivative of t(l). Factor f(h).
(3*h - 1)**3
Let f(j) be the first derivative of -2*j**5/45 - 8*j**4/9 + 74*j**3/27 + 16*j**2/9 - 8*j - 215. Suppose f(z) = 0. Calculate z.
-18, -1, 1, 2
Factor -52*l**2 + 19*l**3 + 0*l**4 + 175*l**2 - 51*l**2 - 24*l**2 + l**4.
l**2*(l + 3)*(l + 16)
Let q be (-99)/(-18) - 12/8. Let m(h) be the third derivative of 1/180*h**6 + 1/90*h**5 + 0 + 3*h**2 + 0*h + 1/108*h**q + 1/945*h**7 + 0*h**3. Factor m(s).
2*s*(s + 1)**3/9
Let l(a) be the third derivative of -1/240*a**5 + 0*a**4 - 1/840*a**7 - 12*a**2 + 0 - 1/240*a**6 + 0*a**3 + 0*a. Factor l(p).
-p**2*(p + 1)**2/4
Solve 2120*z**2 - 25*z**5 - 148*z**4 - 3*z**5 - 40*z**3 - 2120*z**2 = 0.
-5, -2/7, 0
Factor 3*w**4 - 4 + 24*w**2 + 3 + 32*w - 7*w**4 + 13.
-4*(w - 3)*(w + 1)**3
Suppose 0 = -3*u + 2*g + 10, u + g + 0*g - 10 = 0. Let n(o) be the third derivative of 0*o**4 - 1/105*o**5 - 1/84*o**u + 0 + 7*o**2 + 0*o**3 + 0*o. Factor n(i).
-2*i**2*(5*i + 2)/7
Let p(f) be the third derivative of f**8/1344 + f**7/168 + f**6/72 + 11*f**4/24 + 13*f**2. Let d(v) be the second derivative of p(v). Let d(q) = 0. Calculate q.
-2, -1, 0
Let r(v) = v**3 + 5*v**2 - 6*v + 10. Let m be r(7). Let u = 6120/11 - m. Suppose 0*l + 2/11*l**4 + 2/11*l**2 + 0 + u*l**3 = 0. Calculate l.
-1, 0
Suppose -4*g = -8*g + 76. Let 2*j**3 - 7*j**3 + 19*j**2 - g*j**2 + 5*j = 0. Calculate j.
-1, 0, 1
Let d(c) be the first derivative of -1/39*c**6 + 11 + 0*c - 3/26*c**4 - 2/39*c**3 + 0*c**2 - 6/65*c**5. Find o, given that d(o) = 0.
-1, 0
Let n be (-4)/12*0/7. Let x(d) be the first derivative of 0*d**3 - 1/14*d**4 + 0*d**2 + 7 + n*d. Suppose x(p) = 0. What is p?
0
Let w(t) be the third derivative of -t**6/180 - t**5/6 + 500*t**3/9 + 167*t**2. Factor w(m).
-2*(m - 5)*(m + 10)**2/3
Let p be 702/28 + 87/203. Let q(f) be the first derivative of 16*f**3 - 4 + 7/2*f**6 + 78/5*f**5 - 6*f + p*f**4 - 3/2*f**2. Solve q(v) = 0 for v.
-1, 2/7
Let f = -1220 - -3662/3. Factor f*l**3 + 0*l + 0 - 4/9*l**2.
2*l**2*(3*l - 2)/9
Let h(i) be the third derivative of -i**8/3360 + 11*i**7/5040 - i**6/288 - i**5/120 + 3*i**4/8 + 8*i**2. Let g(x) be the second derivative of h(x). Factor g(b).
-(b - 2)*(b - 1)*(4*b + 1)/2
Let x(g) be the second derivative of g**5/5 - g**4 - 6*g**3 - 10*g**2 - 246*g. Let x(b) = 0. What is b?
-1, 5
Determine n so that -45*n**3 - 480*n**2 + 15*n**3 + 17*n**3 - 8243*n + 22643*n + 17*n**3 = 0.
0, 60
Let y(j) be the third derivative of -j**8/6720 + j**7/2520 + j**6/720 - j**5/120 + 35*j**4/24 + 10*j**2. Let q(a) be the second derivative of y(a). Factor q(u).
-(u - 1)**2*(u + 1)
Let y(o) be the third derivative of -o**6/75 + 17*o**5/75 - 16*o**4/15 + 8*o**3/5 + 48*o**2 + 4*o. What is u in y(u) = 0?
1/2, 2, 6
Let a(z) be the third derivative of 1/4*z**3 - 1/120*z**5 + 0*z + 1/24*z**4 + 0 + 5*z**2. Suppose a(i) = 0. Calculate i.
-1, 3
Let z(m) be the third derivative of -5*m**9/6048 + m**8/224 - m**7/112 + m**6/144 - 7*m**3/6 + 7*m**2. Let p(k) be the first derivative of z(k). Solve p(f) = 0.
0, 1
Factor 1/6*z**2 + 0*z + 0 - 1/6*z**3 + 1/6*z**5 - 1/6*z**4.
z**2*(z - 1)**2*(z + 1)/6
Let a = 29215/27 - 1082. Let j(x) be the third derivative of 0 + 0*x + 7*x**2 + 1/945*x**7 + 0*x**3 - 1/108*x**6 - a*x**4 + 4/135*x**5. Factor j(b).
2*b*(b - 2)**2*(b - 1)/9
Let i = 1/2 - 1/3. Let r(x) be the first derivative of 1/20*x**5 - 1/4*x**2 + 1/4*x - 1/12*x**6 + 1/4*x**4 + 4 - i*x**3. Find u, given that r(u) = 0.
-1, 1/2, 1
Suppose -2*f - 12 = -4*t, 0 = -3*f + 2*t - 0*t - 10. Let z be 1 + 3*f/(-6). Determine l, given that 4*l + 2 - 8 + 8 + z*l**2 = 0.
-1
Let h(v) be the first derivative of -v**6/3 - 2*v**5 - 3*v**4 + 4*v**3/3 + 7*v**2 + 6*v - 220. Factor h(m).
-2*(m - 1)*(m + 1)**3*(m + 3)
Suppose -2*s = -3*a + 19, -s + 5*s + 32 = 4*a. Factor -2*k**3 + 26*k**2 - 41*k**2 + 21*k**2 - k**a.
-3*k**2*(k - 2)
Let z(v) = 4*v**3 - 41*v**2 + 144*v + 7. Let n(h) = -2*h**3 + 21*h**2 - 72*h - 3. Let b(f) = 7*n(f) + 3*z(f). Factor b(r).
-2*r*(r - 6)**2
Let y = -23 + -33. Let p = y - -83. Factor 28*w**4 - 2*w**5 - p*w**4 + w**5.
-w**4*(w - 1)
Let x(d) = -d + 7. Let b be x(5). Factor 2*a**2 + 0*a**5 - 21*a + 20*a - b*a**4 + a**5.
a*(a - 1)**3*(a + 1)
Let f be (-5)/(-25 + (-456)/(-19)). Find d, given that 1/5*d**f - 2/5*d**3 + 3/5 - 6/5*d**2 + 1/5*d + 3/5*d**4 = 0.
-3, -1, 1
Factor -1/2*k**2 + 107*k - 11449/2.
-(k - 107)**2/2
Let h be 27898/7659 - (-10)/(-115). Factor -2/9*f**3 - h*f - 16/9*f**2 + 0.
-2*f*(f + 4)**2/9
Let g(k) be the first derivative of 4*k**5/5 + 6*k**4 + 52*k**3/3 + 24*k**2 + 16*k + 16. Solve g(l) = 0.
-2, -1
Let n(d) be the second derivative of 5*d**4/12 + 505*d**3/6 - 255*d**2 - 177*d. Factor n(g).
5*(g - 1)*(g + 102)
Let y = -4843519/102 + 47484. Let i = -5/34 - y. Factor -2/3*s + i - 2/3*s**2.
-2*(s - 1)*(s + 2)/3
Let a be (-3 - 0)*104/6. Let f = a - -158/3. Let -4/9*h**3 - f*h**2 + 0 + 4/9*h = 0. Calculate h.
-2, 0, 1/2
Let n = -7 - -9. Suppose 5*g - 3 = 7. Factor -2*j**4 + 2*j**g + 0*j**4 + j**3 + 0*j + n*j**5 - 7*j**3 + 4*j.
2*j*(j - 2)*(j - 1)*(j + 1)**2
Let w be 260/(-117) + -1 + 5. Let r(l) be the first derivative of -5/4*l**4 + w*l**3 - 2/3*l + 5 + 4/15*l**5 - 1/2*l**2. Let r(f) = 0. Calculate f.
-1/4, 1, 2
Let r = 5110 - 97088/19. Find z, given that -r*z**2 - 72/19 + 24/19*z = 0.
6
Let u = 4624/8043 + -4/1149. Let 2/7*w**3 - 10/7*w - 6/7*w**2 - u + 2/7*w**4 = 0. Calculate w.
-1, 2
Let k(h) be the first derivative of -2*h**7/105 + 4*h**6/15 - 6*h**5/5 + 18*h**3 + 14*h**2 + 24. Let i(r) be the second derivative of k(r). Solve i(g) = 0.
-1, 3
Factor 4*l**3 - 25*l + 9*l + 3*l**2 + l**2 - 18 + 2.
4*(l - 2)*(l + 1)*(l + 2)
Let n(p) be the second derivative of -p**5/150 - p**4/30 - p**3/15 + 13*p**2/2 + 11*p. Let d(o) be the first derivative of n(o). Factor d(r).
-2*(r + 1)**2/5
Let q(p) = -3*p - 7. Let s = -79 + 76. Let o be q(s). Suppose 0 + 9*h**3 + 1/4*h - 3*h**o = 0. Calculate h.
0, 1/6
Let w(n) be the second derivative of n**5/20 - 17*n**4/6 + 65*n**3/6 - 16*n**2 + 373*n. Factor w(x).
(x - 32)*(x - 1)**2
Let 98/9*g**4 + 278/9*g**2 + 2/9*g**5 + 94/3*g**3 + 0 + 92/9*g = 0. What is g?
-46, -1, 0
Let a be -3 - 123/(-39) - (-472)/6903. Let o(d) be the first derivative of -a*d**3 + 3/4*d**2 + 10 - 1/3*d. Factor o(b).
-(b - 2)*(4*b - 1)/6
Suppose 25 = -3*v - 17. Let j be (3 + 28/(-8))*v. Factor -2*u**5 - j*u**4 - 6*u**4 - 32*u**2 + u**4 - 18*u - 28*u**3 - 4.
-2*(u + 1)**4*(u + 2)
Let p(g) = -7*g**3 + 31*g**2 - 71*g + 44. Let w(q) = 12*q**3 - 60*q**2 + 141*q - 88. Let y(c) = 5*p(c) + 3*w(c). Determine j, given that y(j) = 0.
1, 2, 22
Suppose -56 = -7*c + 35. Factor -v - 5*v**3 + 3*v - 10*v**2 + c*v.
-5*v*(v - 1)*(v + 3)
Suppose -71*a - 7*a + 592 = 70*a. What is o in -40 - 280*o - 760*o**3 - 125/2*o**5 - 725/2*o**a - 700*o**2 = 0?
-2, -1, -2/5
Let q(r) = r**3 - 31*r**2 + 16*r + 1222. Le