- 3*l**4 - 15*l**3 + 476*l**2 - v*l**2.
5*l**2*(l - 2)*(l - 1)
Let i(g) be the third derivative of -49*g**6/24 - 187*g**5/12 - 100*g**4/3 + 30*g**3 + 72*g**2 + 5*g. Suppose i(p) = 0. Calculate p.
-2, 9/49
Factor -32/9*i + 0 - 2/9*i**3 - 16/9*i**2.
-2*i*(i + 4)**2/9
Factor 39*y + 87*y - 508138 + 10*y**3 + y**4 + 508138 - 137*y**2.
y*(y - 7)*(y - 1)*(y + 18)
Let v(h) be the third derivative of h**7/315 + 3*h**6/10 - 19*h**5/30 - 55*h**4/18 - 5*h**2 - 2*h. Factor v(g).
2*g*(g - 2)*(g + 1)*(g + 55)/3
Let l(v) be the second derivative of v**5/30 - 500*v**4 + 3000000*v**3 - 9000000000*v**2 - 2488*v + 2. Determine b, given that l(b) = 0.
3000
Factor -5*q + 1/3*q**3 + 4/3*q**2 - 6.
(q - 3)*(q + 1)*(q + 6)/3
Factor 66*x - 1/6*x**4 + 95/6*x**3 + 196/3*x**2 + 0.
-x*(x - 99)*(x + 2)**2/6
Let r be 2/(-6) - 1452/(-36). Factor 3*x**2 + 278*x + r + 7*x**2 - 2*x**2 + 0*x**2 - 110.
2*(x + 35)*(4*x - 1)
Let i(n) be the second derivative of n**7/1260 - 49*n**6/180 + 2401*n**5/60 + 29*n**4/6 - 90*n. Let p(a) be the third derivative of i(a). Factor p(m).
2*(m - 49)**2
Let c(t) = 14*t**2 + 88*t - 93. Let r(j) = 3*j**2 + 22*j - 23. Let y = -143 - -125. Let i(d) = y*r(d) + 4*c(d). Factor i(w).
2*(w - 21)*(w - 1)
Let v(i) be the first derivative of i**6/27 + 22*i**5/45 + i**4 - 260*i**3/27 - 275*i**2/9 + 250*i/3 + 4781. Find y such that v(y) = 0.
-5, 1, 3
Let t(h) be the second derivative of h**6/120 - 17*h**5/40 + 2*h**4/3 + 17*h**3/12 - 33*h**2/8 + 2*h + 1732. Factor t(z).
(z - 33)*(z - 1)**2*(z + 1)/4
Let r = -1991612/5 + 398348. Factor r - 4/5*b**2 - 124/5*b.
-4*(b - 1)*(b + 32)/5
Let s be -1 - -5 - 4/((-150)/(-80) - (-20)/(-32)). Solve -4/5*g**3 - 6/5 + 16/5*g**2 - 2*g**4 + s*g = 0.
-1, 3/5, 1
Let n(x) be the first derivative of -1/24*x**4 + 20*x + 25 - 1/12*x**3 + 1/2*x**2. Let t(w) be the first derivative of n(w). Let t(l) = 0. Calculate l.
-2, 1
Let o(c) be the first derivative of 11*c**4/12 - 7*c**3/18 - 10906. Factor o(v).
v**2*(22*v - 7)/6
Let q be (-25)/20*2856/(-255) - 12. Factor -1/7*n**3 + 0 + 1/7*n**q + 0*n.
-n**2*(n - 1)/7
Let z be (40/25 - 2) + (-12)/(-5). Factor 16*a**3 + 5*a**z + 0*a**4 - 36*a + 17*a**2 - 2*a**4.
-2*a*(a - 9)*(a - 1)*(a + 2)
Let r(g) = 7*g + 66. Let a be r(-9). Solve 3*n + 21*n**4 - 33*n**2 - 9*n**5 - 3*n - 18*n**a + 12 + 27*n**3 = 0.
-1, -2/3, 1, 2
Let l(a) be the second derivative of 70*a**7/3 + 126*a**6 - 111*a**5/4 + 5*a**4/3 + 37*a + 3. Factor l(t).
5*t**2*(t + 4)*(14*t - 1)**2
Let r = 42 - 32. Suppose -23*v = -18*v - r. Suppose 4*x**3 - 9*x**v + x**2 - 2*x**4 + 4*x**3 = 0. Calculate x.
0, 2
Let a(o) = o**3 - 9*o**2 + 6*o - 15. Let g be a(9). Find m such that g + 41 + 2*m**2 - 74 + 8*m = 0.
-3, -1
Factor -4*a**3 + 64/7*a**2 + 0 - 48/7*a + 4/7*a**4.
4*a*(a - 3)*(a - 2)**2/7
Let f(s) be the second derivative of 0*s**5 + 0 + 0*s**3 - 2/63*s**7 + 4/15*s**6 + 0*s**2 - 32/9*s**4 - 336*s. Factor f(n).
-4*n**2*(n - 4)**2*(n + 2)/3
Let v(g) be the first derivative of -g**4/54 - 4*g**3/27 - 4*g**2/9 - 69*g + 121. Let o(y) be the first derivative of v(y). Determine l so that o(l) = 0.
-2
Suppose -1 = -g + z, 5*g + 31*z - 6214 = -6173. Find r, given that -1/4*r - 3/2 + 1/4*r**g = 0.
-2, 3
Factor 44521 + 1/4*l**2 + 211*l.
(l + 422)**2/4
Let u be ((-156)/20 + 8)/(51/1955) + -7. Factor u - 2/3*s**2 - 2/3*s + 2/3*s**3.
2*(s - 1)**2*(s + 1)/3
Let p(u) be the second derivative of u**6/105 + 32*u**5/35 + 92*u**4/21 - 1280*u**3 + 25200*u**2 - 4204*u. Let p(y) = 0. Calculate y.
-42, 10
Let s be (-154)/22*(4 - (-1)/(5/(-25))). Let m(v) be the second derivative of 0 - 1/6*v**4 + 4*v**2 + v**3 + s*v. Determine p, given that m(p) = 0.
-1, 4
Suppose -y - 1369597 = -3*v, -30*y = -25*y - 10. Let 231*g**2 - 13*g**3 + 8446*g + 9341*g + v + 14*g**3 = 0. What is g?
-77
Determine z so that -30*z - 8*z**4 - 62*z**2 - 3*z**4 - 49*z**3 + 9*z**4 + 44*z**3 - 29*z**3 = 0.
-15, -1, 0
Let q(n) = 0*n**3 - n**3 - 2*n - 484*n**2 + 488*n**2. Let b be q(3). Determine w, given that -25*w + w**2 - 19*w**2 - 3 - 5*w**b - 7 - 2*w**2 = 0.
-2, -1
Let b(d) = 2*d**2 - 902*d - 32. Let f(k) = 32. Let s(h) = b(h) + f(h). Factor s(p).
2*p*(p - 451)
Let c(a) be the first derivative of a**3/18 + 275*a**2/12 - 277*a/3 + 2658. Suppose c(i) = 0. What is i?
-277, 2
Let k be 4/(-7)*((-20)/34)/5. Let l = 6/17 - k. Factor -6/7 - l*m**2 + 2/7*m**3 - 10/7*m.
2*(m - 3)*(m + 1)**2/7
Solve 2/7*s**2 + 392*s + 134456 = 0.
-686
Factor -15/2 - 9/2*p**2 + 3/2*p**3 - 27/2*p.
3*(p - 5)*(p + 1)**2/2
Let l(u) = -14*u**3 - 4*u**2 + 12. Let k(r) = 2*r**3 - r**2 - 2*r - 2. Let w(v) = -6*k(v) - l(v). Factor w(j).
2*j*(j + 2)*(j + 3)
Let m be 2 + (-4)/10*(-90)/36. Solve 120*l**4 + 16*l**5 + 271*l**2 + 127*l**m + 100*l**3 + 9 + 87*l + 70*l**3 = 0.
-3, -1, -1/4
Let m(f) be the second derivative of -f**6/10 - 3*f**5/10 + 27*f**4 - 215*f**3 + 975*f**2/2 - 1779*f - 2. Solve m(r) = 0.
-13, 1, 5
Let o(q) = 129098*q + 258199. Let f be o(-2). Factor -1/2*d**4 - 5/2*d**f + 3*d**2 + 16*d - 16.
-(d - 2)*(d - 1)*(d + 4)**2/2
What is k in -40/3*k**2 - 64 - 500*k**3 + 2192/9*k + 250/9*k**4 = 0?
-4/5, 2/5, 18
Let n(m) be the second derivative of 1/4*m**4 + 0*m**2 + 113*m + 0 - 3/2*m**3. Solve n(i) = 0.
0, 3
Let r be (1*4)/((-66)/(-9) - 6). Let s be 4/6 + r - 3/(-9). Factor -47*w**2 + 9*w - 2*w**3 - s*w**4 + 28*w**2 + 31*w**2 + w**5.
w*(w - 3)**2*(w + 1)**2
Let -7 - 57*y - 15 + 9*y**2 - 6 - 67*y = 0. What is y?
-2/9, 14
Suppose 0 = 173*c + 128*c - 266 - 938. Let h be 16/9*1/4. What is t in 0 + 20/9*t**2 + h*t**c + 2*t**3 + 2/3*t = 0?
-3, -1, -1/2, 0
Let z = -24412/45 - -4886/9. Determine d so that 3/5*d**3 - 12/5*d - 1/5*d**4 + z*d**2 + 8/5 = 0.
-2, 1, 2
Let a = 1 - 1. Suppose 2*z + 3*w - 9 = 13, -z - 3*w + 17 = a. Determine u so that 16*u + 12*u + 20*u**4 - 5*u**z - 20*u**2 - 8*u - 15*u**3 = 0.
-1, 0, 1, 2
Suppose 11*a - 6 = -2*c + 6*a, 0 = -3*c + 3*a + 51. Suppose -c*o + 12*o**2 - 31 - 7*o + 10 + 13 = 0. What is o?
-1/3, 2
Let q(p) be the third derivative of 0*p - 13/20*p**6 - 1/3*p**4 - 54*p**2 - 3/56*p**8 - 31/105*p**7 - 7/10*p**5 + 0 + 0*p**3. Let q(j) = 0. Calculate j.
-1, -4/9, 0
Let x(v) be the second derivative of 11 - 1/6*v**4 + 8/3*v**3 + 12*v**2 - 1/10*v**5 + 4*v. Find h, given that x(h) = 0.
-2, 3
Suppose -2 = -2*y - h, 0 = 4*y + y + h - 8. Let i(n) be the first derivative of -4/3*n**y - 8/3*n - 3 - 2/9*n**3. Find c, given that i(c) = 0.
-2
Let l be 32/(-16) + (18 - 4/(-1)). Let q be (-3 + (-170)/(-90))*(-24)/l. Factor -q*s - 2/3*s**2 + 0 + 4/3*s**3 + 2/3*s**4.
2*s*(s - 1)*(s + 1)*(s + 2)/3
Suppose g + 12 = 4*q, 32*g - 16 = 33*g - 5*q. Suppose -2*l = -g*l - 14*l. Suppose -2/23*r**3 + l*r + 0 + 4/23*r**2 = 0. Calculate r.
0, 2
Let q(b) be the first derivative of 4*b**3/15 - 184*b**2/5 + 144*b + 570. Let q(k) = 0. Calculate k.
2, 90
Let m(y) be the first derivative of y**6/4 - 39*y**5/5 + 135*y**4/4 - 20*y**3 - 273*y**2/4 + 99*y + 9386. Solve m(h) = 0.
-1, 1, 3, 22
Factor 3072/11 - 28*b**2 + 10/11*b**3 + 2176/11*b.
2*(b - 16)**2*(5*b + 6)/11
Let f(s) = -195*s**2 - 377596*s + 126035. Let k(q) = -105*q**2 - 203320*q + 67865. Let c(x) = -20*f(x) + 37*k(x). Let c(m) = 0. What is m?
-1939, 1/3
Suppose 347*o + 239*o + 232*o - 2454 = 0. Factor 3/4*p**o + 765/4*p - 675/4 - 93/4*p**2.
3*(p - 15)**2*(p - 1)/4
Factor -20 - 15 - 17*b**3 - 6*b - 79*b**2 + b**4 - 7 - 97*b.
(b - 21)*(b + 1)**2*(b + 2)
Let i(k) = -k**2 - 5*k + 2. Let z = 207 + -209. Let p(x) = 6*x**2 + 36*x - 15. Let w(d) = z*p(d) - 15*i(d). Factor w(c).
3*c*(c + 1)
Let g = 1273 - 1269. Let o(l) be the third derivative of 1/48*l**g + 0*l**3 + 0*l - 1/120*l**5 + 20*l**2 + 0. Factor o(f).
-f*(f - 1)/2
Let o(u) be the third derivative of -3*u**8/224 + 5*u**7/42 - 19*u**6/80 - 3*u**5/10 - 22*u**2 - 2*u - 5. Factor o(f).
-f**2*(f - 3)**2*(9*f + 4)/2
Let b(i) = -845*i**2 + 410*i - 75. Let n(q) = 2*q - 3. Let t(w) = -b(w) + 10*n(w). Factor t(o).
5*(13*o - 3)**2
Suppose -174*k - 64 + 412 = 0. Let b(p) be the first derivative of 0*p + 1/18*p**6 + 0*p**3 + 0*p**k + 1/12*p**4 - 3 + 2/15*p**5. Suppose b(i) = 0. Calculate i.
-1, 0
Factor 26/7*b + 16/7*b**2 + 2/7*b**3 + 12/7.
2*(b + 1)**2*(b + 6)/7
Let m(w) be the second derivative of -4*w**3 - 106*w + 33/20*w**5 + 0*w**2 - 3/10*w**6 + 3/2*w**4 + 0. Solve m(j) = 0 for j.
-1, 0, 2/3, 4
Find z such that -4/7*z**2 - 14379264/7 -