et p = -3913/2 - -1957. Factor p*q**2 + 1/2*q**4 + 0 + 0*q - q**3.
q**2*(q - 1)**2/2
Let y(n) be the second derivative of 0 + 1/40*n**5 + 7/72*n**4 - 1/180*n**6 + 34*n - 3/2*n**2 - 5/12*n**3. Factor y(d).
-(d - 3)**2*(d + 1)*(d + 2)/6
Let k(m) be the second derivative of 0 + 0*m**3 + 1/33*m**4 + 0*m**2 - 19*m + 16/165*m**6 + 1/33*m**7 + 1/10*m**5. Factor k(j).
2*j**2*(j + 1)**2*(7*j + 2)/11
Let j(r) be the third derivative of -r**8/48 - 2*r**7/105 + 41*r**2. Factor j(b).
-b**4*(7*b + 4)
Suppose 5*l + 350 = -2*a, -2*a - 2*l = -0*a + 344. Let r = -168 - a. Determine t, given that -5/4*t - 1/2 + 3*t**r = 0.
-1/4, 2/3
Let k(j) be the third derivative of j**8/1008 - j**7/126 + j**6/360 + 13*j**5/180 - j**4/36 - 4*j**3/9 - j**2 - 8*j. Find o, given that k(o) = 0.
-1, 1, 2, 4
Suppose -5*p + 255 = -4*x, -x - 54 = -4*p - 4. Let u = x - -70. Determine v so that 0*v + u*v**2 + 3/5*v**3 + 0 = 0.
0
Let z = -48 + 62. Determine d, given that -21*d**3 - 50 - z*d - 56*d - 22*d**2 + 19*d**3 = 0.
-5, -1
Let k(m) be the second derivative of -6*m**6/5 - 29*m**5/5 - 8*m**4 - 8*m**3/3 + 51*m. Factor k(v).
-4*v*(v + 1)*(v + 2)*(9*v + 2)
Let x(m) = -2*m. Let f(d) = d. Let s(n) = -3*f(n) - x(n). Let w be s(-2). Suppose 0 - 2*u**2 + 0*u**2 - u**w + 3 = 0. What is u?
-1, 1
Let i(c) be the first derivative of 4*c**3/3 - 16*c**2 + 64*c - 44. Factor i(a).
4*(a - 4)**2
Let n(f) be the second derivative of f**5/190 - f**4/57 + 49*f. Factor n(q).
2*q**2*(q - 2)/19
Let r(k) be the second derivative of -5*k**4/3 - 28*k**3 - 32*k**2 - 35*k + 2. Suppose r(i) = 0. Calculate i.
-8, -2/5
Suppose 80/9 + 112/9*v - 212/9*v**2 + 20/9*v**3 = 0. Calculate v.
-2/5, 1, 10
Let f be -8 + 190/10 + -9. Let s(a) be the first derivative of -6 + 1/6*a**4 - 2/3*a + 2/9*a**3 - 1/3*a**f. Factor s(d).
2*(d - 1)*(d + 1)**2/3
Let x = 18 - 16. Factor -11 + 5*y**x - 10*y + 9 - 13.
5*(y - 3)*(y + 1)
Let l(p) = p**2 - 10*p + 11. Let g be l(9). Factor -8*r - 8*r**4 + r**3 + 12*r**g - r**4 - 3*r**4 + 3*r**3 + 4*r**5.
4*r*(r - 2)*(r - 1)**2*(r + 1)
Let q = 82119/5 + -16353. Let w = 71 - q. Factor -1/5*h**2 - 2/5*h - w.
-(h + 1)**2/5
Suppose 5*j - 5 = 0, -5*h - 5*j + 35 = -0*j. Let p(v) be the third derivative of -2*v**3 + 0 - h*v**2 - 1/20*v**5 + 1/2*v**4 + 0*v. Factor p(u).
-3*(u - 2)**2
Let i(c) be the second derivative of -2/9*c**3 + 0 + 1/3*c**2 - 1/45*c**6 + 1/15*c**5 - 9*c + 0*c**4. Find u such that i(u) = 0.
-1, 1
Let q be -1 + (-27)/(-6) - (-69)/(-138). Solve -16/7*w - 19/7*w**q - w**4 - 4/7 - 1/7*w**5 - 25/7*w**2 = 0 for w.
-2, -1
Let v(h) = -h**2 + 2. Let q be v(0). Factor 4*z**4 - 28*z + 7 + 36*z**2 + 3 - q - 20*z**3.
4*(z - 2)*(z - 1)**3
Let w(t) be the first derivative of -2*t**3/9 + 29*t**2/3 - 19. Determine c so that w(c) = 0.
0, 29
Determine h so that 3*h - 4*h**3 + h - 16*h**4 + 42*h**4 + 2*h**2 - 25*h**4 - 3 = 0.
-1, 1, 3
Factor 46208/7 + 608/7*h + 2/7*h**2.
2*(h + 152)**2/7
Let q(s) = s**3 - 10*s**2 - 4*s + 40. Let j be q(10). Factor 0*m + 1/2*m**2 + j.
m**2/2
Let h be (8/(-144))/((-6)/9). Let t(u) be the third derivative of 0 + 1/7*u**3 + 1/420*u**6 + h*u**4 + 3*u**2 + 0*u + 1/42*u**5. Factor t(v).
2*(v + 1)**2*(v + 3)/7
Suppose 5*p + 18 = z, 5*z + 5*p = 3*p + 9. Let n be ((-4)/(-6))/(z/18). Factor -2*h**2 + 10/3*h - 2/3*h**3 + 2/3*h**n - 4/3.
2*(h - 1)**3*(h + 2)/3
Let b = -652 - -654. Factor -5*c - 37/4*c**b - 9/4*c**4 - 1 - 15/2*c**3.
-(c + 1)**2*(3*c + 2)**2/4
Suppose 5*o - 9 = 21. Suppose -o*g - 10 = -34. Factor -v + 0 + 3/2*v**2 - 1/2*v**g + 0*v**3.
-v*(v - 1)**2*(v + 2)/2
Let t = 26 + -30. Let c(z) = 10*z**3 - 5*z**2 - 6*z + 4. Let a(q) = -48*q**2 + 2*q**2 + 10*q**2 + 27 + 69*q**3 - 42*q. Let d(f) = t*a(f) + 27*c(f). Factor d(k).
-3*k*(k - 2)*(2*k + 1)
Determine r, given that 8*r**2 + 0 + 0*r - 1/2*r**4 - 3*r**3 = 0.
-8, 0, 2
Let d(p) = 39 - 10*p - p**3 - 26 + p**3 + 10*p**2 + p**3. Let z be d(-11). Determine y so that -2*y + 4 + 1/4*y**z = 0.
4
Let j(b) be the third derivative of b**7/1995 + b**6/570 + b**5/570 - 39*b**2. Solve j(k) = 0 for k.
-1, 0
Let a(v) = -v**2 - 5*v + 12. Let r be a(-6). Suppose -7*b + 18 = -r*b. Factor 4*l**3 + 12*l**2 - 2*l**3 + 36*l - b*l.
2*l*(l + 3)**2
Let y be (-23)/(-6) - (-9)/54. Suppose 10 - 1 + 4*z**3 + 12*z**2 - 4*z**y - 20*z - 1 = 0. What is z?
-2, 1
Let q = 164/115 + 4/23. Let x(i) be the third derivative of -q*i**5 + 4/15*i**6 - 2/105*i**7 - 32/3*i**3 + 16/3*i**4 + 0*i - 10*i**2 + 0. Factor x(k).
-4*(k - 2)**4
What is s in 2 + 11/2*s + 7/2*s**2 = 0?
-1, -4/7
Let a = 60 - -32. Factor 24 - 34*i + 26*i + a*i + 27*i**3 - 102*i**2.
3*(i - 2)**2*(9*i + 2)
Let p(s) be the first derivative of s**5/25 - 6*s**3/5 - 16*s**2/5 - 3*s + 164. Factor p(t).
(t - 5)*(t + 1)**2*(t + 3)/5
Let f(r) be the third derivative of -1/1344*r**8 - 1/24*r**5 + 1/24*r**4 + 1/3*r**3 + 0 + 1/210*r**7 - 1/480*r**6 - 2*r**2 + 0*r. Factor f(g).
-(g - 2)**3*(g + 1)**2/4
Let d = 4296/5 - 859. Let i(o) be the second derivative of 0 + 8*o + 1/30*o**4 + 0*o**2 - d*o**3. Factor i(z).
2*z*(z - 3)/5
Let y(t) be the first derivative of -t**6/240 - t**5/30 + t**4/16 - 7*t**3/3 + 12. Let n(m) be the third derivative of y(m). Let n(k) = 0. What is k?
-3, 1/3
Let x(b) be the third derivative of -b**5/210 - 3*b**4/28 + 10*b**3/21 - 628*b**2. Find w, given that x(w) = 0.
-10, 1
Let x(l) be the third derivative of -l**10/216 + 2*l**9/315 - l**8/420 - l**4/6 - 7*l**3/6 + 33*l**2. Let p(r) be the second derivative of x(r). Factor p(n).
-4*n**3*(5*n - 2)*(7*n - 2)
Let b(g) be the third derivative of -3*g**6/80 + 17*g**5/40 - 7*g**4/4 + 3*g**3 - 173*g**2. Factor b(q).
-3*(q - 3)*(q - 2)*(3*q - 2)/2
Suppose 2*h - 5*z - 620 = 0, -3*h - z + 777 = -119. Let k be (270/h)/(2/4). Determine l, given that k*l - 2/5 - 7/5*l**2 = 0.
2/7, 1
Let q(u) be the third derivative of -u**6/1260 + u**4/63 - u**2 - 427*u. Factor q(p).
-2*p*(p - 2)*(p + 2)/21
Let q = 3675/544 + -3/544. Factor 225/4*s + 125/4 + q*s**3 + 135/4*s**2.
(3*s + 5)**3/4
Let l be (0 - 4/(-10))/(3/60). Factor -13*j**3 + 9*j**3 + 4*j + l*j**2 - 4*j.
-4*j**2*(j - 2)
Let i(w) be the third derivative of -1/5*w**5 + 4*w + 1/168*w**8 - 2/35*w**7 + 5*w**2 + 0*w**4 + 11/60*w**6 + 0 + 0*w**3. Factor i(m).
2*m**2*(m - 3)*(m - 2)*(m - 1)
Let z(s) be the first derivative of s**7/3780 + s**6/405 + s**5/135 - 2*s**3/3 - 4. Let q(u) be the third derivative of z(u). Solve q(h) = 0.
-2, 0
Suppose 376 = -563*s + 657*s. Solve 0*w + 0*w**2 + 2/9*w**5 - 16/9*w**3 - 4/9*w**s + 0 = 0 for w.
-2, 0, 4
Let y be 2/(1 - -3)*37/74. Factor 3/4*l - y*l**2 + 1.
-(l - 4)*(l + 1)/4
Let l(y) = -y**2 - 10*y - 12. Let a be l(-6). Let i be a/8*82/3. What is w in 12*w - 56*w**3 + 3*w**4 + i*w**3 + 7*w**2 - 24 + 11*w**2 = 0?
-1, 2
Let x(q) be the first derivative of -3 - 5/24*q**4 + 0*q**5 + 5/3*q**3 + 0*q**2 + 0*q + 1/72*q**6. Let l(i) be the third derivative of x(i). Factor l(b).
5*(b - 1)*(b + 1)
Let f(v) be the second derivative of 2/27*v**3 + 0 + 0*v**2 - 1/54*v**4 - 3*v - 1/90*v**5. Factor f(t).
-2*t*(t - 1)*(t + 2)/9
Suppose -5*b - 11 = -9*b + 3*r, -b + 4*r = -6. Let v = -8 + 19. Factor -v - b*s**2 + 10*s + s**2 - 10 - 4.
-(s - 5)**2
Let l be 3/7 + 218/(-672). Let r(c) be the second derivative of 1/2*c**2 - 1/2*c**3 - 4*c + 0 + l*c**4. What is y in r(y) = 0?
2/5, 2
Let k = -171 - -174. Let o(j) be the first derivative of -5 - 2/15*j**k - 6/5*j + 4/5*j**2. Factor o(h).
-2*(h - 3)*(h - 1)/5
Let b be 3/(-2)*26/(-3). Let h = 27 - b. Let 7*k**3 - 10*k**2 - h*k**3 - k**3 - 2*k = 0. Calculate k.
-1, -1/4, 0
Let i be ((-47647)/(-203))/31 - (-1 - -8). Find m such that 1/7*m**4 + i + 15/7*m**2 + m**3 + 13/7*m = 0.
-4, -1
Let r be 8/36 - (-142)/9. Let m = r + -14. Solve c**4 + 4*c + c**4 - 4*c**3 + 52*c**m - 54*c**2 = 0 for c.
-1, 0, 1, 2
Let y(l) be the third derivative of -l**6/1140 - l**5/570 + l**4/228 + l**3/57 + 136*l**2. What is s in y(s) = 0?
-1, 1
What is h in 18/7*h - 2/7*h**3 - 4 + 12/7*h**2 = 0?
-2, 1, 7
Factor 5*f**2 + 484 + 3033 + 1784 - 181 + 320*f.
5*(f + 32)**2
Suppose 4*p + 21 - 157 = 0. Let v be p/8 + (-8)/2. Factor 0 + v*s**3 + 1/4*s + 1/2*s**2.
s*(s + 1)**2/4
Let i(c) be the second derivative of 0 + 2/5*c**5 - 4/3*c**3 - 6*c**2 + 8/9*c**4 - 10*c + 2/45*c**6. What is y in i(y) = 0?
-3, -1, 1
Let u = 140/127 - 713/762. Factor -2/3*l - 5/6 + u*l**2.
(l - 5)*(l + 1)/6
Supp