 9*j**2.
2*j*(j - 2)**2
Suppose -4*k + 12 = -2*w, 5 = -4*k - w + 17. Determine v so that -2/7*v**k + 0*v + 0 - 2/7*v**2 = 0.
-1, 0
Let v(q) be the second derivative of 11*q**5/10 + 19*q**4/6 - 10*q**3 - q + 16. Let v(j) = 0. Calculate j.
-30/11, 0, 1
Let l(p) be the third derivative of 1/15*p**3 - 1/24*p**4 - 17*p**2 + 0 + 0*p - 1/600*p**6 + 1/75*p**5. Let l(z) = 0. What is z?
1, 2
Suppose 0 = -5*q - 9*a + 7*a + 28, 0 = -6*q + a + 20. Let d(v) be the first derivative of -5 + 6/7*v**3 + 0*v + 2/7*v**2 + 2/7*v**q. Factor d(x).
2*x*(x + 2)*(4*x + 1)/7
Let u(q) be the second derivative of 5/2*q**3 + 11/4*q**4 + 0 + 16*q + 3/5*q**5 - 3*q**2. Suppose u(x) = 0. What is x?
-2, -1, 1/4
Suppose h + 1540 = -13*h. Let p be 8/6*((-135)/h)/9. Find b, given that 0*b**2 + 0 + 2/11*b - p*b**3 = 0.
-1, 0, 1
Let a(u) be the first derivative of u**3/3 + 5*u**2 + 9*u + 593. Factor a(o).
(o + 1)*(o + 9)
Let f = 31 + -11. Determine r so that -4*r**3 - 8*r - 2*r**5 + 14*r**5 - 35*r**4 + 15*r**4 + f*r**2 = 0.
-1, 0, 2/3, 1
Let u be -2 + 8 + 0 + -4. Suppose -9 = -3*y - 3*m, -y - u*m + 6 = 2. What is f in -2 - 1/2*f**y + 2*f = 0?
2
Suppose 7*a + 105 = 42*a. Let -w**4 + w - 5/2*w**a - 1/2*w**2 + 0 = 0. Calculate w.
-2, -1, 0, 1/2
Find v such that -117/2*v - 4563/4 - 3/4*v**2 = 0.
-39
Let d(x) be the third derivative of -1/78*x**5 - 1/78*x**4 + 0*x + 0 - 1/1365*x**7 - 9*x**2 + 0*x**3 - 1/195*x**6. Factor d(v).
-2*v*(v + 1)**2*(v + 2)/13
Let p = 54/35 + -5183/70. Let i = -72 - p. Suppose -i*f**2 + 0*f + 1/2 = 0. Calculate f.
-1, 1
Let v be (116/(-87))/(16/(-6)). Solve o**2 - v*o**4 - 1/2*o - 1/2 + o**3 - 1/2*o**5 = 0.
-1, 1
Suppose -5*f + 7 + 13 = 0. Let x(w) = -4*w - 9. Let z be x(-3). Factor -3*y**z - 4*y**4 + y**f + 3*y**2 + y**5 + 2*y**5.
3*y**2*(y - 1)**2*(y + 1)
Let a(q) be the first derivative of 0*q**2 + 2/7*q**3 - 8 + 1/28*q**4 + 0*q - 1/35*q**5. Factor a(w).
-w**2*(w - 3)*(w + 2)/7
Suppose -v + 1 = 4*z - 5*z, 5 = 4*v - 5*z. What is l in 2/9*l**2 + v*l - 2/9 = 0?
-1, 1
Suppose 0*b - 80 = -4*b. Factor b*j**2 - 10 - 8*j**3 - 7*j**3 - 19*j + 20*j + 24*j.
-5*(j - 2)*(j + 1)*(3*j - 1)
Let -31 - 5*j**2 + 3*j + 860*j**3 - 859*j**3 + 40 = 0. Calculate j.
-1, 3
Let c be (205/(-30))/41*0. Factor 2/3*p**4 + 0*p**2 + 7/3*p**5 + 0*p**3 + 0 + c*p.
p**4*(7*p + 2)/3
Let s be -2 - (-7 - -7) - (-3 - 1). Let v(w) be the second derivative of -6*w + 1/42*w**4 + 4/21*w**3 + 0 + 4/7*w**s. Factor v(m).
2*(m + 2)**2/7
Let v = 3328/3 - 1094. Let u = v - 44/3. Let -2/3*p**2 + 5/3*p + u - 5/3*p**3 = 0. Calculate p.
-1, -2/5, 1
Let l be ((1188/(-69))/4)/1 + 0. Let s = -233/161 - l. Find p, given that 0 - s*p**2 + 4/7*p**5 - 8/7*p - 12/7*p**3 + 4/7*p**4 = 0.
-1, 0, 2
Let b(k) be the third derivative of k**6/216 + k**5/36 + 16*k**3/3 + 12*k**2. Let n(y) be the first derivative of b(y). Determine w, given that n(w) = 0.
-2, 0
Suppose 0 = -0*w + 5*w - 65. Let u = 13 - w. Factor -3/5*v**3 + 9/5*v + 6/5*v**2 + u.
-3*v*(v - 3)*(v + 1)/5
Let g(d) be the third derivative of -d**8/50400 - d**7/3150 - d**6/600 - d**5/5 + 17*d**2. Let h(y) be the third derivative of g(y). Solve h(a) = 0 for a.
-3, -1
Let w be 0 - 2 - (-4)/1. Suppose 5*d = -2*j + 14, 4*j + 61*d - 59*d = 12. Let -9*f + 2*f**j + f**2 - 3*f**w + 3*f**2 = 0. Calculate f.
0, 3
Let d(o) be the third derivative of 20*o**2 + 1/12*o**5 - 1/40*o**6 + 0 - 7/72*o**4 + 1/18*o**3 + 0*o. Factor d(j).
-(j - 1)*(3*j - 1)**2/3
Suppose 2/5*i**3 + 0 + 2/5*i**2 + 0*i = 0. Calculate i.
-1, 0
Let 125*h + 332*h**2 - 257*h**2 - 55*h**3 + 10*h**3 + 5*h**4 = 0. What is h?
-1, 0, 5
Suppose 64*n = 59*n + 2215. Suppose -435 = 2*a - n. Factor -2/9*m + 0 - 16/9*m**3 + 8/9*m**a + 10/9*m**2.
2*m*(m - 1)*(2*m - 1)**2/9
Find a, given that 175760 + 10116*a**2 + 108160*a + 400*a**3 - 15*a**4 + 27*a**4 - 7*a**4 + 804*a**2 = 0.
-26, -2
Let t(v) be the first derivative of 2/27*v**3 + 0*v**2 + 0*v**4 - 2/45*v**5 + 0*v + 18. Determine f, given that t(f) = 0.
-1, 0, 1
Let -290*t**2 - 959/2*t**4 - 36*t - 709*t**3 + 0 - 49/2*t**5 = 0. What is t?
-18, -1, -2/7, 0
Let p = -366 + 2197/6. Let d(z) be the second derivative of 0*z**2 + 3/8*z**4 - 6*z - 7/40*z**5 + 0 - p*z**3. Factor d(i).
-i*(i - 1)*(7*i - 2)/2
Factor -519/7*w + 12/7*w**2 + 129/7.
3*(w - 43)*(4*w - 1)/7
Let f = -41 + 48. Let y be 35/50*8/f. Factor 4/5*g + 0 - y*g**2.
-4*g*(g - 1)/5
Suppose 2*m + 3 = 6*m + j, 2*j = 5*m - 20. Factor -2*a**2 + 1/2*a**5 + 1/2*a + 0 + 3*a**3 - m*a**4.
a*(a - 1)**4/2
Suppose 3*c - 2*c = 9. Let s be 86/18 + 2/c. Factor 0*w - 2*w + 7*w**3 + 10*w**2 - s*w**2.
w*(w + 1)*(7*w - 2)
Let u(n) be the first derivative of n**5/20 - n**4/8 + n**3/12 - 51. Factor u(s).
s**2*(s - 1)**2/4
Suppose -11*o**3 + 2 - 17/2*o - 1/2*o**5 + 4*o**4 + 14*o**2 = 0. Calculate o.
1, 4
Suppose 4*l = -2*b + 279 + 407, -5*l - 5*b + 845 = 0. Let n = -171 + l. Solve -2/3 + 2/3*u**2 + u - u**n = 0 for u.
-1, 2/3, 1
Let x be (1 - 2)/(5/(-10)). Suppose 6*g + g = 14. Determine i so that -i**g - i + 0*i + x*i**2 = 0.
0, 1
Let m be 7*4/154 + (-1047)/5940. Let j(k) be the third derivative of 1/36*k**4 + 0*k - m*k**6 + 2/9*k**3 + 0 - 6*k**2 - 1/45*k**5. Factor j(l).
-2*(l - 1)*(l + 1)*(l + 2)/3
Let s = 3 + 0. Suppose 47*w - 9*w - 152 = 0. Factor 2*b**2 + 10*b**w + 0*b + 0*b + 4*b**s - 8*b**4.
2*b**2*(b + 1)**2
Let v(j) = 241*j**4 + 1151*j**3 + 62*j**2 - 671*j + 143. Let q(h) = 30*h**4 + 144*h**3 + 8*h**2 - 84*h + 18. Let a(g) = -17*q(g) + 2*v(g). Solve a(s) = 0 for s.
-5, -1, 2/7, 1/2
Let k(x) = 10*x**4 - 2*x**3 + 10*x**2 - 6*x. Let c = -33 - -27. Let y(f) = -29*f**4 + 7*f**3 - 29*f**2 + 17*f. Let u(l) = c*y(l) - 17*k(l). Factor u(b).
4*b**2*(b - 1)**2
Suppose -2*w = 13*w - 30. Let c(v) = 3*v**2 - 6*v + 3. Let y be c(w). Let 8/3 + 16/3*a + 2/3*a**y + 10/3*a**2 = 0. What is a?
-2, -1
Let a(r) be the first derivative of -r**5/510 - r**4/102 - r**3/51 - 7*r**2/2 + 4. Let p(b) be the second derivative of a(b). Suppose p(j) = 0. Calculate j.
-1
Let t(r) be the second derivative of r**4/42 - 5*r**3/21 - 3*r + 7. Factor t(b).
2*b*(b - 5)/7
Suppose 3*c - 2*c + x - 7 = 0, 0 = 3*x - 15. Factor -6 + 45*g**2 + 22*g - c - 59*g**2 - 2 + 2*g**3.
2*(g - 5)*(g - 1)**2
Factor 2*w**2 - 15*w - 2 - w**2 + 24 - 1 + 15.
(w - 12)*(w - 3)
Let r(b) be the first derivative of -3/5*b**4 + 6/5*b + 5 + 2/5*b**3 - 12/25*b**5 + 3/2*b**2 - 1/10*b**6. What is p in r(p) = 0?
-2, -1, 1
Let n(k) be the first derivative of 2*k**5/5 - 5*k**4/2 - 38*k**3/3 + 65*k**2 + 300*k - 326. Factor n(o).
2*(o - 5)**2*(o + 2)*(o + 3)
Let z(p) be the third derivative of -p**7/735 + 13*p**6/420 + p**5/70 - 37*p**4/84 - 26*p**3/21 - 29*p**2 - p. What is y in z(y) = 0?
-1, 2, 13
Let m(u) be the third derivative of -u**7/140 - 7*u**6/40 - 3*u**5/5 - 187*u**2. Solve m(k) = 0 for k.
-12, -2, 0
Let g be -1*85/(-102) + (1 - 1). Let m(u) be the first derivative of -3/10*u**5 + g*u**3 + 0*u - 1/2*u**4 - 9 + 1/2*u**2. Factor m(c).
-c*(c - 1)*(c + 2)*(3*c + 1)/2
Let s(b) be the third derivative of b**6/40 - 11*b**5/20 + 7*b**4/2 - 5*b**2 - 10*b. What is v in s(v) = 0?
0, 4, 7
Let u be (-16)/(-24) - (-16)/24. Let -2/3*t**3 + 1/3*t**4 - t**2 + 4/3*t + u = 0. Calculate t.
-1, 2
Let q(t) be the first derivative of -t**4/19 - 2*t**3/57 + 216. Solve q(h) = 0.
-1/2, 0
Let o(b) be the second derivative of -b**5/5 + 4*b**4/3 + 48*b. Factor o(y).
-4*y**2*(y - 4)
Let w(b) = -30*b**3 - 202*b**2 + 438*b - 230. Let a(m) = 11*m**3 + 67*m**2 - 146*m + 77. Let q(x) = 8*a(x) + 3*w(x). Factor q(l).
-2*(l - 1)**2*(l + 37)
Let x(o) be the first derivative of 0*o - 1/3*o**3 - 36 + 1/12*o**4 - 2/3*o**2. Factor x(k).
k*(k - 4)*(k + 1)/3
Let c be 0 - (1 - (3 - 2)). Let f be ((-10)/(-120))/(6/16). Factor -f*y**2 + c + 0*y.
-2*y**2/9
Let l = 41181 - 41178. Find g such that -l + 8*g**2 - 7/2*g**3 + 17/2*g = 0.
-1, 2/7, 3
Let w(l) = -l**2 + 11*l + 14. Let m be w(12). Suppose m*b + 4 = 0, -3*d + 6*b = 4*b - 10. Factor 2 + 2/9*a**d - 4/3*a.
2*(a - 3)**2/9
Let c(i) be the second derivative of i**4/12 - 5*i**3/3 - 12*i**2 + 25*i. Let p be c(12). Find y such that 0 - 1/4*y**2 - y**3 + p*y = 0.
-1/4, 0
Let z(i) = 6*i**3 + 47*i**2 + 31*i - 78. Let j(x) = -x**3 - 2*x**2 - x - 2. Let f(q) = j(q) + z(q). Factor f(h).
5*(h - 1)*(h + 2)*(h + 8)
Suppose 9*r + g = 5*r + 7, g + 11 = 5*r. Let -10*q - 12*q**4 + 2*q - 40*q**3 - 3*q**r + 8*q**