5/3*q**3 + z + 5/3*q**2 = 0.
-1, 0, 1
Let s(b) be the second derivative of b**6/360 - b**4/24 + b**3/9 - 13*b**2/2 - 4*b. Let a(t) be the first derivative of s(t). Let a(d) = 0. What is d?
-2, 1
Let p(w) be the second derivative of -w**7/210 - w**6/20 - 3*w**5/20 + 23*w**2/2 - 3*w. Let g(q) be the first derivative of p(q). Determine j so that g(j) = 0.
-3, 0
Let a(x) = x. Let m(r) = 5*r**2 - 40*r. Let j(t) = -5*a(t) - m(t). Find c such that j(c) = 0.
0, 7
Suppose 2*n - 36 = -2*d, -5*n + 112 = -3*d - 2. Factor 3/2*h**5 + 0 - 18*h**2 + n*h**3 + 4*h - 19/2*h**4.
h*(h - 2)**3*(3*h - 1)/2
Let q(j) = -4*j**2 + 3*j - 7. Suppose -21*n + 20 = -26*n. Let m(x) = -x**2 + x - 2. Let p(h) = n*q(h) + 14*m(h). Suppose p(u) = 0. What is u?
-1, 0
Factor -29 - 30*k**2 - 58*k - 5*k**3 - 11 - 59*k + 57*k.
-5*(k + 2)**3
Let x(r) = -r**3 + 2*r**2 - 2*r. Let p(l) = 3*l**3 - 16*l**2 + 42*l - 24. Let j(z) = 2*p(z) + 10*x(z). Determine m, given that j(m) = 0.
-6, 1, 2
Let y(i) be the second derivative of -2*i**6/15 + 7*i**5/15 + 7*i**4/9 - 2*i**3/3 - 90*i + 2. Let y(v) = 0. What is v?
-1, 0, 1/3, 3
Factor 0*j**5 - 881*j**2 + 5*j**4 + 5*j**5 + 2*j**3 - 7*j**3 + 876*j**2.
5*j**2*(j - 1)*(j + 1)**2
Suppose 0 = -141*r + 149*r - 24. Let x(u) be the first derivative of 0*u - u**r + 3/5*u**5 + 0*u**2 - 3/4*u**4 - 8 + 1/2*u**6. Factor x(f).
3*f**2*(f - 1)*(f + 1)**2
Let m = 479 - 475. Let v(q) be the second derivative of -1/3*q**m + 5*q + 2/3*q**3 + 4*q**2 + 0. Find i, given that v(i) = 0.
-1, 2
Let i be (16/126 - 0) + (-260)/(-585). Suppose -16/7 + 16/7*a**2 - 4/7*a + i*a**3 = 0. Calculate a.
-4, -1, 1
Let w = -31/4 - -95/12. What is a in -2/3 + 0*a + w*a**2 = 0?
-2, 2
Let m = -31349 - -31349. Determine c so that 0*c + 0*c**2 - 2/5*c**4 + m - 2/5*c**3 = 0.
-1, 0
Let m(i) be the first derivative of -2*i**5/15 + i**4/4 + 16*i**3/9 + 5*i**2/2 + 4*i/3 - 464. Find u, given that m(u) = 0.
-1, -1/2, 4
Let a(t) be the second derivative of 1/14*t**7 - 3/5*t**5 + 27*t + 0*t**3 + 0 + 0*t**2 + 0*t**4 + 0*t**6. Let a(d) = 0. What is d?
-2, 0, 2
Let -24*t**3 - 51*t**3 - 50*t - 25*t**3 - 15*t**4 - 175*t**2 + 40 = 0. Calculate t.
-4, -2, -1, 1/3
Let g(s) be the first derivative of -s**3/18 - 35*s**2/6 - 1225*s/6 - 140. Factor g(h).
-(h + 35)**2/6
Factor 20/3 - 32/9*y**2 + 2/9*y**3 + 26/9*y.
2*(y - 15)*(y - 2)*(y + 1)/9
Suppose 1248 = -0*r + 2*r. Factor -45*y**5 - 83*y**5 - 436*y**3 + r*y**2 + 28*y**5 - 273*y**4 - 247*y**4 - 144*y.
-4*y*(y + 3)**2*(5*y - 2)**2
Let g(j) be the first derivative of j**5/10 - 23*j**4/8 - j**3/2 + 67*j**2/4 + 23*j - 68. Find r such that g(r) = 0.
-1, 2, 23
Let w(k) be the third derivative of 1/5*k**3 + 0*k - 8*k**2 + 1/60*k**4 + 2/525*k**7 + 0 - 3/50*k**5 + 1/100*k**6. Suppose w(r) = 0. What is r?
-3, -1/2, 1
Let o = 16 + -13. Let k(d) = -o*d**3 + d**3 + 2*d**3 + 5*d**3 + 2*d**2 + 5*d + 4. Let t(x) = 4*x**3 + 2*x**2 + 4*x + 3. Let w(v) = 3*k(v) - 4*t(v). Factor w(u).
-u*(u + 1)**2
Let p(o) = 4*o**2 + 28*o - 118. Let l be p(-10). Let -8/3*n + 1/3*n**l + 0 = 0. What is n?
0, 8
Suppose -2*n - 6 = -4*n. Suppose n*w = 4*d - 289, d + 3*w - 20 - 71 = 0. Let 2*j + d*j**2 + 0*j - 2*j**4 - 74*j**2 - 2*j**3 = 0. What is j?
-1, 0, 1
Factor -3/7*x**4 + 3/7*x**5 + 0 + 0*x + 3/7*x**2 - 3/7*x**3.
3*x**2*(x - 1)**2*(x + 1)/7
Find v such that 22*v**2 + 0 - 4*v + v**3 - 11/2*v**4 = 0.
-2, 0, 2/11, 2
Let f(q) be the second derivative of -q**8/315 - q**7/70 + q**6/27 + q**5/30 + 7*q**3/3 + 6*q. Let u(i) be the second derivative of f(i). Solve u(p) = 0 for p.
-3, -1/4, 0, 1
Let f(v) be the second derivative of -v**7/735 - v**6/420 + v**5/210 + v**4/84 + 11*v**2/2 + 43*v. Let y(j) be the first derivative of f(j). Factor y(u).
-2*u*(u - 1)*(u + 1)**2/7
Let o(l) be the first derivative of 2*l**3/27 - 4*l**2/9 - 64*l/9 + 280. Factor o(k).
2*(k - 8)*(k + 4)/9
Suppose -5*m = 5*a - 125, 6*a - m - 149 = a. Find g such that -3*g**5 - 3*g - a*g**3 + 0*g**5 + 35*g**3 = 0.
-1, 0, 1
Suppose -7*i + 2*i + 4*h = -2, 5*i + 7*h = 24. Suppose -2/7*n**i - 450/7 + 60/7*n = 0. What is n?
15
Let s(r) be the first derivative of -r**6/6 + r**5 - 9*r**4/4 + 7*r**3/3 - r**2 + 3. Let s(b) = 0. What is b?
0, 1, 2
Suppose -6 = -2*g - 4. Let k(n) = 9*n - 1. Let y be k(g). Factor -y*s**2 - 1 + 1 + 17*s**2 - 3*s - 9*s**3 + 3*s**4.
3*s*(s - 1)**3
Let p(f) = -245*f**3 + 1791*f**2 - 495*f + 29. Let a(r) = -2205*r**3 + 16120*r**2 - 4455*r + 260. Let d(j) = -6*a(j) + 55*p(j). Factor d(b).
-5*(b - 7)*(7*b - 1)**2
Let f(t) be the first derivative of -3/4*t**3 + 23 + 3/20*t**5 + 0*t**4 + 3/4*t**2 + 0*t. Find y, given that f(y) = 0.
-2, 0, 1
Let o(j) be the first derivative of -j**8/3360 - j**7/1680 + j**6/180 + j**5/60 - 7*j**3/3 - 8. Let f(y) be the third derivative of o(y). Factor f(p).
-p*(p - 2)*(p + 1)*(p + 2)/2
Let t(b) be the second derivative of b**5/50 + b**4/3 + 8*b**3/5 + 5*b + 3. Find p, given that t(p) = 0.
-6, -4, 0
Let i(w) = w**2 + w - 8. Suppose -2*t + b + 5 = 0, 0*b - 12 = -5*t + 2*b. Let q(x) = x**2 + x - 9. Let p(y) = t*q(y) - 3*i(y). Factor p(z).
-(z - 2)*(z + 3)
Let b(z) be the second derivative of 6*z**5/5 - 51*z**4/4 + 29*z**3 - 45*z**2/2 + 265*z. Factor b(t).
3*(t - 5)*(t - 1)*(8*t - 3)
Let j(m) be the first derivative of -6*m + 3/2*m**3 - 3/5*m**5 + 17 + 6*m**2 - 15/8*m**4. Suppose j(y) = 0. What is y?
-2, 1/2, 1
Let o(g) be the second derivative of g**5/5 - 7*g**4/3 + 16*g**3/3 + 32*g**2 - 426*g. Factor o(d).
4*(d - 4)**2*(d + 1)
Let b(a) = -a**3 + 12*a**2 - 13*a + 2. Let g be b(10). Let c be (5/2)/(30/g). Factor 7 + 3 - c*j**3 + 2*j**3 - 10*j**2 - 5*j + 9*j**3.
5*(j - 2)*(j - 1)*(j + 1)
Suppose -2 = 3*h - 8. Solve -z**h + 3*z**2 + 5*z + 6*z - 7*z = 0 for z.
-2, 0
Let u be 26/65 + (-4)/10. Determine v, given that u + 1/11*v**4 + 0*v + 0*v**2 + 0*v**3 = 0.
0
Let d(t) be the second derivative of t**8/448 + t**7/63 + t**6/36 - 11*t**4/12 + 7*t. Let h(u) be the third derivative of d(u). Suppose h(r) = 0. What is r?
-2, -2/3, 0
Factor 1/6*p**3 - 3 + 4/3*p**2 - 11/6*p.
(p - 2)*(p + 1)*(p + 9)/6
Let q(g) be the first derivative of -1/2*g**2 + 1/2*g**3 + 0*g + 3/2*g**5 + 2*g**4 + 1/3*g**6 - 35. Let q(p) = 0. What is p?
-2, -1, 0, 1/4
Let h(r) be the second derivative of 11*r**7/7 + 59*r**6/10 + 24*r**5/5 + r**4 + 7*r + 8. Solve h(i) = 0.
-2, -1/2, -2/11, 0
Factor -2/3*y + 0 + 1/6*y**4 + 0*y**2 + 1/2*y**3.
y*(y - 1)*(y + 2)**2/6
Let u be (-2 - -1) + 5 - (-1 - 5). Suppose 2*o = u - 4. Determine m, given that 64/3 - 1/3*m**o + 4*m**2 - 16*m = 0.
4
Suppose 0 = -4*r - 2 + 10. Suppose -10*m + 73 = -7. Factor a + 5*a + 5*a**r - m - 3*a**2.
2*(a - 1)*(a + 4)
Let s be 7 - 3 - 602/150. Let l = 17/25 + s. Factor l*g**3 + 0 + 2/9*g**4 + 2/9*g + 2/3*g**2.
2*g*(g + 1)**3/9
Let n(l) be the first derivative of 4 + 16/5*l - 36/5*l**2 + 7*l**3 - 49/20*l**4. Find s such that n(s) = 0.
4/7, 1
Suppose -7 = -3*w - 1. Factor -8*l + 32 + 21 + l**3 - 7*l**w - 62 + 23*l.
(l - 3)**2*(l - 1)
Let i(h) = -h**3 + 65*h - 60. Let m(z) = -10*z**3 + 715*z - 660. Let t(k) = -45*i(k) + 4*m(k). Let t(f) = 0. What is f?
-4, 1, 3
Let a(c) be the first derivative of -c**5/45 + 5*c**4/9 - 52*c**3/27 - 80*c**2/3 - 64*c + 131. Determine q, given that a(q) = 0.
-2, 12
Let t(h) be the second derivative of h**5/5 - 2*h**4/3 - 40*h**3/3 - 48*h**2 + 21*h. Factor t(k).
4*(k - 6)*(k + 2)**2
Let s(c) be the third derivative of 0*c**6 + 26*c**2 - 1/616*c**8 + 0*c + 0*c**3 + 0 - 2/385*c**7 + 1/55*c**5 + 1/44*c**4. Determine n, given that s(n) = 0.
-1, 0, 1
Let f(b) = 7*b - 47. Suppose 4*s - 4*r - 32 = 0, -13*r + 8*r - 5 = 0. Let z be f(s). Solve -1/2*g + 1/2*g**4 + 3/2*g**z + 0 - 3/2*g**3 = 0 for g.
0, 1
Let a(j) be the third derivative of -j**6/300 - j**5/30 - j**4/15 - 32*j**2. Factor a(k).
-2*k*(k + 1)*(k + 4)/5
Let p(a) = -15*a**4 - 20*a**3 - 25*a**2 - 10*a + 10. Let b(o) = 7*o**4 + 3 - 13*o**4 + 7*o**4 - 4. Let d(n) = 10*b(n) + p(n). Factor d(s).
-5*s*(s + 1)**2*(s + 2)
Let m be 4/84 - ((-99)/126 + (-5)/(-10)). Determine g so that m*g**5 + 0 + 0*g - g**4 + 0*g**3 + 4/3*g**2 = 0.
-1, 0, 2
Let s be 640/(-240)*(-9)/8. Determine w, given that -2/9 + 2/9*w**4 + 4/9*w**s - 4/9*w + 0*w**2 = 0.
-1, 1
Let 0 - 1/2*m**3 + m**2 + 0*m = 0. What is m?
0, 2
Let u(w) = 482*w + 3376. Let d be u(-7). Let 0 - 1/6*b**d + 0*b = 0. What is b?
0
Suppose 0 = -66*o + 40 - 40.