- m**5/10 - 3*m**4/8 + 46*m**2. Determine a so that b(a) = 0.
-1, 0, 1, 3
Let c = 16 + -24. Let p = 5 + c. Let y(w) = -2*w**3 + 4*w**2 + 2*w + 2. Let q(d) = -d**3 - d. Let r(s) = p*q(s) + y(s). Let r(b) = 0. What is b?
-2, -1
Determine x, given that -1/8*x**4 - 1/4*x**2 + 0 + 0*x + 3/8*x**3 = 0.
0, 1, 2
Let n = -7 + 9. Let y be -8*((-94)/40 + n). Let 2*t**2 + 4/5 + y*t = 0. What is t?
-1, -2/5
Let q(f) be the first derivative of -2*f**5/45 + f**4/18 + 2*f**3/9 - 5*f**2/9 + 4*f/9 - 6. Factor q(v).
-2*(v - 1)**3*(v + 2)/9
Let i(n) be the third derivative of -1/210*n**7 - 1/24*n**4 + 0 + 0*n + 1/20*n**5 + 1/120*n**6 - 1/3*n**3 + 3*n**2. Factor i(c).
-(c - 2)*(c - 1)*(c + 1)**2
Let o be (-18)/(-8) - (-2)/(-1). Let f = 2 - 0. Find x such that 1/4*x**3 + 0 - o*x**f + 1/4*x**4 - 1/4*x = 0.
-1, 0, 1
Let o(w) be the third derivative of w**6/120 - w**5/60 + 6*w**2. What is n in o(n) = 0?
0, 1
Let p be (-4)/9 - (-88)/36. Let 4/5*j - 2/5 - 2/5*j**p = 0. Calculate j.
1
Let o be 6/(-2)*(2 + (-19)/9). Factor o*i**3 + 0*i - 2/3*i**4 + 0 + 1/3*i**5 + 0*i**2.
i**3*(i - 1)**2/3
Suppose -2*m = 3*l - 25, 2*l - 23 = m + 4*m. Solve 5*p - 5*p - 3 + l*p - 12*p**3 = 0 for p.
-1, 1/2
Let i(k) = -4*k**3 - 4*k**2 + 7*k + 1. Let m(v) = -2*v**3 + v**2 + 1. Let n(o) = -i(o) + 3*m(o). Find c such that n(c) = 0.
1/2, 1, 2
Suppose 25 = 5*h + 5. Suppose -13 - 22 = -5*q + 3*l, -3*l = -4*q + 31. Find o such that -q*o**h + 5*o**4 - 2*o**2 - 3*o**4 + 4*o**4 = 0.
-1, 0, 1
Suppose 0 = 4*s - 9*s + 35. Let g(f) = 3*f**2 - 10*f - 6. Let o(a) = -8*a**2 + 31*a + 19. Let x(w) = s*g(w) + 2*o(w). Let x(t) = 0. What is t?
-2/5, 2
Let c(t) be the first derivative of 12*t**3 - 40*t**2 + 16*t - 19. Suppose c(w) = 0. Calculate w.
2/9, 2
Let o(z) = 9*z**4 + 18*z**3 - 10*z**2 - 23*z - 4. Let f(m) = -4*m**4 - 9*m**3 + 5*m**2 + 12*m + 2. Let r(d) = 5*f(d) + 3*o(d). Factor r(l).
(l - 1)*(l + 1)**2*(7*l + 2)
Let s(d) = -11*d**4 + 9*d**3 - 3*d**2 - 3*d - 3. Let r(y) = 12*y**4 - 8*y**3 + 4*y**2 + 4*y + 4. Let w(i) = 3*r(i) + 4*s(i). Factor w(h).
-4*h**3*(2*h - 3)
Let z(m) be the second derivative of m**6/10 + 3*m**5/5 + m**4 + 8*m + 1. Find f, given that z(f) = 0.
-2, 0
Factor 2/9*f**4 + 0 - 4/9*f + 0*f**3 - 2/3*f**2.
2*f*(f - 2)*(f + 1)**2/9
Let u(i) = i**3 - 6*i**2 + 16*i - 18. Let y be u(3). Let j = -115/2 - -59. Factor j*c + y*c**2 + 3/2*c**3 + 0.
3*c*(c + 1)**2/2
Let x = 54 + -52. Let c(m) be the first derivative of 1/5*m**x + 3 + 2/15*m**3 - 2/25*m**5 - 1/10*m**4 + 0*m. Factor c(n).
-2*n*(n - 1)*(n + 1)**2/5
Factor 4/5 + 0*m - 4/5*m**2.
-4*(m - 1)*(m + 1)/5
Factor 0 + 0*l**2 - 2/7*l + 2/7*l**3.
2*l*(l - 1)*(l + 1)/7
Let a be (-4)/(-8) + (-5)/(-14). Determine r, given that -2/7*r + 2/7*r**4 + 0 - a*r**3 + 6/7*r**2 = 0.
0, 1
Factor 4 + 342*d + 3*d**2 + 2 - 351*d.
3*(d - 2)*(d - 1)
Let m = 353/40 - 61/8. Solve m*z**3 + 0 + 2/5*z**2 + 2/5*z**5 + 6/5*z**4 + 0*z = 0 for z.
-1, 0
Let f(n) = -160*n**3 + 72*n**2 - 8*n. Let u(c) = -c**3. Let s(o) = f(o) + 2*u(o). Factor s(q).
-2*q*(9*q - 2)**2
Let w(d) = d + 1. Let b be w(1). Let j = -1 + 3. Solve j*f**2 - f**b - 2*f**2 = 0 for f.
0
Let a(n) = n**2 - 9*n + 2. Let h be a(9). Factor -y - y + 0*y**h + 7*y**2 - y**5 - 9*y**3 + 5*y**4.
-y*(y - 2)*(y - 1)**3
Let s = -109439/120 - -912. Let c(k) be the third derivative of 0*k + 1/24*k**4 - 2*k**2 + 0*k**5 + 0*k**3 - s*k**6 + 0. Determine j so that c(j) = 0.
-1, 0, 1
Let d(x) = x - 6. Let q be d(8). Factor 13*j - 4 + 12*j**2 - 3*j + 2*j**q.
2*(j + 1)*(7*j - 2)
Find u such that 16*u**2 + 0*u**5 - 2471*u - 2*u**5 + 22*u**3 + 2431*u - 32 - 4*u**4 = 0.
-4, -1, 2
Let q(x) = 3*x**4 - 29*x**3 + 148*x**2 - 264*x + 143. Let m(l) = -l**4 - l**3 + 1. Let c(k) = 2*m(k) + 2*q(k). Factor c(u).
4*(u - 6)**2*(u - 2)*(u - 1)
Let q(i) be the first derivative of i**4/10 - 26*i**3/15 + 48*i**2/5 - 72*i/5 + 12. Find a, given that q(a) = 0.
1, 6
Let v be (66/27)/(4/(-174)). Let t = -105 - v. Suppose -t - 16/3*f - 7/3*f**2 = 0. What is f?
-2, -2/7
Let r be -2 - 2/(-10)*9. Let w = r + 7/10. Factor w*u**3 - 1/4*u**4 + 0*u + 0 - 1/4*u**2.
-u**2*(u - 1)**2/4
Let m(l) = -l**3 + 3*l**2 - l - 2. Let z be m(2). Let b = z - -2. Factor -2*q**2 - 4*q + 3*q**b - 3*q**2.
-2*q*(q + 2)
Let b(t) be the first derivative of t**7/840 - t**6/360 + t**3 + 3. Let n(a) be the third derivative of b(a). Solve n(i) = 0.
0, 1
Suppose -2*i - 3*j = 8, -19*j + 15*j - 10 = 3*i. Let 1/2*g**3 - 1/4*g - 1/2*g**i + 1/4 - 1/4*g**5 + 1/4*g**4 = 0. Calculate g.
-1, 1
Let n(t) be the second derivative of -t**9/30240 - t**8/13440 + t**7/1008 - t**6/480 + t**4/3 + t. Let a(q) be the third derivative of n(q). Factor a(w).
-w*(w - 1)**2*(w + 3)/2
Let z(b) = -b**2 - 8*b + 9. Let m(i) = 4 - i - 18 + 13*i + 2*i**2. Suppose 0*a - 24 = -3*a. Let v(h) = a*z(h) + 5*m(h). Factor v(l).
2*(l - 1)**2
Let p(u) be the first derivative of -2*u**3/15 + 2*u**2/5 - 2*u/5 + 5. Find c, given that p(c) = 0.
1
Factor 6*w**2 + 155 + 2*w - 155.
2*w*(3*w + 1)
Factor -1/9*x**2 + 0*x**3 + 1/9*x**4 + 0*x + 0.
x**2*(x - 1)*(x + 1)/9
Let r(q) = 63*q**2 - 78*q + 69. Let j be ((-5)/(-3) + -3)*3. Let d(s) = 9*s**2 - 11*s + 10. Let o(m) = j*r(m) + 27*d(m). Solve o(z) = 0.
2/3, 1
Let t = -110 + 116. Let k(c) be the third derivative of -5/72*c**t - 1/18*c**4 + 0*c + 0*c**3 - 4*c**2 + 1/9*c**5 + 0. Find a, given that k(a) = 0.
0, 2/5
Let o(k) be the first derivative of -3*k**4/16 - k**3/2 + 39*k**2/8 - 15*k/2 + 55. Factor o(s).
-3*(s - 2)*(s - 1)*(s + 5)/4
Let q(k) = 2 + 3*k - 4*k - 6*k**3 + k - 2*k**2 - 2*k. Let g(w) = -w**3 - w**2 - w + 1. Let d(l) = 4*g(l) - q(l). Factor d(o).
2*(o - 1)**2*(o + 1)
Let x be ((-108)/(-28))/3 - 3*-1. Factor -x*y**2 - 2*y**4 + 38/7*y**3 + 2/7*y + 4/7.
-2*(y - 1)**3*(7*y + 2)/7
Let m(d) be the first derivative of d**6/21 + 4*d**5/35 - 1. Find g, given that m(g) = 0.
-2, 0
Let f = -90959/120 + 758. Let s(a) be the third derivative of -3*a**2 - f*a**5 + 0 + 0*a + 0*a**4 + 0*a**3 + 1/240*a**6. Factor s(v).
v**2*(v - 1)/2
Let h(d) = 6*d**3 - 4*d**2 + 6*d + 8. Let r(b) = 4*b**3 - 3*b**2 + 4*b + 5. Let a(w) = -5*h(w) + 8*r(w). Let a(o) = 0. Calculate o.
0, 1
Let b(f) = -5*f**3 - 5*f**2 - 8*f - 9. Let r(w) = w + 7. Let q be r(-5). Let h(t) = -t**3 - t**2 - 2*t - 2. Let o(g) = q*b(g) - 9*h(g). Factor o(v).
-v*(v - 1)*(v + 2)
Let q(y) be the second derivative of y**5/20 + y**4/12 - y**3/3 + 7*y. Factor q(u).
u*(u - 1)*(u + 2)
Let o(b) be the second derivative of -b**6/180 - b**5/120 + 13*b**4/72 + 25*b**3/36 + b**2 - 23*b. Factor o(g).
-(g - 4)*(g + 1)**2*(g + 3)/6
Let t(i) = 3*i**5 - 8*i**4 + 9*i**3 + i**2 - 2*i + 7. Let r(m) = 3*m**5 - 8*m**4 + 8*m**3 + 2*m**2 - 3*m + 6. Let c(b) = 5*r(b) - 4*t(b). Factor c(z).
(z - 1)**3*(z + 1)*(3*z - 2)
Let h = -200338/105 - -1908. Let d(o) be the third derivative of 0*o**3 + 1/60*o**6 + 3*o**2 + 0 + 0*o**5 - h*o**7 + 0*o + 0*o**4 + 1/168*o**8. Factor d(q).
2*q**3*(q - 1)**2
Suppose f**2 - 3*f**3 + 9 + f**2 + f**5 - 9 = 0. What is f?
-2, 0, 1
Suppose 0 = 4*t + 20, -2*t - 30 = -5*p + 3*t. Let v(u) be the first derivative of 1/3*u**2 + 0*u - 8/9*u**3 - p + 1/2*u**4. Factor v(h).
2*h*(h - 1)*(3*h - 1)/3
Let n = 37 + -24. Suppose -n*m + 11*m = 0. Factor m - 3/4*a + 3/4*a**2.
3*a*(a - 1)/4
Let x(y) be the second derivative of -3*y**5/20 - 11*y**4/2 - 121*y**3/2 + 50*y. Factor x(n).
-3*n*(n + 11)**2
Let j = -25 + 35. Let -4 + 6*l**3 + 2 - j*l**3 + 7*l - 4*l**2 + 9*l**2 = 0. Calculate l.
-1, 1/4, 2
Let u = -174/5 - -36. What is i in -u*i**3 + 0*i + 0 + 3/5*i**4 + 3/5*i**2 = 0?
0, 1
Let o be -2*((-63)/(-35) + -2). Determine m so that -1/5*m + 0 + 7/5*m**3 - o*m**2 - 4/5*m**4 = 0.
-1/4, 0, 1
Let x(n) = 7*n**5 + 5*n**4 - 4*n**3 - 14*n**2 - 6*n - 6. Let j(b) = 13*b**5 + 9*b**4 - 9*b**3 - 27*b**2 - 11*b - 11. Let u(k) = -6*j(k) + 11*x(k). Factor u(t).
-t**2*(t - 4)*(t + 1)*(t + 2)
Suppose d - 22 = 5*m - 4, -4 = 2*d. Let z be (-6)/m + 1/2. Factor -3*h**z + 2 + 3*h**2 - 4*h - 5*h**4 + 3*h**4 + 4*h**3.
-2*(h - 1)**3*(h + 1)
Let f be 2/(-10) + (-2784)/(-45). Let x = f - 61. Suppose -1/3*z - x + 1/3*z**2 = 0. Calculate z.
-1, 2
Factor 152 - 152 - 5*b**2.
-5*b**2
Let j be -1*64/39 + 2. Let r = j - -4/13. Factor 0 + 1/3*b + r*b**2 + 1/3*b**3.
b*(b + 1)**2/3
Factor 5 - 4*y**2 + 2*y**2 - 1 - 7*y.
-(y + 4)*(2*y - 1)
Suppose 6 = 2*g + 5*l, 2*g - 6*g + 2*l = -12. Let u(k) be