s) be the third derivative of 5*s**8/168 + 3*s**7/14 + 13*s**6/24 + 5*s**5/12 - 5*s**4/8 - 5*s**3/3 - 11*s**2. Factor t(n).
5*(n + 1)**3*(n + 2)*(2*n - 1)
Suppose -11*o + 10*o = -1. Let i(h) = h + 7. Let u be i(-4). Factor -1/2*w + o + 1/2*w**u - w**2.
(w - 2)*(w - 1)*(w + 1)/2
Suppose -s + 3*s - 4*u = 36, 20 = -4*u. Factor 72*w + 14*w**2 + 91*w**2 - 5 + s + 9.
3*(5*w + 2)*(7*w + 2)
Let p = 778 - 778. Determine m, given that -1/2*m**2 - m + p = 0.
-2, 0
Let y = -1/208 + 431/3120. Let a(h) be the third derivative of y*h**5 + 0*h - 1/4*h**4 + 0 + 2*h**2 - 1/3*h**3. Factor a(c).
2*(c - 1)*(4*c + 1)
Let w(b) be the second derivative of -5*b**4/12 + 7*b**3/6 - b**2 + 16*b. Factor w(m).
-(m - 1)*(5*m - 2)
Let d be 1*((3 - 1) + 5). Let k = d + -3. Factor -5 + 2*q + k - q**2 + 0.
-(q - 1)**2
Let j be (-1 - 5 - 32/(-5)) + 6. Factor -j - 2/5*l**2 - 16/5*l.
-2*(l + 4)**2/5
Let i be (2 - 28/8)*-2. Let g(u) be the first derivative of 1/2*u**2 + 2 + 1/3*u**i + 0*u. Find j such that g(j) = 0.
-1, 0
Suppose 3*a = 2*t + 51, -44 = 4*t - a + 83. Let s be (4 + t/9)/1. Suppose u**3 - 1/3*u**4 + s*u - u**2 + 0 = 0. Calculate u.
0, 1
Let i be -3*(0 - -1)/1. Let h(a) = a**2 + 2*a. Let x be h(i). Determine y so that -x*y**2 + 0 + 4 + y - 2 + 0 = 0.
-2/3, 1
Let z(t) = 5*t**2 + 2*t + 1. Let h be z(-1). Suppose y = h*y - 12. Factor i**y + i**4 - i**4.
i**4
Suppose 2406*t = 2405*t + 6. Solve 0*b - 9/2*b**2 - t*b**3 - 9/4*b**4 + 3/4 = 0.
-1, 1/3
Let n(t) be the second derivative of t**5/30 - t**4/9 - 4*t**3/9 + 8*t**2/3 - 34*t. Factor n(f).
2*(f - 2)**2*(f + 2)/3
Let a(n) be the first derivative of n**5/3 + 35*n**4/24 - 5*n**3/3 - 35*n**2/12 + 10*n/3 + 44. Suppose a(w) = 0. Calculate w.
-4, -1, 1/2, 1
Let h(s) = 5*s**4 - 16*s**3 + 6*s**2 + 16*s - 11. Let d(c) = c**4 - 3*c**3 + c**2 + 3*c - 2. Let r(f) = -11*d(f) + 2*h(f). Find p, given that r(p) = 0.
-1, 0, 1
Suppose -11 = -7*y + 3. Let o(u) be the third derivative of 3*u**y + 0*u**4 - 1/336*u**8 + 1/120*u**6 + 0*u**3 + 0 - 1/210*u**7 + 0*u + 1/60*u**5. Factor o(z).
-z**2*(z - 1)*(z + 1)**2
Let r(a) be the third derivative of -a**6/240 + a**5/30 - 5*a**4/48 + a**3/6 - 19*a**2. Factor r(q).
-(q - 2)*(q - 1)**2/2
Let n(g) be the first derivative of 2*g**3/3 - 7*g**2/2 - 4*g - 21. Find l, given that n(l) = 0.
-1/2, 4
Solve -2*g**2 - g**2 - 18 - 64*g + 85*g = 0 for g.
1, 6
Let c(a) be the first derivative of -a**6/1620 + a**5/540 + a**4/54 - a**3 - 2. Let r(y) be the third derivative of c(y). Factor r(m).
-2*(m - 2)*(m + 1)/9
Factor -20 - 265*h**2 + h**5 + 23*h**5 - 135*h**4 + 275*h**3 + h**5 + 0*h**5 + 120*h.
5*(h - 2)*(h - 1)**3*(5*h - 2)
Let p be 18/(-15) - (-10)/5*1. Factor 2/5*w**4 + 16/15*w**3 - 2/15 + 0*w + p*w**2.
2*(w + 1)**3*(3*w - 1)/15
Let a(k) be the second derivative of 0 + 3*k - 2/9*k**3 - 1/3*k**2 - 1/18*k**4. Suppose a(i) = 0. Calculate i.
-1
Suppose -2/5*m**4 + 0*m**3 + 0 + 0*m + 0*m**2 - 2/5*m**5 = 0. Calculate m.
-1, 0
Let k(o) be the first derivative of -o**4/14 - 8*o**3/7 - 48*o**2/7 - 128*o/7 - 14. Let k(q) = 0. What is q?
-4
Let m(r) be the second derivative of 0*r**4 + 0*r**6 + 1/35*r**5 + 3*r + 0 - 1/21*r**3 - 1/147*r**7 + 0*r**2. Factor m(q).
-2*q*(q - 1)**2*(q + 1)**2/7
Suppose 7/2*o - 3 - 1/2*o**2 = 0. What is o?
1, 6
Suppose 4*a - 20 = -n, 2*n + 2*a - 24 = -2*a. Factor 2*b**2 + 4/3*b - 2/3*b**n + 0*b**3 + 0.
-2*b*(b - 2)*(b + 1)**2/3
Factor 0 - 6/5*k - 2/5*k**2.
-2*k*(k + 3)/5
Let m be (-120)/18*6/4. Let j = -5 - m. Factor -1/2*a**2 + 0*a**3 + 1/2*a**4 + 0 - 1/4*a**j + 1/4*a.
-a*(a - 1)**3*(a + 1)/4
Let g(m) = -m**3 - 2*m**2 + 3*m - 4. Let c be g(-3). Let i = c + 6. Factor 3*l**3 - i*l - 4*l**3 + 3*l**3 + l**4 - 1.
(l - 1)*(l + 1)**3
Let s(o) be the third derivative of -o**5/360 + o**3/9 + 11*o**2. Let s(l) = 0. What is l?
-2, 2
Let d(f) be the third derivative of -f**5/360 + 5*f**4/36 - 25*f**3/9 + 19*f**2. Find s such that d(s) = 0.
10
Let c(a) be the first derivative of -2/15*a**3 - 2 + 1/5*a**2 + 4/5*a. Factor c(z).
-2*(z - 2)*(z + 1)/5
Let g(m) be the second derivative of -1/9*m**4 + 3*m - 1/90*m**5 + 0 - 4/9*m**3 + m**2. Let q(l) be the first derivative of g(l). Suppose q(k) = 0. What is k?
-2
Factor 4/13 + 6/13*h + 2/13*h**2.
2*(h + 1)*(h + 2)/13
Let z(i) = i - 6. Let o be 1 + (-18 - 2)/(-4). Let a be z(o). Let 1/3*f**3 - 1/3*f + a*f**2 + 0 = 0. What is f?
-1, 0, 1
Let h(y) = -y + 8. Let k be h(6). Factor -4*b**4 + b**5 + 6*b**5 + 10*b**k + 20*b**4 + 11*b**3 - 8*b**2.
b**2*(b + 1)**2*(7*b + 2)
Let a(m) = -9*m**2 - 9*m + 3. Let z(b) = -28*b**2 - 28*b + 8. Let h(c) = 16*a(c) - 5*z(c). Find r, given that h(r) = 0.
-2, 1
Let m(v) be the first derivative of 1/2*v**2 + 1/150*v**5 + 0*v + 4/15*v**3 - 1 - 1/15*v**4. Let u(q) be the second derivative of m(q). Factor u(x).
2*(x - 2)**2/5
Factor 3/7*m**2 - 24/7*m + 48/7.
3*(m - 4)**2/7
Find i such that -2 - 6*i**2 - 6*i**3 - 3*i**4 + 5 + 8*i**4 + 3*i**5 + 3*i - 2*i**4 = 0.
-1, 1
Let y(h) be the first derivative of -h**6/30 + h**5/5 - 5*h**4/12 + h**3/3 - 3*h - 3. Let k(p) be the first derivative of y(p). Suppose k(o) = 0. Calculate o.
0, 1, 2
Let f(h) be the second derivative of h**7/525 - h**6/75 + h**5/25 - h**4/15 + h**3/15 + 5*h**2/2 + 3*h. Let r(p) be the first derivative of f(p). Factor r(s).
2*(s - 1)**4/5
Let l(f) be the first derivative of f**9/1512 + f**8/280 + f**7/140 + f**6/180 + 2*f**3/3 - 4. Let m(x) be the third derivative of l(x). Factor m(g).
2*g**2*(g + 1)**3
Solve -3/4 + 1/2*v + 1/4*v**2 = 0.
-3, 1
Let m(q) be the second derivative of 2*q**7/63 - q**6/90 - 4*q**5/15 + q**4/9 + 8*q. What is b in m(b) = 0?
-2, 0, 1/4, 2
Let a(l) be the first derivative of -l**3/18 + l**2/2 - 3*l/2 + 46. Factor a(w).
-(w - 3)**2/6
Let c(b) be the second derivative of 0*b**2 + 0 - 2/15*b**6 + 2*b + 1/3*b**4 - 1/20*b**5 + 1/6*b**3. Suppose c(s) = 0. Calculate s.
-1, -1/4, 0, 1
Let n(q) be the first derivative of -1/6*q**4 + 0*q**3 + 2*q + 1/10*q**5 + 0*q**2 - 1. Let p(g) be the first derivative of n(g). Solve p(a) = 0.
0, 1
Solve 1/3*u - 1/3*u**3 + 2/3*u**2 - 2/3 = 0 for u.
-1, 1, 2
Let x = 26 - 26. Let r(k) be the third derivative of x*k + 3*k**2 + 1/6*k**3 + 1/8*k**4 + 0 + 1/20*k**5 + 1/120*k**6. Solve r(o) = 0.
-1
Suppose o = -0*o. Suppose o*p + 5*p = 0. Factor p*h - 1/3*h**2 + 1/3*h**3 + 0.
h**2*(h - 1)/3
Let j(r) be the first derivative of 1/3*r**3 - r + 2 + 0*r**2. Determine d so that j(d) = 0.
-1, 1
Let p = 7 + -5. Suppose -r + 2 = p*i, 4*i = i + 3. Factor 2*w**5 - 2*w**3 + 2*w**2 + w**4 - 3*w**4 + r*w**2.
2*w**2*(w - 1)**2*(w + 1)
Suppose 7*o = 2*o. Determine w, given that -1/3*w**2 - 1/3*w + o = 0.
-1, 0
Let g(m) be the second derivative of m**3/6 + 19*m**2/2 - 14*m. Let f be g(-14). Suppose 0 - 2/5*i**3 - 2/5*i**2 + 2/5*i**f + 0*i + 2/5*i**4 = 0. What is i?
-1, 0, 1
Let y be (-3 - 22/(-6))*3. Factor y*p**2 + 6*p**2 + 4*p + 3*p**3 + p**3.
4*p*(p + 1)**2
Suppose -2*v + 7 = -2*q - 3, -5*v + 19 = -3*q. Suppose 0*s**4 - 54*s**3 - 46*s**4 - 4*s - 32*s**2 - 14*s**5 + 6*s**v = 0. What is s?
-1, -2/7, 0
Suppose 0 = 5*h - q + 16 - 2, 4*h - 5*q + 28 = 0. Let i be (8/25)/(h/(-5)). Let 4*w**4 - 58/5*w**3 - 26/5*w + i + 12*w**2 = 0. Calculate w.
2/5, 1/2, 1
Suppose -3*c - 14 = -5*p, -4*c - 6*p = -p - 28. Let u be (30/225)/(c/10). Factor -2/3*h**3 + 2/3*h - u*h**2 + 0 + 2/3*h**4.
2*h*(h - 1)**2*(h + 1)/3
Factor 2/21*c - 2/21*c**2 + 0.
-2*c*(c - 1)/21
Let d(u) = -5*u**3 + 60*u**2 - 251*u + 331. Let l(x) = -x**3 + 12*x**2 - 50*x + 66. Let i(n) = -2*d(n) + 11*l(n). Factor i(h).
-(h - 4)**3
Let m be ((-456)/(-420) - 4/14) + 0. Find r such that 2/5*r**5 - m + 6/5*r + 4/5*r**2 - 8/5*r**3 + 0*r**4 = 0.
-2, -1, 1
Let r(q) be the third derivative of 0*q**3 - 1/90*q**5 + 0 + 1/18*q**4 + 3*q**2 + 0*q. Determine a, given that r(a) = 0.
0, 2
Let g be ((-2)/(-4))/((-9)/(-2)). Let b = 2/9 + g. Suppose 1/3*h**4 + 0*h - b*h**5 - 1/3*h**2 + 1/3*h**3 + 0 = 0. What is h?
-1, 0, 1
Let j = 1 + 1. Suppose 0*m + 3*m - 14*m**j + 17*m**2 = 0. What is m?
-1, 0
Suppose 6/7*u**4 + 10/7*u**3 + 12/7 - 26/7*u**2 - 2/7*u = 0. Calculate u.
-3, -2/3, 1
Let i = 92 - 90. Solve 4/7*y**3 + 16/7*y**2 + 4/7 - 4/7*y**4 - 2/7*y**5 + i*y = 0.
-1, 2
Find q such that -8*q + 3*q**2 - 4*q**2 + q**4 + 5*q**3 + 8 - 10 - q**5 - 2 = 0.
-1, 2
Let v(q) = -q**3 + 7*q**2 - 2*q - 1. Let n be v(7). Let r = -9 