*(t - 1)*(t + 1)
Let l be (-18)/(-10)*((-66)/18 - -5). What is y in 0 + 2/5*y + 8/5*y**2 + 8/5*y**4 + l*y**3 + 2/5*y**5 = 0?
-1, 0
Let v(r) = -7*r**2 + 80*r + 105. Let f(y) = -2*y**2 + 20*y + 26. Let k(t) = 9*f(t) - 2*v(t). Factor k(g).
-4*(g - 6)*(g + 1)
Let u be 5*(24/(-100))/(-1). Let -u*k**2 + 8/5 + 0*k - 2/5*k**3 = 0. Calculate k.
-2, 1
Suppose 0 = -5*h - 14 + 24. Suppose 0 = -v + 5*y + 13, 0 = v + h*v - 5*y - 19. Factor -4/3*i**v + 0*i**2 + 2/3*i**5 + 0 + 0*i**4 + 2/3*i.
2*i*(i - 1)**2*(i + 1)**2/3
Let y(m) be the first derivative of 1/5*m**3 + 0*m + 3 + 0*m**2. Solve y(x) = 0.
0
Let j(c) = -4*c**2 - 11*c. Let p(i) = 3*i**2 + 10*i - 1. Let l(o) = 4*j(o) + 5*p(o). Factor l(x).
-(x - 5)*(x - 1)
Let w(y) be the third derivative of y**2 + 5/144*y**4 - 1/252*y**7 + 0 + 0*y - 1/36*y**3 - 1/36*y**5 + 1/2016*y**8 + 1/72*y**6. Determine s so that w(s) = 0.
1
Let x(i) be the third derivative of i**8/120 + 16*i**7/525 + 11*i**6/300 + i**5/75 - 17*i**2. Factor x(m).
2*m**2*(m + 1)**2*(7*m + 2)/5
What is a in -289*a**2 - 222*a**3 - 863*a**2 - 54 - 802*a**3 - 432*a = 0?
-3/8
Let q(y) = -y. Suppose 0 = -5*w - 4*i + 14, 4*w - 3 = i + 4*i. Let n(d) = -d**2 + 5*d - 2. Let p(g) = w*q(g) + n(g). Factor p(j).
-(j - 2)*(j - 1)
Let o = -169/35 - -27/5. Find z such that -o + z**2 + 4/7*z - 4/7*z**3 - 3/7*z**4 = 0.
-2, -1, 2/3, 1
Let w(h) = -h**3 + 5*h**2 + 6*h. Let o be w(6). Let p = 4 - o. Factor 0 + 2/7*b**2 - 2/7*b**p + 0*b + 2/7*b**3 - 2/7*b**5.
-2*b**2*(b - 1)*(b + 1)**2/7
Let u(g) = -5*g**3 - 8*g**2 + g - 6. Let n be 37/7 + 2/(-7). Let t(q) = 7*q**2 - 6*q - 18*q**3 + 5*q + 22*q**3 + 5. Let y(m) = n*u(m) + 6*t(m). Factor y(p).
-p*(p - 1)**2
Let k(l) be the third derivative of l**7/210 - l**6/40 + l**5/20 - l**4/24 - 4*l**2. Factor k(r).
r*(r - 1)**3
Suppose 0 = -3*n + 14 + 10. Determine v so that -4*v**2 + 2*v**3 - 4*v**2 - 3*v**3 + 3*v**3 + n*v = 0.
0, 2
Let n = 14945/13 - 1149. Determine x, given that 16/13 - 12/13*x**2 + n*x - 2/13*x**4 - 10/13*x**3 = 0.
-2, 1
Let y(a) be the first derivative of -a**6/14 + 3*a**5/35 + 3*a**4/14 - 2*a**3/7 - 3*a**2/14 + 3*a/7 + 18. Factor y(n).
-3*(n - 1)**3*(n + 1)**2/7
Let i(j) be the first derivative of -j**5/5 + j**4 - 4*j**3/3 + 7. Suppose i(n) = 0. Calculate n.
0, 2
Suppose -i - 14 + 2 = 3*u, -3*i = 5*u + 20. Let h = 4 + i. Factor -h*r - 6*r**2 + 8*r - 8*r**2.
-2*r*(7*r - 2)
Let s = 83 - 75. Let f(w) be the third derivative of 0*w**6 + 0*w**4 + 0*w**5 + 0*w + 2*w**2 - 1/168*w**s - 1/105*w**7 + 0*w**3 + 0. Factor f(j).
-2*j**4*(j + 1)
Let m(u) be the first derivative of -4*u**5/45 - 2*u**4/9 + 4*u**3/27 + 4*u**2/9 - 2. Factor m(o).
-4*o*(o - 1)*(o + 1)*(o + 2)/9
Let f(m) be the first derivative of 9/5*m**5 - m - 8/3*m**3 + 1/2*m**4 - 3*m**2 - 1 + 2/3*m**6. Factor f(t).
(t - 1)*(t + 1)**3*(4*t + 1)
Determine m, given that 10/7 + 2/7*m**2 + 12/7*m = 0.
-5, -1
Let r = 7 + -5. Factor 3*k**3 - 2*k**4 + 0*k**3 - 13*k**r + 12*k**2.
-k**2*(k - 1)*(2*k - 1)
Let n be (-21)/(-4) + 15/20. Let l = n - -1. Factor -3*d - 2*d**3 - d**2 - 2*d**3 + 2 + l*d**3 - d**4.
-(d - 2)*(d - 1)**2*(d + 1)
Let l(t) be the third derivative of t**5/120 - t**4/48 - t**3/6 - 7*t**2. Factor l(x).
(x - 2)*(x + 1)/2
Let x(s) be the third derivative of s**5/30 + 5*s**4/3 + 100*s**3/3 + 11*s**2. Solve x(c) = 0 for c.
-10
Let r(s) be the first derivative of -s**7/14 + 3*s**5/20 - 5*s + 5. Let m(x) be the first derivative of r(x). Suppose m(u) = 0. What is u?
-1, 0, 1
Factor -3/2*c - 1/2 - 1/2*c**3 - 3/2*c**2.
-(c + 1)**3/2
Let s(g) be the first derivative of -3*g**4/10 - 22*g**3/15 - 12*g**2/5 - 8*g/5 + 4. Find h, given that s(h) = 0.
-2, -1, -2/3
Let p be -2 + 2 - (-4)/10. Let o(k) = -k**3 - 17*k**2 - 2*k - 32. Let h be o(-17). Factor 1/5*l**3 + p + 0*l**h - 3/5*l.
(l - 1)**2*(l + 2)/5
Let x be (-40)/50*5/(-2). Let 6 + 10*d - 5*d - 8*d - 3*d**x = 0. What is d?
-2, 1
Let x be -1 + 4 + (-5 - (-30)/12). Determine w so that -x*w**2 + w - 1/2 = 0.
1
Let g(u) be the third derivative of -u**7/3780 + u**6/540 - u**5/180 - u**4/12 + 3*u**2. Let z(q) be the second derivative of g(q). Factor z(b).
-2*(b - 1)**2/3
Suppose 0 = 16*s - 14*s - 2. Let a be -2 - (s/(-3) + -2). Solve -a*m + 2/3 - 1/3*m**2 = 0.
-2, 1
Let q(o) be the third derivative of -1/1365*o**7 + 1/39*o**4 - 6*o**2 + 0 + 1/195*o**6 - 1/39*o**3 - 1/65*o**5 + 0*o. Determine c so that q(c) = 0.
1
Let c(l) be the first derivative of 2*l**4 + 14*l**3/3 + l**2 - 6*l + 3. Let d(i) = -i**3 - i**2 + i + 1. Let k(p) = c(p) + 6*d(p). Factor k(a).
2*a*(a + 2)**2
Let r(i) be the second derivative of -i**4/12 - 5*i**3/6 + 3*i**2 - 18*i. Factor r(c).
-(c - 1)*(c + 6)
Let w(n) be the first derivative of -1/10*n**4 + 2/15*n**3 + 0*n**2 + 0*n - 1. Solve w(g) = 0.
0, 1
Suppose -6*g - 2 = 3*s - 2*g, -2*g = -2*s + 8. Let a = 255 + -1781/7. Factor 2/7 - 2/7*n**4 - 4/7*n**3 + 0*n**s + a*n.
-2*(n - 1)*(n + 1)**3/7
Let n(f) be the third derivative of 4*f**2 + 0 + 1/20*f**6 + 0*f**3 + 0*f + 1/168*f**8 - 1/35*f**7 + 0*f**4 - 1/30*f**5. Factor n(h).
2*h**2*(h - 1)**3
Let g = 3 + -3. Factor v**3 + g*v**3 - 2*v**3 - 3*v**2 - 3*v - 1.
-(v + 1)**3
Suppose -4*x + 3*d = 9, -5*x + 2*d - 2 = 4. Let b(r) be the third derivative of 0*r**6 + x*r**3 + 0*r**4 + 1/210*r**7 - 1/60*r**5 + 0 - r**2 + 0*r. Factor b(a).
a**2*(a - 1)*(a + 1)
Let r(t) = -t**3 + 3*t**2 + 2*t - 2. Let y be r(3). Suppose 20 = 6*a - a. Factor 6*q**4 - 8*q**5 + 2*q**2 + 8*q**4 - y*q**2 - a*q**3.
-2*q**2*(q - 1)**2*(4*q + 1)
Let w(o) be the second derivative of o**4/6 - o**2 - 4*o. Factor w(j).
2*(j - 1)*(j + 1)
Let i = -1/81 - -169/567. Let j(a) be the first derivative of i*a**2 + 0*a - 6/7*a**5 - 2 - 8/7*a**4 + 2/21*a**3. Suppose j(s) = 0. What is s?
-1, -2/5, 0, 1/3
Let g be (2 - (2 + -1)) + -1. Let l(d) be the first derivative of 0*d**4 + 0*d**5 - 1/6*d**6 + 2 + 0*d**3 + g*d + 0*d**2. Factor l(q).
-q**5
Let h(b) be the first derivative of b**6/9 - b**4/3 + b**2/3 - 2. Factor h(j).
2*j*(j - 1)**2*(j + 1)**2/3
Let o(q) be the third derivative of -q**2 + 0*q**4 + 0*q + 1/1260*q**6 + 0 + 1/3*q**3 - 1/420*q**5. Let d(f) be the first derivative of o(f). Factor d(n).
2*n*(n - 1)/7
Determine u so that 4/15*u**2 + 8/5*u - 2/15*u**4 - 8/15*u**3 - 6/5 = 0.
-3, 1
Suppose 2*w + 3*y = 4*w + 9, w - 3*y = -9. Suppose -1/3*j**2 + 0*j + j**4 + 0 + w*j**3 + 2/3*j**5 = 0. Calculate j.
-1, 0, 1/2
Let -86*s**4 + 85*s**4 - 2*s**2 + s**2 + 2*s**3 = 0. What is s?
0, 1
Let t(k) be the second derivative of 3*k**7/7 - 4*k**6/3 + 13*k**5/10 - k**4/3 - 15*k. Factor t(u).
2*u**2*(u - 1)**2*(9*u - 2)
Let z be (-36)/30*15/(-9). Let m be (-52)/(-30) - z/5. Factor -8/3*c**2 - 10/3*c - 2/3*c**3 - m.
-2*(c + 1)**2*(c + 2)/3
Solve 0*t**2 - 3*t**3 + 0 - 3/2*t**4 + 0*t = 0 for t.
-2, 0
Let p(j) be the third derivative of 1/4*j**4 + 2/3*j**3 + 0 + 1/240*j**6 + 0*j + 1/20*j**5 - 8*j**2. Determine r so that p(r) = 0.
-2
Let r(a) be the second derivative of 1/2*a**3 + 6*a - 3/10*a**5 + 0*a**4 + 0*a**6 + 0 + 1/14*a**7 + 0*a**2. What is g in r(g) = 0?
-1, 0, 1
Let o(c) = -2*c**2 + 3*c. Let l(z) = z**2 - z. Let w(m) = 15*l(m) + 6*o(m). Factor w(a).
3*a*(a + 1)
Let t(c) be the second derivative of -c**4/3 - 2*c**3/3 + 4*c**2 + 9*c. Suppose t(u) = 0. What is u?
-2, 1
Suppose -5*a - 13 = r, r + 0*a + 5 = -3*a. Let j be (2/(-3))/((-12)/54). Suppose -r*k**2 - 2*k**j + 7*k**2 - 4 + 6*k = 0. What is k?
-2, 1
Let p(n) be the first derivative of -4*n**3/3 - 6*n**2 + 23. Solve p(u) = 0 for u.
-3, 0
Let m(h) be the first derivative of -2*h**5/15 - h**4/2 - 2*h**3/9 + h**2 + 4*h/3 - 11. Solve m(d) = 0 for d.
-2, -1, 1
Let p(f) be the first derivative of f**3/3 - 4*f + 4. Factor p(g).
(g - 2)*(g + 2)
Let y be (-94)/(-6) + 2/(-3). Suppose -o = -6*o + y. What is b in 74 - 74 - 3*b**o + 6*b**2 = 0?
0, 2
Let l(z) = -z - 2 - 3 + 4. Let b(s) = -2*s**2 - 4*s - 10. Let w(q) = b(q) - 8*l(q). Suppose w(j) = 0. What is j?
1
Let x = 144 + -430/3. Factor -2/3 + 0*z + x*z**2.
2*(z - 1)*(z + 1)/3
Let h(k) be the first derivative of -2 + 2/3*k + 1/6*k**2 - 2/9*k**3 - 1/12*k**4. Suppose h(u) = 0. Calculate u.
-2, -1, 1
Determine p so that 6 - 3/2*p**5 - 12*p + 3/2*p**2 - 3/2*p**4 + 15/2*p**3 = 0.
-2, 1
Let x(a) be the third derivative of -a**7/105 - a**6/12 - 3*a**5/10 - 7*a**4/12 - 2*a**3/3 + 3*a**2. Find p such that x(p) = 0.
-2, -1
Suppo