*s**2 + 2*s - 6. Let p(i) = -6*m(i) - 13*o(i). Factor p(q).
q*(q - 2)*(q - 1)*(q + 2)
Factor 1/4*o**2 + 31/2*o - 63/4.
(o - 1)*(o + 63)/4
Let c(h) = -3*h**2 - 5*h. Let s(g) be the first derivative of -g**2/2 - 13. Let b(d) = c(d) - 2*s(d). What is y in b(y) = 0?
-1, 0
Suppose 1/5*v**3 + 1/5*v**2 + 0 + 0*v - 1/5*v**4 - 1/5*v**5 = 0. Calculate v.
-1, 0, 1
Let c(b) be the first derivative of 124/9*b**3 + 8 + 16/3*b + 7/2*b**4 + 44/3*b**2. What is q in c(q) = 0?
-2, -2/3, -2/7
Suppose -3*v - 2*r = -9, -4*v - r + 14 = r. What is b in -2 + 3*b**5 - 2*b**2 + v*b**4 + 0 + 11*b + 1 - 2 - 14*b**3 = 0?
-3, -1, 1/3, 1
Let a(s) = -4*s**2 + 8*s + 2. Let r = 47 + -36. Let n(q) = 7*q**2 - 15*q - 3. Let d(k) = r*a(k) + 6*n(k). Find f such that d(f) = 0.
-2, 1
Let y(j) be the second derivative of 6/5*j**2 + 2/5*j**4 + 5/3*j**3 + 0 - 7/50*j**5 + 11*j. Determine t so that y(t) = 0.
-1, -2/7, 3
Suppose -95 = 103*v - 122*v. Let w(a) be the first derivative of -2/3*a**3 - 1/4*a**6 + 1/4*a**4 + 0*a + 2/5*a**v + 1/4*a**2 + 6. Determine i so that w(i) = 0.
-1, 0, 1/3, 1
Let u(g) be the second derivative of -g**5/80 - 11*g**4/48 + 5*g**3/3 - 7*g**2/2 - 4*g. Factor u(t).
-(t - 2)*(t - 1)*(t + 14)/4
Let o(n) be the first derivative of n**4/36 - n**3/3 + 12*n + 219. Factor o(s).
(s - 6)**2*(s + 3)/9
Suppose 2*u + 4*r - 30 + 10 = 0, 3*u - 5 = -r. Let x(j) be the second derivative of -1/15*j**6 + u*j**2 - 3*j - 1/10*j**5 + 0*j**3 + 1/3*j**4 + 0. Factor x(y).
-2*y**2*(y - 1)*(y + 2)
Let a(s) be the third derivative of 2*s**7/105 + 3*s**6/5 + 109*s**5/15 + 42*s**4 + 392*s**3/3 + 151*s**2. Factor a(q).
4*(q + 2)**2*(q + 7)**2
Let p(u) be the third derivative of u**8/84 + 2*u**7/21 + u**6/6 - u**5/3 - u**4 - 6*u**2 - 18*u. Find l such that p(l) = 0.
-3, -2, -1, 0, 1
Let a(d) be the first derivative of 6*d**5/5 + 17*d**4/2 + 14*d**3/3 - 17*d**2 - 20*d - 125. Suppose a(f) = 0. Calculate f.
-5, -1, -2/3, 1
Determine c so that 9*c**2 - 69*c**4 + 116*c**4 - 48*c**4 + c**3 - 9*c = 0.
-3, 0, 1, 3
Let t(j) = -2*j + 54. Suppose 0 = 3*o + 6*a - a - 101, 4*o = 5*a + 88. Let b be t(o). Factor 1/3*w**5 - 1/3*w**3 + 0*w**4 + b*w + 0*w**2 + 0.
w**3*(w - 1)*(w + 1)/3
Let c(o) be the third derivative of 1/10*o**5 + 8*o**2 + 1/20*o**6 - 1/70*o**7 - 1/112*o**8 - 1/8*o**4 - 1/2*o**3 + 0 + 0*o. Factor c(h).
-3*(h - 1)**2*(h + 1)**3
Let s(d) be the third derivative of -32/21*d**3 + 2/105*d**7 + 8/105*d**5 + 0 + 0*d + 8/105*d**6 + 1/588*d**8 - 8/21*d**4 + 21*d**2. What is o in s(o) = 0?
-2, 1
Let n(q) be the first derivative of 5*q**3 + 228*q**2 + 180*q + 95. Factor n(y).
3*(y + 30)*(5*y + 2)
Let n be (-847)/242 - (-30)/4. Factor -q**2 + 1/3*q**n + 1/3*q**3 + 2/3 - 1/3*q.
(q - 1)**2*(q + 1)*(q + 2)/3
Factor 29/3*s + s**2 - 10/3.
(s + 10)*(3*s - 1)/3
Let i(o) be the first derivative of -2*o**5/45 - o**4/18 + 2*o**3/9 + o**2/9 - 4*o/9 + 57. Find p, given that i(p) = 0.
-2, -1, 1
Suppose -38*k = -44*k + 30. Factor i**2 - 3*i**2 + k + 3 + 4*i**2 - 8*i.
2*(i - 2)**2
Factor 8 - 397*b - 8 - 179*b - 352*b**2 - 68*b**3 - 4*b**4.
-4*b*(b + 4)**2*(b + 9)
Let w(b) be the third derivative of 1/420*b**7 + 0*b**4 + 0 + 1/672*b**8 - 1/240*b**6 + 5*b**2 + 0*b**3 + 0*b - 1/120*b**5. Let w(x) = 0. What is x?
-1, 0, 1
Let c(g) be the third derivative of g**6/24 + 13*g**5/12 - 145*g**4/24 + 25*g**3/2 - 6*g**2 - 64*g. Factor c(v).
5*(v - 1)**2*(v + 15)
Let o(t) be the third derivative of -1/360*t**6 + 1/9*t**3 + 0*t - 4*t**2 + 1/72*t**4 - 1/90*t**5 + 0. Suppose o(s) = 0. Calculate s.
-2, -1, 1
Let b(w) be the first derivative of -11 + 0*w - 3/8*w**4 + 3/4*w**2 - 1/2*w**3 + 3/10*w**5. Solve b(m) = 0.
-1, 0, 1
Factor 132/13*y**2 + 2/13*y**3 + 2904/13*y + 21296/13.
2*(y + 22)**3/13
Let c be 6/(-9)*225/(-6). Suppose -j**2 + j**4 - 33*j + 5*j**3 + c*j - 4 + 0*j**3 - j**5 = 0. What is j?
-1, 2
Let f(l) = -7*l**2 + 9*l + 25. Let q(v) = -12*v**2 + 23*v + 50. Let x(z) = -5*f(z) + 3*q(z). Factor x(p).
-(p - 25)*(p + 1)
Let m(h) be the second derivative of -5*h**4/12 - 5*h**3 + 107*h. Factor m(g).
-5*g*(g + 6)
Let i = -23/60 + 39/100. Let f(x) be the third derivative of i*x**5 + 1/20*x**4 + 0 + 5*x**2 + 2/15*x**3 + 0*x. Find b such that f(b) = 0.
-2, -1
Let q(x) be the first derivative of 1/12*x**2 - 1/24*x**4 + 0*x**3 - 2 + 0*x. Factor q(a).
-a*(a - 1)*(a + 1)/6
Let h = -6657 - -46629/7. Factor -3/7*a**2 - 75/7 + h*a.
-3*(a - 5)**2/7
Let l(j) be the third derivative of j**5/30 + 11*j**4/12 + 28*j**3/3 + 2*j**2 - 7*j. Find s, given that l(s) = 0.
-7, -4
Let m be 173/4 + (7/4 - 2). Let d = -85/2 + m. Find h, given that -d + 6*h - 45/2*h**2 + 25*h**3 = 0.
1/5, 1/2
Let i = -7385 - -36931/5. Factor -2/5*r**2 - i - 8/5*r.
-2*(r + 1)*(r + 3)/5
Let u(z) be the third derivative of 7*z**5/15 + 191*z**4/6 + 36*z**3 + 167*z**2. Factor u(y).
4*(y + 27)*(7*y + 2)
Let i(x) be the first derivative of 5*x**2 + 1/15*x**3 - 3 + 1/30*x**4 + 0*x + 1/150*x**5. Let a(w) be the second derivative of i(w). Let a(c) = 0. What is c?
-1
Suppose 56*c**3 + 256*c**3 - 5*c**2 - 216 - 315*c + 66 + 14*c**2 + 144*c**4 = 0. Calculate c.
-5/4, -2/3, 1
Let j be 4*(76/48 + (-1)/3). Let m be (-3)/((j - 11)/3). Determine t so that -2*t**2 - 1/2*t**3 + 0 - m*t = 0.
-3, -1, 0
Suppose -72*k + 48 = -25*k - 35*k. Factor -81/2*j**k + 108*j**2 + 9/2 + 39*j + 81*j**3.
-3*(j - 3)*(3*j + 1)**3/2
Let y = 1388/7 + -198. Let g = 3415/3976 - 1/568. Factor -y*i**2 - 4/7 + g*i.
-2*(i - 2)*(i - 1)/7
Let v(b) be the second derivative of -b**7/840 + b**6/40 - 9*b**5/40 - 13*b**4/12 + 21*b. Let r(j) be the third derivative of v(j). Find t such that r(t) = 0.
3
Factor -32/11*v**4 + 288/11*v**2 + 0 + 2/11*v**5 + 162/11*v + 92/11*v**3.
2*v*(v - 9)**2*(v + 1)**2/11
Let y(v) be the third derivative of v**6/180 + 2*v**5/45 - v**4/36 - 4*v**3/9 + 4*v**2 + 47*v. Factor y(r).
2*(r - 1)*(r + 1)*(r + 4)/3
Let g(l) be the first derivative of l**6/12 - l**5/2 + l**4/4 + 7*l**3/3 - 3*l**2/4 - 9*l/2 - 19. Find d, given that g(d) = 0.
-1, 1, 3
Let g be ((-17)/34)/((-6)/36). Factor 0*i + 0 + 1/3*i**2 + 2/3*i**g + 1/3*i**4.
i**2*(i + 1)**2/3
Suppose 6*w - 7*w = -32. Let u be 0 + -3 + 6 + w. What is a in a**2 - u + 35 - 3*a = 0?
0, 3
Let -s + 0 + 11/4*s**3 - 3*s**4 - 7/4*s**5 + 3*s**2 = 0. What is s?
-2, -1, 0, 2/7, 1
Let x = 11 + -3. Suppose -2*t + 293 = -3*w, 3*t - x*t = -2*w - 738. Factor -146*v**3 - v**2 - v**2 + t*v**3.
2*v**2*(v - 1)
Let j = -128 - -254. Let o be -3 + 6/(j/75). Let -o*a**3 + 0*a**2 + 4/7*a - 2/7*a**4 + 2/7 = 0. Calculate a.
-1, 1
Let j(r) be the second derivative of -r**4/20 + 139*r**3/5 - 57963*r**2/10 - r - 17. Factor j(b).
-3*(b - 139)**2/5
Let i(g) be the first derivative of g**3/9 + 7*g**2/6 - 116. Determine t so that i(t) = 0.
-7, 0
Let t(z) be the first derivative of 3*z**5/5 + 21*z**4/2 - 114. Factor t(s).
3*s**3*(s + 14)
Let q be (2 + 45/(-20))*(-1 - 19). Let a(z) = -z + 1. Let b be a(-4). Factor 16*v**3 + 8*v**4 - 24*v**4 + 5*v**b - v**q.
4*v**3*(v - 2)**2
Let n(l) be the third derivative of l**7/210 - 13*l**6/120 + 11*l**5/60 + 13*l**4/24 - 2*l**3 - 43*l**2 + l. Factor n(v).
(v - 12)*(v - 1)**2*(v + 1)
Let y(h) = -3*h**3 + 4*h**2 + 11*h - 32. Let k(b) = -b**3 + 3*b**2 + 6*b - 16. Let q(l) = -5*k(l) + 2*y(l). What is f in q(f) = 0?
-4, 1
Suppose -4*u - 2*q + 1496 = 0, q + 1112 = -2*u + 5*u. Let g = u + -1851/5. Let -g - 1/5*t**2 - 6/5*t = 0. Calculate t.
-3
Let f(a) be the third derivative of a**5/60 - 17*a**4/24 - 4*a**2 + 10*a. Let f(c) = 0. What is c?
0, 17
Let w(f) be the third derivative of f**5/690 + 2*f**4/23 - f**2 - 18. Solve w(n) = 0.
-24, 0
Let k(w) = w**2 - 3*w + 4. Let f be k(2). Factor 5*v**f - 5*v**2 + 7*v**2 + 9*v**2 - 4*v**3 - 12*v.
-4*v*(v - 3)*(v - 1)
Let f(s) = s**2 - 6*s - 22. Let q be f(9). Let n(a) be the third derivative of a**2 + 1/120*a**q + 0*a - 1/6*a**3 + 1/48*a**4 + 0. Factor n(j).
(j - 1)*(j + 2)/2
Let u(m) be the first derivative of 4*m**3/3 - 58*m**2 + 216*m - 102. Factor u(f).
4*(f - 27)*(f - 2)
Let z(a) be the first derivative of 21 + 0*a + 1/6*a**2 + 1/9*a**3. What is m in z(m) = 0?
-1, 0
Let v = 3391/45 - 349/5. Let l = 56/9 - v. Determine m so that l*m + m**2 - 43/3*m**4 - 7*m**5 + 0 - 7*m**3 = 0.
-1, -1/3, 0, 2/7
Let r(b) = -10*b + 123*b**2 + 127*b**2 - 248*b**2 - 8. Let u be r(6). Factor -7/3*v**3 + 0*v + 0 - 2/3*v**2 - 5/3*v**u.
-v**2