). Factor c(a).
(a - 3)*(a + 1)
Suppose -84 = 59*u - 261. Factor 12/7*j**2 + 4/7 + 4/7*j**u + 12/7*j.
4*(j + 1)**3/7
Factor 27 - 16*s**3 + 2*s**5 + 12*s - 3 - 16 - 8*s**2 + s**5 + s**5.
4*(s - 2)*(s - 1)*(s + 1)**3
Let p be (0 - -5) + (1 - 2). Suppose 52 = p*w - q, w = -5*q + 16 - 3. Factor -5*x**2 + 12*x - 3*x**3 - 8*x**2 + w*x**2.
-3*x*(x - 2)*(x + 2)
Let d = -593 - -597. Find v, given that -16/7*v**3 - 32/7*v - 4/7 - 72/7*v**2 + 48/7*v**5 + 76/7*v**d = 0.
-1, -1/3, -1/4, 1
Let z be 3/7 - (-32)/7. Suppose 2*q + z*b = q + 128, 4*b = -5*q + 556. Solve -r**3 + 5*r**3 + 2*r**2 + 108*r - q - 38*r**2 = 0.
3
Let t(j) = 2*j**2 + 10*j - 4. Let x(m) = -2*m**2 - m - 1. Let r(f) = t(f) + 2*x(f). Find i, given that r(i) = 0.
1, 3
Determine u so that 18/5 + 56/15*u + 2/15*u**2 = 0.
-27, -1
Let z(a) = -5*a**2 + 9*a. Let f(j) = 6*j**2 - 9*j + 2. Let m(s) = -6*f(s) - 7*z(s). Let b be m(-7). Factor 8/7 + 0*n - 2/7*n**b.
-2*(n - 2)*(n + 2)/7
Let s(t) be the second derivative of 4805*t**4/48 - 155*t**3/6 + 5*t**2/2 - 38*t. Factor s(y).
5*(31*y - 2)**2/4
Suppose 33/4 + 3/4*s**4 + 27*s**2 - 51/2*s - 21/2*s**3 = 0. Calculate s.
1, 11
Let o = 14/1325 - -237/2650. Factor -1/5 + 3/10*y**2 + o*y**3 - 1/10*y - 1/10*y**4.
-(y - 2)*(y - 1)*(y + 1)**2/10
Let g be 1 - (-96)/(-52) - 20/(-8 - 12). Factor g*v**5 - 146/13*v**2 - 22/13*v**4 + 112/13*v - 32/13 + 86/13*v**3.
2*(v - 4)**2*(v - 1)**3/13
Find n such that 76/5*n**2 + 0 - 24*n + 0*n**3 - 4/5*n**4 = 0.
-5, 0, 2, 3
Let f(v) be the third derivative of -5*v**8/288 + 101*v**7/1260 - 17*v**6/180 + v**5/30 + 224*v**2. Solve f(d) = 0.
0, 2/7, 3/5, 2
Let w be 7/((-945)/387) - (-4 + 1). Let m(d) be the second derivative of 5/18*d**4 + 1/45*d**6 + 0*d**2 + 4*d - 2/9*d**3 + 0 - w*d**5. Factor m(g).
2*g*(g - 2)*(g - 1)**2/3
Find p such that -44/13*p**4 - 2/13*p**5 + 88/13*p**2 - 44/13 - 2/13*p + 4/13*p**3 = 0.
-22, -1, 1
Let i be 13/(25 - 12) + -3 + 3. Find f such that -i + 2*f - 5/4*f**2 + 1/4*f**3 = 0.
1, 2
Let u be -5 + 28/(2 + 2). Suppose -3*x + u*g + 16 = 0, g - 5*g = 20. Determine k, given that k - 1/3*k**3 - 2/3 + 0*k**x = 0.
-2, 1
Let m = 16 + -20. Let a = 5 + m. Let b(n) = n. Let j(d) = -4*d**2 + 17*d - 16. Let c(o) = a*j(o) - b(o). Factor c(u).
-4*(u - 2)**2
Let z(n) be the first derivative of n**4/2 + 16*n**3/3 - 45*n**2 + 72*n + 130. Let z(c) = 0. Calculate c.
-12, 1, 3
Let l(i) be the third derivative of i**7/3780 + i**6/540 - 2*i**5/45 - 25*i**4/12 - 32*i**2. Let f(d) be the second derivative of l(d). Solve f(h) = 0 for h.
-4, 2
Factor 3/4*n**2 - 27/4 + 0*n.
3*(n - 3)*(n + 3)/4
Let h(z) = 30*z**2 + 2125*z + 3745. Let k(d) = -5*d**2 - 355*d - 624. Let a(f) = 6*h(f) + 35*k(f). Factor a(m).
5*(m + 2)*(m + 63)
Let s(g) be the first derivative of -5*g**6/4 - g**5/2 + 205*g**4/24 + 55*g**3/18 - 25*g**2/3 + 10*g/3 + 95. Solve s(n) = 0 for n.
-2, -1, 1/3, 2
Let f(k) = k**5 - k**4 - 15*k**3 + 9*k**2 + 28*k - 22. Let g(q) = -q**5 + 16*q**3 - 8*q**2 - 30*q + 23. Let n(l) = 3*f(l) + 2*g(l). Factor n(i).
(i - 5)*(i - 1)**2*(i + 2)**2
Factor 3/7*x**3 - 12/7*x + 1/7*x**4 - 8/7 - 2/7*x**2.
(x - 2)*(x + 1)*(x + 2)**2/7
Factor 225 - 6*z**4 - 9*z + 3*z**4 - 171 - 59*z**2 + 20*z**3 + z**3 + 20*z**2.
-3*(z - 3)**2*(z - 2)*(z + 1)
Suppose 1646*h = 1666*h - 60. Factor 3/7*p**h - 18/7*p**2 + 0 + 0*p.
3*p**2*(p - 6)/7
Factor -14*n + 4*n + 15 + 2*n**3 - 20*n**2 + 8*n**3 + 5*n**4.
5*(n - 1)**2*(n + 1)*(n + 3)
Let y(m) be the first derivative of m**3/9 + 39*m**2/2 + 116*m/3 - 109. Let y(p) = 0. What is p?
-116, -1
Let b(g) be the first derivative of 23 - 2/3*g**2 + 1/3*g + 1/15*g**5 + 2/3*g**3 - 1/3*g**4. Factor b(x).
(x - 1)**4/3
Let w(j) be the second derivative of -j**4/54 - j**3/27 + 2*j**2/9 - 4*j - 18. Factor w(c).
-2*(c - 1)*(c + 2)/9
Let o = 344 - 339. Let r(a) be the first derivative of 0*a - 3/14*a**2 - 1 - 1/14*a**6 + 0*a**3 + 3/14*a**4 + 0*a**o. Factor r(c).
-3*c*(c - 1)**2*(c + 1)**2/7
Let y(x) be the first derivative of -1/30*x**4 - 4/15*x + 6 + 0*x**3 + 1/5*x**2. Factor y(b).
-2*(b - 1)**2*(b + 2)/15
Let j = 26 + -22. Suppose -q + 7 = -s - 0*s, 2*q - j*s - 24 = 0. Determine n so that 0 + 3/7*n**4 + 0*n**q + 0*n + 3/7*n**3 = 0.
-1, 0
Let d be (-3)/2*(-20)/165. Suppose 4*a + 5*t = 1, -t - 4*t - 35 = -5*a. Find m such that 0*m + 0 + 2/11*m**2 + 0*m**3 - d*m**a = 0.
-1, 0, 1
Let v(f) be the first derivative of f**5/210 + f**4/21 + f**3/7 + f**2/2 - 4. Let m(q) be the second derivative of v(q). Factor m(r).
2*(r + 1)*(r + 3)/7
Let j(x) be the first derivative of 0*x**2 - 1/2*x**4 + 0*x + 4/3*x**3 + 13. Let j(a) = 0. What is a?
0, 2
Determine n, given that 0*n + 9/2 - 1/2*n**2 = 0.
-3, 3
Let j(v) = -v**3 + 6*v**2 - 3*v + 14. Let q be j(6). Let w be ((-108)/(-18))/((-54)/q). Factor 2/9*p**4 - 4/9*p**3 - 2/9 + 0*p**2 + w*p.
2*(p - 1)**3*(p + 1)/9
Let f(a) = 3*a**4 - 2*a**3 - 6*a**2 + 12*a - 7. Let j = 113 - 115. Let l(x) = x**2 - 1. Let c(v) = j*f(v) + 6*l(v). Suppose c(n) = 0. Calculate n.
-2, 2/3, 1
Let m = -3 - -5. Let z be (-2 - 10/(-6)) + -3 + 4. Suppose -8/3*f**m + 0 - z*f = 0. What is f?
-1/4, 0
Let q(x) be the third derivative of x**8/504 + 3*x**7/140 + 13*x**6/144 + 31*x**5/180 + x**4/12 - 2*x**3/9 + 13*x**2. Factor q(d).
(d + 1)*(d + 2)**3*(4*d - 1)/6
Let m(w) = w**5 - 10*w**4 + 13*w**3 - 6*w**2 + 2*w + 2. Let h(n) = -3*n**5 + 31*n**4 - 39*n**3 + 18*n**2 - 7*n - 7. Let p(l) = -2*h(l) - 7*m(l). Factor p(v).
-v**2*(v - 6)*(v - 1)**2
Let m(l) be the first derivative of l**6/15 + 2*l**5/5 + 2*l**4/5 + 192. Factor m(b).
2*b**3*(b + 1)*(b + 4)/5
Let h be -39*78/(-378) - 8. Let i(o) be the second derivative of 0 - 7*o + h*o**3 - 1/42*o**4 + 0*o**2. Factor i(f).
-2*f*(f - 1)/7
Let p(h) be the second derivative of h**7/42 + h**6/10 + 3*h**5/20 + h**4/12 - 81*h. Factor p(n).
n**2*(n + 1)**3
Let z(x) be the third derivative of x**6/720 + x**5/60 - 5*x**4/48 + 13*x**3/3 + 16*x**2. Let q(p) be the first derivative of z(p). Let q(a) = 0. What is a?
-5, 1
Let f(h) be the third derivative of h**5/60 + 3*h**4/2 + 54*h**3 - 18*h**2 - 2. Let f(j) = 0. What is j?
-18
Let c(j) be the third derivative of 11*j**9/272160 - j**8/45360 - j**5/30 - 9*j**2. Let z(i) be the third derivative of c(i). Determine d so that z(d) = 0.
0, 2/11
Let q(x) be the first derivative of 4*x**3 + 4*x**2 - 4*x - 41. Determine f, given that q(f) = 0.
-1, 1/3
Factor -1190 + 1694 + 272*r**2 + 318*r - 2*r**3 - 228*r**2.
-2*(r - 28)*(r + 3)**2
Let c be ((-5)/(-5))/(7/(-63)). Let n be (0/1)/(-1) + c/(-21). Let n*o**5 + 0 + 0*o + 0*o**2 + 9/7*o**3 + 12/7*o**4 = 0. What is o?
-3, -1, 0
Let y be ((-106)/(-5))/((-15)/75). Let x = -103 - y. Suppose 0 + 8*n + 4*n**2 + 1/2*n**x = 0. Calculate n.
-4, 0
Let g(b) = b + 1. Let v(m) = -6*m**2 - 5*m + 1. Let r(w) = 5*w**2 + 4*w - 1. Let h(x) = -7*r(x) - 6*v(x). Let o(z) = 6*g(z) - 3*h(z). Factor o(d).
-3*(d - 1)*(d + 1)
Suppose -5*l = 17*l - 44. Suppose 2*o + 2 = 2*t, o + 16 = 6*o + 2*t. Factor 2 - 2*q**3 - q + 3*q + l - 4*q**o.
-2*(q - 1)*(q + 1)*(q + 2)
Let -30 + 2*t + 14/5*t**2 - 2/5*t**3 = 0. Calculate t.
-3, 5
Let v(r) be the first derivative of -r**3/12 - r**2/4 - r/4 - 161. Factor v(j).
-(j + 1)**2/4
Let m be 3/2*48/108*12/32. Find d such that 13/4*d**2 + m*d**3 + 35/4*d - 49/4 = 0.
-7, 1
Let c be 1616/(-505) - (-52)/10. Find v, given that 7/6*v**3 - 1/2*v**c - 1/3 + 5/6*v**4 - 7/6*v = 0.
-1, -2/5, 1
Factor 12*u**2 + 210*u**3 + 209*u**3 - 20*u + 11*u**2 - 4 - 425*u**3.
-(u - 2)**2*(6*u + 1)
Let r(b) be the third derivative of -b**7/70 + b**6/8 + 9*b**5/20 - 81*b**4/8 + 54*b**3 + 414*b**2. Factor r(g).
-3*(g - 3)**3*(g + 4)
Suppose 506/9*z**2 + 280/3*z**3 + 392/9*z**4 + 20/3*z + 2/9 = 0. What is z?
-1, -1/14
Suppose -6/11*p**4 - 2/11*p**5 - 2/11*p - 6/11 + 4/11*p**3 + 12/11*p**2 = 0. What is p?
-3, -1, 1
Let o(s) be the second derivative of -3*s**5/10 + 23*s**4/24 + s**3 + 12*s**2 - 7*s. Let f(w) be the first derivative of o(w). Find a such that f(a) = 0.
-2/9, 3/2
Suppose -10*v - 78/11 - 2/11*v**3 - 34/11*v**2 = 0. Calculate v.
-13, -3, -1
Suppose -6*v = -3 + 21. Let w be (4 - 6) + v/(-2) - -1. Factor 1/2 - 1/2*r**2 - w*r + 1/2*r**3.
(r - 1)**2*(r + 1)/2
Determine v, given that 0 - 16/5*v - 22/5*v**4 + 2*v**2 + 28/5*v**3 = 0.
-8/11, 0, 1
Suppose 2*x = 22*a - 17*a - 10, 8 = -3*x + 4*a. Let t(p) be the second derivative of 9*p + x*