3 - 3*z**2 + z - 1. Let n(p) = -3*a(p) - 21*k(p). Find v such that n(v) = 0.
-13, -2, 0, 2
Suppose 4*y + 5*g - 147 = 0, -5*y - 34*g = -26*g - 189. Determine m so that 15*m**2 - 12/5 + y*m**3 + 27/5*m**5 - 12/5*m + 117/5*m**4 = 0.
-2, -1, -2/3, 1/3
Let f(n) = -14*n**2 - 4*n + 12. Suppose 2*y - 7*y + 10 = 0. Let s(q) = -2*q**y - 12 + q**2 + 13. Let z(l) = -f(l) + 12*s(l). Factor z(c).
2*c*(c + 2)
Factor 0 + 0*k + 0*k**2 - 4*k**3 - 2/3*k**5 - 14/3*k**4.
-2*k**3*(k + 1)*(k + 6)/3
Let a be ((-90)/36)/(2 - (-5)/(-2)). Let v(r) be the third derivative of 0*r**3 + 0 - a*r**2 + 0*r - 1/210*r**5 + 0*r**4. Find u, given that v(u) = 0.
0
Let p = 6995/3 + -2331. Let d(u) be the second derivative of -2*u**2 - 1/5*u**5 + p*u**3 + 1/3*u**4 + 0 + u. Factor d(x).
-4*(x - 1)**2*(x + 1)
Let r(i) be the first derivative of i**3 - 12*i**2 + 45*i + 210. Factor r(p).
3*(p - 5)*(p - 3)
What is k in 2/5*k - 2/5*k**3 + 2 - 2*k**2 = 0?
-5, -1, 1
Determine x so that -10*x - 12*x**2 + 0 - 1/2*x**4 - 9/2*x**3 = 0.
-5, -2, 0
Factor 3/8*h - 1/8*h**2 + 5/4.
-(h - 5)*(h + 2)/8
Let r(x) be the third derivative of x**7/42 - 5*x**6/24 - 3*x**2 - 16*x. Suppose r(y) = 0. Calculate y.
0, 5
Let a(z) = 23*z + 1403. Let d be a(-61). Factor d - 4/23*n**2 + 2/23*n**3 + 2/23*n.
2*n*(n - 1)**2/23
Let d = -773 + 777. Let i(r) be the first derivative of 0*r - 1/2*r**d + 4 + 2/3*r**3 + r**2 - 2/5*r**5. Factor i(x).
-2*x*(x - 1)*(x + 1)**2
Let i(p) = -14*p**2 - 18*p. Let h(n) = -5*n - n + 2*n**2 - 7*n**2. Suppose 5*o - 24 = 2*o. Let d(x) = o*h(x) - 3*i(x). Factor d(c).
2*c*(c + 3)
Let q = 742 - 6676/9. Let c(f) be the second derivative of -1/36*f**4 + q*f**3 + 1/6*f**2 + 0 + 7*f - 1/15*f**5. Factor c(m).
-(m - 1)*(m + 1)*(4*m + 1)/3
Let x(b) be the third derivative of b**8/420 - b**6/75 + b**4/30 - 66*b**2. Factor x(o).
4*o*(o - 1)**2*(o + 1)**2/5
Suppose 39*h**2 + 145 - 65 + 18*h**3 + 3*h**4 - 68 + 36*h = 0. What is h?
-2, -1
Let b(p) = -p**2 - 3*p + 15. Let g be b(-4). Let w be (1 - g/15)/(8/12). Determine u, given that -2/5 - w*u**3 - 6/5*u - 6/5*u**2 = 0.
-1
Let f(q) = 6*q + 31. Let v be f(-7). Let l(c) = -c**3 + 7*c**2 - 6*c - 2. Let s(b) = -5*b**3 + 36*b**2 - 31*b - 11. Let w(a) = v*l(a) + 2*s(a). Factor w(r).
r*(r - 4)*(r - 1)
Factor -265*f**3 - 6*f**2 - 3*f**4 + 257*f**3 + f**4.
-2*f**2*(f + 1)*(f + 3)
Let y(u) be the first derivative of u**5/45 + 19*u**2/2 - 11. Let q(p) be the second derivative of y(p). Factor q(w).
4*w**2/3
Suppose -g - 5*o - 43 = 0, 4*g - 3*o - 10 - 25 = 0. Let b = 0 - 0. Determine r so that b + 8/3*r + 4*r**g = 0.
-2/3, 0
Let b be (18/140)/((-32)/28 + 2). Let j(s) be the first derivative of -6 - 3/8*s**4 + 3/2*s**2 + 3/4*s**3 - b*s**5 - 3*s. Factor j(i).
-3*(i - 1)**2*(i + 2)**2/4
Suppose 2*v - 246 = -80*v. Factor 10 - 1125/2*n**v + 825/2*n**2 + 140*n.
-5*(n - 1)*(15*n + 2)**2/2
Let t(o) = o**2 + 41*o + 80. Let d be t(-39). Let u(i) be the second derivative of 0 + 0*i**4 - 3/80*i**5 + 4*i + 1/8*i**3 + 0*i**d. Factor u(p).
-3*p*(p - 1)*(p + 1)/4
Let t be (16/(-20)*-2)/(56*8/160). Factor -2/7*s + 2/7*s**3 + t - 4/7*s**2.
2*(s - 2)*(s - 1)*(s + 1)/7
Let z(h) = h**2 + 8*h - 27. Let f = -29 + 35. Let v(g) = 7*g**2 + 47*g - 163. Let l(k) = f*v(k) - 39*z(k). Solve l(c) = 0.
5
Suppose -5422 = -3*s - 19618. Let q be (-2)/(6*1) - s/588. Factor -18/7*b**2 + 2/7*b**3 - q + 54/7*b.
2*(b - 3)**3/7
Factor 0 + 0*p - 21/2*p**4 + 10/3*p**3 + 2/3*p**2 - 54*p**5.
-p**2*(4*p - 1)*(9*p + 2)**2/6
Let x = -165 - -183. Factor -6*i**4 + 9*i**5 - 21*i - i**3 - 6*i**5 + 6*i**2 + x*i**2 - 5*i**3 + 6.
3*(i - 1)**4*(i + 2)
Let q be (-13)/((63/(-6))/3 + 3). Suppose 2*o**2 - q*o**3 - 13*o**3 + o - 18*o**4 + 5*o - 5*o**2 = 0. What is o?
-2, -1/2, 0, 1/3
Let y(r) be the second derivative of -1/4*r**3 + 0 + 5/48*r**5 - 6*r + 3*r**2 - 5/96*r**4. Let g(q) be the first derivative of y(q). What is m in g(m) = 0?
-2/5, 3/5
Let l be 10 + (0 - ((-42)/(-6) + -4)). Let p(i) be the first derivative of 3 + 6*i - 27/2*i**2 + l*i**3. Find y such that p(y) = 0.
2/7, 1
Let 15*t - 327*t**2 - 25 + 307*t**2 + 13*t - 4*t**4 + 49 - 28*t**3 = 0. What is t?
-6, -1, 1
Suppose 0 = -3*a - 1 + 7. Suppose 19 - 35 = -4*u. Factor 8/3*s**3 + 2/3*s**u + 4*s**a + 2/3 + 8/3*s.
2*(s + 1)**4/3
Let l be (-2)/1*1*(0 - (-10)/(-50)). Let 2*s - l*s**3 - 2/5*s**2 - 6/5 = 0. Calculate s.
-3, 1
Factor 63/4 - 3/8*b**2 + 3/8*b.
-3*(b - 7)*(b + 6)/8
Let r be (9*1/6)/((-30)/(-8)). Let m(x) be the first derivative of -1/6*x**4 - r*x**5 + 2*x**3 - 4/3*x - x**2 - 3. Solve m(w) = 0.
-2, -1/3, 1
Let s(r) = -3*r**3 - 3*r - 18. Let c(j) = -2*j**3 + 2*j**2 - 3*j - 17. Let i(f) = 6*c(f) - 5*s(f). Factor i(k).
3*(k - 1)*(k + 1)*(k + 4)
Suppose -i - 5 = -0*i + 2*m, -2*m - 2 = 0. Let n be (-14)/24 + i/(-4). Find k, given that 1/6*k**2 - 1/3*k + n = 0.
1
Let z(p) be the first derivative of 5*p**4/4 + 20*p**3/3 + 5*p**2/2 - 30*p + 218. Factor z(w).
5*(w - 1)*(w + 2)*(w + 3)
Let m(o) = -o**3 + o - 1. Suppose 0 = -2*y + 2. Let p(u) = 5*u**3 + 6*u**2 - 41*u + 32. Let f(x) = y*p(x) + 2*m(x). Let f(c) = 0. Calculate c.
-5, 1, 2
Let r = 3249 - 3247. Find b, given that -1/7 - 1/7*b**r + 2/7*b = 0.
1
Let p(j) be the first derivative of -1/2*j**4 + 4/9*j**3 + 2/15*j**5 - 17 + 0*j + 0*j**2. Determine b so that p(b) = 0.
0, 1, 2
Suppose -192 + 52 = -70*q. Solve 8/11*v**q + 2/11*v**3 + 0 + 6/11*v = 0.
-3, -1, 0
Let v(b) be the first derivative of 129/14*b**4 + 60/7*b**2 + 16/7*b + 19 + 16/5*b**5 + 268/21*b**3 + 3/7*b**6. Suppose v(w) = 0. Calculate w.
-2, -1, -2/9
Let j = -100 + 113. Let n be (j/208)/(1/(-6)*-3). What is v in -1/8*v**2 - 1/4*v + n*v**3 + 0 = 0?
-1, 0, 2
Factor 13*z**3 - 200 - 10*z**2 - 26*z**2 + 41 - 9*z**3 - 192*z - 49.
4*(z - 13)*(z + 2)**2
Let x be (-8)/14 + (-29)/(4060/(-192)). Suppose -2/5*c**2 + x*c**3 - 2/5*c + 0 = 0. Calculate c.
-1/2, 0, 1
Let r(h) be the second derivative of -h**8/4200 - h**7/1050 - h**6/900 - 29*h**3/6 + 19*h. Let z(k) be the second derivative of r(k). Factor z(p).
-2*p**2*(p + 1)**2/5
Let m = -108 + 110. Let p(q) be the first derivative of m*q**2 - 2/3*q**3 + 5 - q**4 + 2/5*q**5 + 0*q. Factor p(s).
2*s*(s - 2)*(s - 1)*(s + 1)
Determine k so that 2/5*k**2 + 0 - 18/5*k = 0.
0, 9
Let k(q) be the first derivative of -q**5/20 + 15*q**4/16 - 37*q**3/6 + 33*q**2/2 - 18*q + 180. Factor k(f).
-(f - 6)**2*(f - 2)*(f - 1)/4
Factor 4/3*j**3 + 3*j**2 + 0*j + 0.
j**2*(4*j + 9)/3
Let p(o) = -o**3 - 4*o**2 + 6*o + 6. Let w be p(-5). Let b(m) = 9*m**2 - 1. Let l be b(w). Solve 33*r**3 + r**2 - 9*r**4 - 5*r**2 - l*r**2 - 9*r**3 = 0 for r.
0, 2/3, 2
Let t(m) = m**3 + 12*m**2 + 10*m - 6. Let q be t(-11). Suppose -q = -5*d + 20. Factor 3 + 10*g**3 + 0*g**3 + d - 4*g - 6*g**3 - 8*g**2.
4*(g - 2)*(g - 1)*(g + 1)
Suppose 0 = 5*j + 5 + 15. Let d(q) = q**2 - q. Let r(i) = -5*i**2 + 5*i. Let a(g) = j*d(g) - r(g). Suppose a(n) = 0. What is n?
0, 1
Let c(p) be the first derivative of -2*p**3/27 - 62*p**2/9 - 80*p/3 + 295. What is v in c(v) = 0?
-60, -2
Let b be (-17)/21 + 1 + 5/((-75)/(-10)). Factor 2/7*c**3 + 2*c + 10/7*c**2 + b.
2*(c + 1)**2*(c + 3)/7
Suppose 0 = 4*o - 0*o + y - 115, -4*y = 3*o - 83. Let b(z) = -2*z - 12. Let f be b(-8). Factor 29 - f*p**2 + 3*p - o + 2*p**5 - 5*p + 4*p**4.
2*p*(p - 1)*(p + 1)**3
Let p(w) = -6*w**2 - 11*w + 7. Let s be p(5). Let a = s + 1388/7. Let 2/7*z**2 + a*z - 4/7 = 0. What is z?
-2, 1
Let i(c) be the third derivative of c**7/70 + 11*c**6/5 + 526*c**5/5 + 924*c**4 + 3528*c**3 - 76*c**2. Let i(z) = 0. What is z?
-42, -2
Let f be 3/(-4)*24/(-117). Suppose -5*b + 14 = 4*n - 0*n, 4*b + 4*n = 12. Suppose -6/13*g**3 - 6/13*g**b + 0 - f*g**4 - 2/13*g = 0. Calculate g.
-1, 0
Suppose -40 = 9*c - 5*c. Let v = 31/3 + c. Factor -1/3*j**2 + 2/3 - v*j.
-(j - 1)*(j + 2)/3
Factor 0*x + 4/13*x**2 + 0 + 38/13*x**3.
2*x**2*(19*x + 2)/13
Suppose 0*s + 28/3*s**2 - 20*s**3 - 4/3*s**5 + 12*s**4 + 0 = 0. What is s?
0, 1, 7
Let y(l) = 13*l**3 - 45*l**2 + 168*l + 7. Let q(m) = 9*m**3 - 29*m**2 + 112*m + 5. Let i(j) = 7*q(j) - 5*y(j). Find v such that i(v) = 0.
0, 4, 7
Let n(c) be the first derivative of -4*c + 1/3*c**3 + 1/4*c**4 - 2*c**2 + 2. Factor n(v).
(v - 2)*(v + 1)*(v + 2)
Determine j so that -11/2 + 79/4*j - 31/2*j**2 + 5/4*j**3 = 0.
2/5, 1, 11
Factor 2/5*p**4 + 6/5*p**2 - 8/5 - 2*p**3 + 2*p.
2*(p - 4)*(p - 1)**2*(p + 1)/5
Fact