6. Let q = 138 - l. Find r, given that -2*r + 4 + q*r**2 = 0.
4
Let m be -1 + (-8)/(-1) + -4. Let r = -488/7 - -70. Let r*i**m + 2/7*i**2 - 2/7*i**4 - 2/7*i + 0 = 0. What is i?
-1, 0, 1
Suppose 2 = -2*x + 3*x - f, 34 = 5*x + 3*f. Determine p so that 5*p**3 + x*p**4 - 6*p**3 + 7*p**2 - 40*p - 22*p**2 - 20 + 11*p**3 = 0.
-2, -1, 2
Let v = -3164 - -3166. Determine m, given that -2/5*m - 2/5*m**v + 0 = 0.
-1, 0
Let v(b) be the third derivative of 2/3*b**3 - 1/6*b**4 + 5 - 1/15*b**5 + 1/30*b**6 + 0*b - 4*b**2. Factor v(a).
4*(a - 1)**2*(a + 1)
Let w(n) = 4*n**4 + 4*n**3 + 26*n**2 - 5*n + 25. Let r(z) = z**4 + z**2 - z + 5. Let v(g) = 10*r(g) - 2*w(g). Let v(l) = 0. What is l?
-3, 0, 7
Factor 10/3 - 1/6*n**3 + 8/3*n + 1/6*n**2.
-(n - 5)*(n + 2)**2/6
Suppose -5*r = 3*d + 20, -2*r - 4 = 7*d - 5*d. Let j be (54/126)/((-2)/r). Factor 1/6*i**2 + j - i.
(i - 3)**2/6
Let u be ((-28)/756)/(2/(-6)). Let f(b) be the third derivative of -1/72*b**4 + 0 + u*b**3 + 0*b + 2*b**2 - 1/180*b**5. Let f(t) = 0. What is t?
-2, 1
Let q = 75 - 72. Factor -9*o**2 + 3*o**3 - 5*o**q + 2*o - o**4 + 2*o**2 + 8*o**2.
-o*(o - 1)*(o + 1)*(o + 2)
Let x(d) be the second derivative of d**9/2268 - d**7/630 + 14*d**3/3 - 11*d. Let v(k) be the second derivative of x(k). Factor v(r).
4*r**3*(r - 1)*(r + 1)/3
Factor -283 + 180 - 5*p**2 - 45*p + 213.
-5*(p - 2)*(p + 11)
Let 2/7*q**2 + 1250/7 + 100/7*q = 0. Calculate q.
-25
Let p(t) be the second derivative of t**8/12600 - t**7/1260 + t**6/675 + 13*t**3/3 + 12*t. Let x(a) be the second derivative of p(a). Factor x(k).
2*k**2*(k - 4)*(k - 1)/15
Let g(u) be the second derivative of -16/27*u**3 - 1/54*u**4 + 2/45*u**5 + 4/9*u**2 - 6*u + 0. Factor g(z).
2*(z - 2)*(z + 2)*(4*z - 1)/9
Let b(j) be the third derivative of j**9/3024 + j**8/840 + j**7/840 + 4*j**3/3 - 7*j**2. Let y(k) be the first derivative of b(k). Factor y(g).
g**3*(g + 1)**2
Let w(x) be the second derivative of x**6/210 - x**5/105 - x**4/21 - 10*x**2 - 6*x. Let o(c) be the first derivative of w(c). Factor o(y).
4*y*(y - 2)*(y + 1)/7
Let j be (444/140 - 3)*(-1360)/(-408). Factor -10/7*c**3 + 4/7*c**2 - j + 10/7*c.
-2*(c - 1)*(c + 1)*(5*c - 2)/7
Determine t, given that -2/5*t + 0 - 2/5*t**2 + 1/2*t**3 + 3/10*t**4 = 0.
-2, -2/3, 0, 1
Find l, given that 361*l**2 - 351*l**2 + 11*l**3 + 28*l - 25*l + 4*l**4 = 0.
-1, -3/4, 0
Let s = -26/723 - -89/241. Factor 0 - s*h**2 - 1/3*h.
-h*(h + 1)/3
Let u be ((-16)/84*-3)/(4/28). Let 187*z**2 - 387*z**2 - 4*z**u + 192*z**2 + 20*z**3 - 32*z = 0. Calculate z.
-1, 0, 2, 4
Let j(u) be the third derivative of 1/1620*u**6 - 1/6*u**3 + 1/12*u**4 - 1/90*u**5 + 0 + 0*u - u**2. Let r(m) be the first derivative of j(m). Solve r(c) = 0.
3
Let p = 867/685 + -9/137. Determine y, given that -2/5*y**2 - p - 8/5*y = 0.
-3, -1
Let g(t) be the third derivative of t**6/1020 + 7*t**5/255 + 49*t**4/204 - 13*t**2 + 5. Factor g(o).
2*o*(o + 7)**2/17
Let v(n) = 4*n**2 + 4*n. Suppose -4*m - 6 = 2*y, 9*y = 4*y - 4*m - 21. Let o(w) = -7*w**2 - 8*w. Let b(p) = y*v(p) - 3*o(p). Factor b(i).
i*(i + 4)
Let p = 927/6097 - 8/871. Suppose -2/7*s + 0 - p*s**2 = 0. What is s?
-2, 0
Let i(r) be the second derivative of 7*r**5/10 + 67*r**4/18 + 6*r**3 + 8*r**2/3 - 871*r. Factor i(o).
2*(o + 1)*(o + 2)*(21*o + 4)/3
Let j(w) be the first derivative of w**5/300 - w**4/60 - 13*w**2 - 9. Let c(r) be the second derivative of j(r). Factor c(s).
s*(s - 2)/5
Suppose -22*u + 13*u = 0. Let q(f) be the second derivative of -1/8*f**2 - 5*f - 1/48*f**4 + u - 1/12*f**3. Factor q(l).
-(l + 1)**2/4
Let b(u) = 1 - 5*u**2 + u - 5 + 2*u. Let k(h) = 6*h**2 - 4*h + 5. Let q(v) = -4*v + 32. Let o be q(9). Let x(c) = o*k(c) - 5*b(c). Factor x(n).
n*(n + 1)
Let y(j) be the first derivative of -20*j + 65/2*j**2 + 35/4*j**4 - j**5 - 46 - 25*j**3. Factor y(q).
-5*(q - 4)*(q - 1)**3
Let d(j) = -4*j**3 + j**2 + 5*j + 5. Let g(y) = -2*y**3 + y + 29 - 28 + y**3. Let w(u) = 4*d(u) - 20*g(u). Factor w(a).
4*a**2*(a + 1)
Let w(m) be the first derivative of m**4/22 + 10*m**3/11 + 63*m**2/11 + 98*m/11 - 24. Factor w(n).
2*(n + 1)*(n + 7)**2/11
Let t be 2 + ((-20)/7 - ((-87)/(-21) - 5)). Factor 8/7 - 2/7*q**2 + t*q.
-2*(q - 2)*(q + 2)/7
Let w(a) be the second derivative of 27*a**4/28 - 12*a**3/7 + 8*a**2/7 - a + 20. Factor w(f).
(9*f - 4)**2/7
Let b be (64/15)/((-774)/15). Let d = 6/43 - b. Factor -d*o**3 + 0*o + 0*o**2 + 0.
-2*o**3/9
Let n = 3337/4758 - 42/61. Let g = n + 49/234. Factor 2/9*k**2 + g*k + 0.
2*k*(k + 1)/9
Let c = 20 + -26. Let r be (6/12)/(c/4) - -1. Factor r*g**2 + 0 - 1/6*g - 2/3*g**4 + 1/6*g**3.
-g*(g - 1)*(g + 1)*(4*g - 1)/6
Suppose -3*n + 97 - 91 = 0. Determine o so that 4 - 1 - o**2 - n*o - 4*o**2 + 4*o**2 = 0.
-3, 1
Suppose -824*h + 32 = -808*h. Factor -2/5*r + 1/10*r**h + 0.
r*(r - 4)/10
Let z be 56/(-40) + 5 + -9 + 6. Factor -9/5*j**4 - 6/5*j**3 - 3/5*j**5 + 6/5*j**2 + z + 9/5*j.
-3*(j - 1)*(j + 1)**4/5
Suppose 297*v = -269*v + 608*v - 84. Factor 2/5*w**4 + 8/5*w**3 - 8/5 + 6/5*w**v - 8/5*w.
2*(w - 1)*(w + 1)*(w + 2)**2/5
Suppose -961/10 + 31/5*i - 1/10*i**2 = 0. What is i?
31
Let w(m) be the first derivative of m**3/6 + 5*m**2/4 + 2*m + 199. Factor w(x).
(x + 1)*(x + 4)/2
Let j be (3 + 12/4)*(-40)/(-3). Let y be ((-2)/8)/((-30)/j). Factor -y*k + 0 + 1/3*k**2 + 1/3*k**3.
k*(k - 1)*(k + 2)/3
Let 4 - 16/3*y**4 - 8*y**3 + 26/3*y + 4/3*y**2 - 2/3*y**5 = 0. Calculate y.
-6, -1, 1
Suppose 3*c + 0*c = 5*l + 14, -3*l - 6 = -c. Suppose m + 1 = c. Solve 0*k**m - 2/7*k**3 + 0 - 2/7*k**4 + 0*k = 0.
-1, 0
Let w(k) be the first derivative of -7*k**3 - 783*k**2/2 - 222*k - 330. Factor w(s).
-3*(s + 37)*(7*s + 2)
Let z(r) be the first derivative of -r**5/80 + r**4/24 + r**3/24 - r**2/4 + 51*r + 35. Let t(f) be the first derivative of z(f). Find w such that t(w) = 0.
-1, 1, 2
Let z be ((-21)/(-49))/(81/63). Let 0*s + 1/3*s**5 + 1/3*s**2 - 1/3*s**3 + 0 - z*s**4 = 0. What is s?
-1, 0, 1
Determine r, given that -1728/5 + 3/5*r**3 + 1872/5*r - 147/5*r**2 = 0.
1, 24
Let l(b) = -b**3 - 3*b**2 - 6*b + 2. Let v(s) = 2*s**3 + 5*s**2 + 13*s - 5. Let n(q) = -5*l(q) - 2*v(q). Factor n(h).
h*(h + 1)*(h + 4)
Solve -4*g**5 - 24*g**4 + 200 + 232*g - 40*g**3 + 8*g**5 + 188*g + 212*g**2 - 4*g**2 = 0.
-2, -1, 5
Let o(x) be the first derivative of x**6/1620 - x**4/108 - 16*x**3/3 + 17. Let m(z) be the third derivative of o(z). Factor m(i).
2*(i - 1)*(i + 1)/9
Let k = 1119 + -5591/5. Factor k*y**3 + 0 + 2/5*y**2 - 2/5*y.
2*y*(y + 1)*(2*y - 1)/5
Suppose 42*n - 36*n = 12. Factor 4*r + 2 - 3*r - 28*r**n + 27*r**2.
-(r - 2)*(r + 1)
Suppose 0 = -7*x - 585 + 102. Let d = 71 + x. Factor -3/5*q + 2/5 - q**d.
-(q + 1)*(5*q - 2)/5
Suppose 2*s = 5*r - 1050, 5*r + 3*s - 1050 = s. Let q be 3/1*40/r. Factor -q*c + 2/7*c**4 + 0*c**3 - 6/7*c**2 + 0.
2*c*(c - 2)*(c + 1)**2/7
Let j = 101111/183 + -1089/61. Let x = -528 + j. Suppose -4/3*g**2 + 4*g**4 + x*g - 8/3 - 20/3*g**3 = 0. What is g?
-1, 2/3, 1
Let p(i) be the first derivative of 0*i**3 - 3*i**5 + 0*i**2 - 5/6*i**6 - 5/2*i**4 + 0*i - 39. Factor p(b).
-5*b**3*(b + 1)*(b + 2)
Let n(r) = -r**2. Let k(s) = -2*s**3 - 62*s**2 - 28*s. Let l(v) = 4*k(v) - 20*n(v). Solve l(h) = 0.
-28, -1/2, 0
Let c be ((24/(-9))/(-4))/((-1)/3). Let p be 14/(c - 0)*24/(-56). Suppose 9/4*u**3 + 0*u**2 + 0 + 3/4*u**4 - p*u = 0. Calculate u.
-2, 0, 1
Let j be (-21)/12*(-1544)/1351. Let 5/3*f**3 - 6 + 28/3*f**j + 11*f = 0. Calculate f.
-3, 2/5
Factor 1047/2*j**2 + 3/2*j**4 - 51*j**3 + 1350 - 1530*j.
3*(j - 15)**2*(j - 2)**2/2
Let v = -164/3 + 57. Let h = -11/6 + v. Factor 1/2*a - h*a**4 - 1/2*a**3 + 1/2*a**2 + 0.
-a*(a - 1)*(a + 1)**2/2
Let z(g) be the third derivative of -g**6/60 + 19*g**5/10 + 39*g**4/4 + 59*g**3/3 - 232*g**2. Factor z(f).
-2*(f - 59)*(f + 1)**2
Factor 111/2*z - 12321/4 - 1/4*z**2.
-(z - 111)**2/4
Let s(g) be the second derivative of -1/9*g**4 + 4/9*g**3 + 0 + 15*g - 2/3*g**2. Factor s(n).
-4*(n - 1)**2/3
Let a(x) be the first derivative of 0*x + 7/4*x**4 - 2/3*x**3 - 1/2*x**2 - 4/5*x**5 + 27. Factor a(f).
-f*(f - 1)**2*(4*f + 1)
Let w(g) be the first derivative of -3/2*g**2 + 3*g**3 + 3/4*g**4 - 9*g + 6. Suppose w(i) = 0. What is i?
-3, -1, 1
Let d(z) be the second derivative of z**5/20 - 2*z**4/3 + 7*z**3/6 + 25*z + 2. Determine j, given that d(j) = 0.
0, 1, 7
Let p(c) = -13*c - 228. Let r be p(-18