alculate n.
1, 13
Let v(z) be the second derivative of 3*z**5/140 + z**4/14 - 2*z**3/7 - 12*z**2/7 - 4*z + 15. Determine s, given that v(s) = 0.
-2, 2
Let j(v) = 2*v**2 - 12*v + 18. Let g be j(6). Let f(i) be the first derivative of -24*i + g*i**2 + 8 - 6*i**3 + 3/4*i**4. Factor f(x).
3*(x - 2)**3
Suppose 7*u = 2*u + 10. Suppose -4*i - u*i + 24 = 0. Factor -10*c**2 + 2*c**3 + i*c**4 - c**3 - 11*c**5 + 12*c**5 + 8 - 4*c.
(c - 1)**2*(c + 2)**3
Let x(b) = -2*b**2 - 120*b + 118. Let u(q) = 4*q**2 + 119*q - 117. Let t(k) = -2*u(k) - 3*x(k). Let t(o) = 0. What is o?
1, 60
Let x(v) = 2*v**4 - v - 1. Let w(o) = -135*o**5 + 116*o**4 + 288*o**3 + 80*o**2 - 20*o - 4. Let a(p) = -w(p) + 4*x(p). Let a(q) = 0. What is q?
-2/3, 0, 2/15, 2
Let r(q) be the third derivative of -q**6/540 - 49*q**5/270 - 95*q**4/108 - 47*q**3/27 + q**2 - 414*q. Factor r(y).
-2*(y + 1)**2*(y + 47)/9
Let g(d) be the first derivative of -d**4/8 - 7*d**3/3 + 15*d**2/4 + 82. Factor g(f).
-f*(f - 1)*(f + 15)/2
Find m such that -24 - 28*m**3 + 0*m**5 + 6*m**5 - 18*m**3 - 5*m + 106*m**2 - 27*m - 10*m**4 = 0.
-3, -1/3, 1, 2
Let 119*n**2 - 13*n - 155*n + 2352 - 116*n**2 = 0. Calculate n.
28
Let z(u) = -2*u + 13. Let k be z(6). Let l(m) = -m**3. Let s(v) = 5*v**3 - 2*v**2. Let f(p) = k*s(p) + 4*l(p). Determine c so that f(c) = 0.
0, 2
Let o(x) be the first derivative of 1/4*x**3 + 1/16*x**4 + 0*x - 6 - 1/10*x**5 + 0*x**2. Determine a so that o(a) = 0.
-1, 0, 3/2
Let a(i) = -70*i**5 - 70*i**4 + 210*i**3 + 155*i**2 - 225*i. Let b(o) = 5*o**5 + 5*o**4 - 15*o**3 - 11*o**2 + 16*o. Let v(z) = 6*a(z) + 85*b(z). Factor v(s).
5*s*(s - 1)**2*(s + 1)*(s + 2)
Let o(s) be the third derivative of s**5/30 - 16*s**4/3 + 21*s**3 + 29*s**2 - 2. Factor o(x).
2*(x - 63)*(x - 1)
Let d(s) be the first derivative of -5*s**4/8 + 44*s**3/3 - 369*s**2/4 - 81*s + 78. Let d(f) = 0. What is f?
-2/5, 9
Let z(x) be the third derivative of 2*x**2 + 0*x**3 - 1/600*x**6 + 0*x + 1/300*x**5 + 0 + 1/60*x**4. Factor z(y).
-y*(y - 2)*(y + 1)/5
Let t(s) be the first derivative of s**3/3 + 18*s**2 + 324*s + 7. Factor t(l).
(l + 18)**2
Let b(d) be the second derivative of -d**7/280 + d**5/40 + d**3/2 + 14*d. Let i(g) be the second derivative of b(g). Find u such that i(u) = 0.
-1, 0, 1
Factor 6*f**2 - 4*f + 0*f**4 + 3*f**4 + f**4 - 6*f**4.
-2*f*(f - 1)**2*(f + 2)
Let g(q) be the second derivative of -q**6/180 - q**5/30 - q**4/12 + 11*q**3/3 + 14*q. Let k(d) be the second derivative of g(d). Find x, given that k(x) = 0.
-1
Let h be ((-2)/28)/(((-49)/(-14))/(-7)). Let r(x) be the first derivative of -h*x**4 + 1/7*x**2 + 0*x - 1 + 1/21*x**6 + 0*x**3 + 0*x**5. Solve r(b) = 0.
-1, 0, 1
Let j(r) = 0*r - r + 4*r**2 - 5*r**2 - 3*r. Let k be j(-4). Let -4/3*a**3 - 16/3 + 4*a**2 + k*a = 0. Calculate a.
-1, 2
Let u = 47 + -33. Suppose -5*b + u = -21. Factor 10*h**2 + 22*h - 56*h + 5 + b.
2*(h - 3)*(5*h - 2)
Let a(g) = g**5 - 2*g**4 + g + 1. Let u(y) = 4*y**5 - 6*y**4 - 2*y**3 - 4*y**2 + 8*y + 8. Let q(b) = 8*a(b) - u(b). Find i such that q(i) = 0.
-1/2, 0, 1, 2
Suppose -3*j - 2 = -5*u + 11, 4*u - 2*j - 12 = 0. Suppose -n = -u*n + 12. Factor -1/4 - 1/4*h**n + 1/4*h + 1/4*h**2.
-(h - 1)**2*(h + 1)/4
Let r be -3 + (-383)/(-193) - -1. Let u = r + 1191/2123. Factor -4/11*s**2 + u*s**4 + 2/11*s**3 + 0*s + 0.
2*s**2*(s + 1)*(3*s - 2)/11
Let s be (((-1764)/56)/(-7))/(33/4). Factor -s*o**2 - 6/11*o**3 + 6/11*o + 6/11.
-6*(o - 1)*(o + 1)**2/11
What is r in 25/6*r - 1/6*r**3 + 1/6*r**2 - 25/6 = 0?
-5, 1, 5
Let y be 5*(-4)/(-100) - (-3)/15. Let o(j) = -j**3 + 20*j**2 - 18*j - 17. Let u be o(19). Factor -y*q**3 - 2/5*q**4 + 0 + 2/5*q + 2/5*q**u.
-2*q*(q - 1)*(q + 1)**2/5
Let s be 5*(-16)/(-30)*25. Factor s*d**3 - 32/3 + 224/3*d - 160*d**2 + 250/3*d**4.
2*(d + 2)*(5*d - 2)**3/3
Let v(l) = -l**2 - 9*l + 6. Let u be v(-9). Suppose 2*j - u*j + 8 = 0. Solve 0*p**j + 0*p + 2/7*p**5 - 2/7*p**4 + 0 - 4/7*p**3 = 0 for p.
-1, 0, 2
Solve -3/2*q**2 - 5/2*q - 1/2*q**4 + 2 + 5/2*q**3 = 0.
-1, 1, 4
Factor 635*d**3 - 925 - 79*d**4 - 239*d**4 + 103*d**4 - 615*d**2 + 185*d + 935.
-5*(d - 1)**3*(43*d + 2)
Suppose 0 = -5*q - 0*q - 25. Let b(g) = 7*g**2 - 2. Let p(w) be the third derivative of w**5/60 + 145*w**2. Let y(z) = q*p(z) + b(z). Factor y(h).
2*(h - 1)*(h + 1)
Let r(q) = -19*q + 14. Let s be r(-6). Determine k so that 3*k**5 - s*k**2 + 112*k**3 - 23*k**5 - 7*k + 64 - 121*k - 88*k**4 + 116*k**4 = 0.
-2, -1, 2/5, 2
Let n be 2 + (-2355)/1575 + (-2)/4. Let b(a) be the third derivative of -4*a**2 + 0*a**3 - n*a**7 + 0 + 0*a - 1/120*a**6 + 1/60*a**5 + 1/24*a**4. Factor b(t).
-t*(t - 1)*(t + 1)**2
Let k(l) be the third derivative of -l**5/100 + 4*l**4/5 + 34*l**3/5 + 419*l**2. Determine n, given that k(n) = 0.
-2, 34
Let i(n) be the first derivative of 1/8*n**2 - 26 + 1/12*n**3 - 3*n. Suppose i(a) = 0. What is a?
-4, 3
Factor -3*y - 39*y**2 - 2*y + 14*y**2 + 20*y**3 + 10*y.
5*y*(y - 1)*(4*y - 1)
Let a(o) be the second derivative of -9/10*o**5 + 1/10*o**6 - 8*o + 3*o**4 + 0 + 0*o**2 - 4*o**3. Find n such that a(n) = 0.
0, 2
Suppose 6*u + 10 = 4*u + 4*t, 3*u = t + 5. Let m(w) be the first derivative of -1/3*w**u + 5 + w + 1/2*w**2 - 1/4*w**4. Suppose m(i) = 0. What is i?
-1, 1
Let y(a) be the third derivative of -a**6/72 - 7*a**5/135 - 11*a**4/216 + a**3/27 + 6*a**2 - 4. Determine l so that y(l) = 0.
-1, 2/15
Let j(k) be the first derivative of -k**4/30 - 16*k**3/45 + 19*k**2/15 - 4*k/3 - 225. Factor j(y).
-2*(y - 1)**2*(y + 10)/15
Find b such that -56/5*b + 1176/5 + 2/15*b**2 = 0.
42
Suppose -14*a = 8*a - 572. Suppose -10 - a = -18*w. Factor -98/11*o**3 - 232/11*o - 448/11*o**w - 32/11.
-2*(o + 4)*(7*o + 2)**2/11
Let z(o) be the first derivative of o**8/112 + o**7/105 - o**6/120 - o**2/2 + 18*o + 5. Let f(p) be the second derivative of z(p). Factor f(k).
k**3*(k + 1)*(3*k - 1)
Let h(r) be the second derivative of -r**5/10 - 31*r**4/6 - 86*r**3/3 - 56*r**2 - 462*r. Solve h(l) = 0 for l.
-28, -2, -1
Let m(x) = 3*x**3 - 19*x**2 - 15*x + 9. Let g be m(7). Suppose -2/5 - 2/5*s**g + 4/5*s = 0. What is s?
1
Let c(y) = y**4 + y**3 + 2*y**2 + y + 1. Let f(h) = -8*h**4 - 14*h**3 - 25*h**2 - 12*h - 7. Let s(i) = -35*c(i) - 5*f(i). Factor s(w).
5*w*(w + 1)**2*(w + 5)
Let f(c) be the third derivative of c**6/8 + 11*c**5/12 + 5*c**4/4 - 10*c**2 + 5. Find q, given that f(q) = 0.
-3, -2/3, 0
Let y(p) be the third derivative of -p**6/300 - 2*p**5/75 + 6*p**2 - 6*p. Factor y(a).
-2*a**2*(a + 4)/5
Let p(o) = 5*o**2 - 3*o. Let h be p(2). Determine f, given that 6*f + 2 - 7*f**5 + 0*f**4 - 3*f + 5*f**4 + 7*f**4 - h*f**2 + 4*f**3 = 0.
-1, -2/7, 1
Let t(o) be the second derivative of -o**7/147 + 2*o**6/21 - 16*o**5/35 + 13*o**4/21 + 11*o**3/7 - 36*o**2/7 + 2*o + 46. Determine m, given that t(m) = 0.
-1, 1, 3, 4
Suppose 485*x + 32 - 994*x + 495*x - x**2 = 0. What is x?
-16, 2
Factor -i**4 - 62*i**2 + 128*i**2 - 65*i**2 + 0*i**4.
-i**2*(i - 1)*(i + 1)
Solve 3*k**4 - 7*k**2 - 14*k**2 - 6*k**4 - 3*k**2 + k**4 - 14*k**3 = 0.
-4, -3, 0
Let o = -78 + 81. Let r(x) = -x**2 + x + 8. Let z be r(0). Factor z*t**3 - 2*t**o - 1 + 8 - 14*t + 4*t**2 - 3.
2*(t - 1)*(t + 2)*(3*t - 1)
Find y, given that 2/5*y + 36/5*y**2 + 0 + 26*y**3 = 0.
-1/5, -1/13, 0
Let g(f) be the second derivative of -f**5/30 + 23*f**4/18 - 40*f**3/3 - 48*f**2 - 2*f - 22. Determine p so that g(p) = 0.
-1, 12
Suppose -9*v + 8*v + 2 = 0. What is k in -3*k**v + 3847*k + 3 - 3847*k = 0?
-1, 1
Let c = -17897/9 + 1989. Factor 0 - c*j - 2/9*j**3 + 2/3*j**2.
-2*j*(j - 2)*(j - 1)/9
Let t(s) be the first derivative of 5 - 8/3*s**3 - 2*s**2 + s**4 + 8*s. Factor t(u).
4*(u - 2)*(u - 1)*(u + 1)
Let i(p) = p**2 - p. Let n(s) = 130*s**2 - 75*s + 12. Let w(y) = 6*i(y) - n(y). Let x(q) = -123*q**2 + 68*q - 11. Let h(u) = -2*w(u) + 3*x(u). Solve h(v) = 0.
3/11
Let p(z) be the third derivative of -z**9/3024 + z**8/448 - z**7/168 + z**6/144 + 5*z**4/24 + 13*z**2. Let g(f) be the second derivative of p(f). Factor g(y).
-5*y*(y - 1)**3
Find f such that -8/3*f + 1/3*f**4 - 1/3*f**5 - 28/3*f**2 + 32/3 + 14/3*f**3 = 0.
-4, -1, 2
Let n be 4/8 - (96/8)/(-72). Factor n + 4/3*z - 2*z**2.
-2*(z - 1)*(3*z + 1)/3
Let r(f) be the second derivative of f**5/5 - 11*f**4/3 - 62*f**3 - 306*f**2 + 355*f. Factor r(p).
4*(p - 17)*(p + 3)**2
Factor -22*r**3 + 17*r + 14*r**3 + 15