- x.
(x - 1)**2*(x + 1)
Let j(y) be the first derivative of y**7/630 + y**6/90 + y**5/30 + y**4/18 + y**3/18 - 3*y**2/2 + 8. Let x(c) be the second derivative of j(c). Factor x(n).
(n + 1)**4/3
Factor -59*w - 43*w - 2*w**3 + 168*w - 52*w - 12.
-2*(w - 2)*(w - 1)*(w + 3)
Let o(y) be the second derivative of -y**7/126 - y**6/10 - 29*y**5/60 - 43*y**4/36 - 5*y**3/3 - 4*y**2/3 - 72*y. Factor o(v).
-(v + 1)**3*(v + 2)*(v + 4)/3
Let u be 20/(-5) + (-1)/(-1). Let h be 2*(u + 45/6). Let 2 + 2 + 13*y**2 + 8*y**2 - h*y**2 + 4*y**3 + 12*y = 0. What is y?
-1
Factor 4/9*t**3 + 0 + 224/9*t + 20/3*t**2.
4*t*(t + 7)*(t + 8)/9
Let q(f) = f**2 + 4*f - 2. Let r be q(-5). Suppose 6*v - 29 = 1. Factor w - 5*w + 7*w + 3*w**v - 6*w**r.
3*w*(w - 1)**2*(w + 1)**2
Suppose 0 = 2*y - 0*y. Suppose y = -3*n - 3, -3*z + 4*n + 16 = -0*n. Solve 2*m**2 + 0*m**3 + 4*m**3 - 18*m**2 + z*m**2 = 0 for m.
0, 3
Let g = 8 + -4. Let x be (2 - -1) + 0/(-10). What is m in 3 - 2*m**5 + 6*m**5 + m**3 - 2 - 5*m**2 + 5*m**g - m + x*m**4 = 0?
-1, 1/2
Factor 0*d**3 + 2/7*d + 0 - 2/7*d**5 + 4/7*d**4 - 4/7*d**2.
-2*d*(d - 1)**3*(d + 1)/7
Let v = 17/12 - 13/12. Determine h so that v*h**3 - 2*h**2 + 3*h + 0 = 0.
0, 3
Let s(q) = 12*q**2 - 366*q - 3. Let o(b) = -27*b**2 + 731*b + 7. Let p(v) = 3*o(v) + 7*s(v). Determine i, given that p(i) = 0.
0, 123
Determine j so that -36*j**3 - 1221*j**4 + 8 - 45*j**2 + 52 - 7*j**2 - 4 + 36*j + 1217*j**4 = 0.
-7, -2, -1, 1
Let k be -73 + 50 + 27 + (-12)/5. Factor 8/5 - 2/5*g**2 + 2/5*g**3 - k*g.
2*(g - 2)*(g - 1)*(g + 2)/5
Let z(d) = d**2 + 19*d + 73. Let y be z(-23). Let w be (462/y)/(1 - 0). Factor 2*x**2 - w*x**3 + 4/5*x + 0.
-2*x*(x - 1)*(7*x + 2)/5
Let n(l) be the third derivative of l**6/360 - l**5/90 - 13*l**4/72 - 5*l**3/9 + 482*l**2. Factor n(x).
(x - 5)*(x + 1)*(x + 2)/3
Let z(v) = v**5 - v**4 + v**3 - v**2. Let n(t) = -9*t**4 + 7*t**3 + 2*t**2. Let c(y) = -n(y) - 4*z(y). Find x, given that c(x) = 0.
0, 1/4, 1, 2
Let a = 786/935 - 56/85. Factor 0*p + 0 + a*p**2.
2*p**2/11
Factor 4*y**3 + 45*y**2 - 3*y**3 - 48*y**2 + 2*y.
y*(y - 2)*(y - 1)
Let y(n) be the first derivative of -5/6*n**4 + 4/3*n**2 + 28 + 16/3*n - 13/3*n**3 + 5/3*n**5. Suppose y(u) = 0. Calculate u.
-4/5, 1
Let z(q) be the first derivative of -1/2*q + 1/12*q**3 - 12 - 1/8*q**2. Let z(n) = 0. Calculate n.
-1, 2
Let u(j) be the first derivative of 2*j**5/5 - 6*j**4/5 + 6*j**3/5 - 2*j**2/5 + 168. Factor u(h).
2*h*(h - 1)**2*(5*h - 2)/5
Let t(r) = r**3 - 6*r**2 - 8*r + 14. Let a be t(7). Let i(o) = 4*o - 28. Let u be i(a). Let -3/4*l**2 + 3/2*l**4 + u - 3/4*l**3 + 0*l = 0. What is l?
-1/2, 0, 1
Let y be 2169/(-27) + 12/(-9). Let h = -81 - y. Factor 2/3 + 4/3*b - 4/3*b**3 + 0*b**2 - h*b**4.
-2*(b - 1)*(b + 1)**3/3
Let o = -1/1307 + 1315/10456. Let x(s) be the second derivative of -1/48*s**4 + 5*s + o*s**2 + 0 + 0*s**3. Factor x(m).
-(m - 1)*(m + 1)/4
Suppose 0*d = -2*d + 32. Let i = d + -13. Let -4 + 6*y**2 - 1 - 4*y + i = 0. Calculate y.
-1/3, 1
Determine h, given that 27/5*h + 2/5 + 13/5*h**2 = 0.
-2, -1/13
Let u(i) = i**3 + 4*i**2 + i. Let n(k) = k**3 + 4*k**2 - 7*k - 7. Let q be n(-5). Let g(l) = 3*l**3 + 11*l**2 + 2*l. Let c(s) = q*g(s) - 8*u(s). Factor c(o).
o*(o - 1)*(o + 2)
Let l(o) be the third derivative of -5*o**8/1008 - o**7/315 + 9*o**2 - 6. Determine u, given that l(u) = 0.
-2/5, 0
Let f(m) = -m**2 - m + 1. Let s(h) = -3*h**2 + 9*h + 2. Let p(w) = 4*f(w) - s(w). Let g be p(-13). Find x, given that 1/2 + 11/4*x + 9/4*x**g = 0.
-1, -2/9
Let c(l) = -5*l + 49. Let g be c(9). Factor 244*u - 4*u**4 - 241*u + 34*u**4 - 14*u**2 + g*u**3 + 9*u**5.
u*(u + 1)*(u + 3)*(3*u - 1)**2
Let d(j) be the first derivative of 18*j**3 + 10*j**2 - 28 - 14*j**3 - 20*j + 8*j - 5*j**4. Factor d(r).
-4*(r - 1)*(r + 1)*(5*r - 3)
Let h(j) = -j**3 - j + 10. Let s be h(0). Let k = -6 + s. Determine q, given that q**2 + 4 - 5 + k*q + 5 = 0.
-2
Let w(u) be the first derivative of u**5/10 + 3*u**4/4 - 47*u**3/6 - 42*u**2 + 392*u - 178. Solve w(h) = 0 for h.
-7, 4
Let j be 1/(-4)*60/105*-7. Let v be (-121)/(-132) + (j/(-4))/1. Factor -1/3*m**3 + v*m**2 + 0 - 1/3*m**4 + 0*m.
-m**2*(m - 1)*(m + 2)/3
Let o = -335 - -6035/18. Let j = o - -2/9. Find c such that 1/2*c - j*c**2 + 0 = 0.
0, 1
Factor -64*p + 4/5*p**2 + 0.
4*p*(p - 80)/5
Let b(c) be the third derivative of 0*c - 19*c**2 + 5/4*c**4 - 8/35*c**5 + 0 + 1/84*c**6 + 50/21*c**3. Find h, given that b(h) = 0.
-2/5, 5
Let i(v) be the first derivative of 7*v**3/3 + 5*v**2 + 3*v + 10. Factor i(d).
(d + 1)*(7*d + 3)
Let i(y) = -9*y**2 - 3*y. Let h(o) = o**3 - 15*o**2 + 16*o - 14. Let f be h(14). Let d(z) = 26*z**2 + 10*z. Let l(k) = f*i(k) + 5*d(k). Solve l(w) = 0 for w.
-2, 0
Let s(j) be the third derivative of 2*j**7/15 - 19*j**6/40 + j**4/6 + 6*j**2 + 9*j. Determine u, given that s(u) = 0.
-1/4, 0, 2/7, 2
Let g be (-108)/(-14) - 2/(-7). Suppose -w = w - r - g, -w = -r - 5. Factor 12*f**3 + 6*f**3 + 4*f**w - 8*f**2 + 36*f**5 - 2*f**3 + 64*f**4.
4*f**2*(f + 1)**2*(9*f - 2)
Determine a so that 17*a**3 + 12*a**4 + 6*a**5 + 11*a**3 - 2*a**5 + 20*a**4 = 0.
-7, -1, 0
Let k(a) = 9*a**3 + 98*a**2 + 60*a + 11. Let x(p) = 9*p**3 + 99*p**2 + 61*p + 11. Let i(h) = 6*k(h) - 7*x(h). Factor i(d).
-(d + 11)*(3*d + 1)**2
Let h(z) = 13*z**3 + 95*z**2 + 535*z + 836. Let s(t) = 4*t**3 + 32*t**2 + 178*t + 280. Let f(x) = 2*h(x) - 7*s(x). Let f(c) = 0. What is c?
-9, -4
Let m = 283 - 279. Let z(d) be the second derivative of -d**3 - 9*d - 1/4*d**m + 0 - 3/2*d**2. Determine n so that z(n) = 0.
-1
Suppose 265 = 9*p - 5. Let h be ((-4)/p)/(3/(-27)). Factor 2/5*t**2 + h*t + 0.
2*t*(t + 3)/5
Let d = 11112 + -66671/6. Factor 2*u + 4/3 + d*u**3 + u**2.
(u + 2)**3/6
Let b(a) be the third derivative of -a**9/98280 + a**8/21840 - a**7/16380 - a**4/8 - 9*a**2. Let c(g) be the second derivative of b(g). Factor c(j).
-2*j**2*(j - 1)**2/13
Let -4/5*i + 0 + 1/5*i**3 - 4/5*i**2 + 1/5*i**4 = 0. Calculate i.
-2, -1, 0, 2
Let j = 2 - 0. Factor -9*d**4 - 4*d**3 - 7*d**2 - 3*d**2 + 13*d**4 + 2*d**j.
4*d**2*(d - 2)*(d + 1)
Let n be (-22)/(-8) + 21/(-28). Let p be (-5)/(15/(-9)) + n. Factor v**2 + 7*v - 5*v**2 + 3*v**3 - p*v**2 - v.
3*v*(v - 2)*(v - 1)
Let g(f) = -9*f**4 + 30*f**3 + 145*f**2 + 138*f + 30. Let n(a) = -a**4 + 2*a**3 + 2*a**2 + a + 1. Let c(u) = g(u) - 2*n(u). Suppose c(o) = 0. Calculate o.
-2, -1, -2/7, 7
Let v(x) be the third derivative of 0*x - 5*x**2 + 7/6*x**4 + 2*x**3 + 0 + 2/15*x**5. Factor v(z).
4*(z + 3)*(2*z + 1)
Let n be 0/(2*(-3)/(-6)). Let k be (((-120)/(-18))/10)/2. Let 0*a + n - k*a**2 = 0. Calculate a.
0
Determine f so that -12*f**4 + 17*f**5 - 20*f**5 - 102*f - 6*f**3 + 12*f**2 + 111*f = 0.
-3, -1, 0, 1
Let w be (-2499)/168 + (-60)/(-4). Solve 0 + 3/8*b**3 + w*b**2 - 1/4*b - 1/8*b**4 - 1/8*b**5 = 0.
-2, -1, 0, 1
Let w(o) be the first derivative of 7 + 5/18*o**4 + 7/9*o**2 - 4/9*o - 2/3*o**3 - 2/45*o**5. Let w(g) = 0. What is g?
1, 2
Suppose 4*n + 20 = 0, -5*z = -5*n - 10 - 15. Suppose 14*b - 5*b = 0. Factor 0*d**2 - 2/7*d**3 + z + b*d + 2/7*d**4.
2*d**3*(d - 1)/7
Let b(m) = m**2 + 9*m + 12. Let j be b(-8). Factor 12 + k**2 - 10*k**3 + 10*k - 17 + 5*k**j - k**2.
5*(k - 1)**3*(k + 1)
Let v(g) be the third derivative of g**9/423360 + g**8/70560 + g**7/35280 - g**5/30 - 8*g**2. Let a(t) be the third derivative of v(t). Factor a(z).
z*(z + 1)**2/7
Let x be (520/(-78))/(2/(-3)). Factor 6*j**4 - 2*j**3 - 8*j**3 - 5 + x*j + 0 - j**4.
5*(j - 1)**3*(j + 1)
Let t(r) be the second derivative of -5*r**7/42 - r**6/3 + 3*r**5/4 - 5*r. Determine p, given that t(p) = 0.
-3, 0, 1
Let t be (-105)/(-28) + 3/(-4). Suppose 4*o + 14 = 3*f, -2*o + 4*o - 2 = -3*f. Factor -10*a - t*a + 2 + 17*a + f*a**2.
2*(a + 1)**2
Let m(g) be the first derivative of 2*g**3/33 - 3*g**2 + 232*g/11 + 201. Factor m(q).
2*(q - 29)*(q - 4)/11
Find a such that -15873/5*a**2 - 1/5*a**4 - 50*a**3 - 15376/5 - 6200*a = 0.
-124, -1
Let m = 1 + 1. Let k be 4*25/(-55) + m. Factor -4/11*j + 0 - k*j**2.
-2*j*(j + 2)/11
Suppose 32*j + 40 = 37*j. Suppose -q + 5*q - j = 0. Factor 1/2*w**q + 9/2 - 3*w.
(w - 3)**2/2
Let w(r) be the third derivative of r**6/50 - r**5/75 + 5*r**3/6 - 9*r**2. Let s(j) be the first derivative of w(j). Factor s(q).
4*q*(9*q - 2)/5
Factor 22/3*p**2 - 4/3 + 8/3*p**3 + 10/3*p.
2*(p + 1)*(p + 2)*(4*p - 1)/3
Let t(n