lculate x.
-1, 0, 2
Let v(k) be the first derivative of -2/3*k - 8 - 1/24*k**4 - 1/3*k**3 - 3/4*k**2. Factor v(w).
-(w + 1)**2*(w + 4)/6
Suppose 1/3*z**2 + 4/3 + 8/3*z - 5/3*z**4 - 7/3*z**3 - 1/3*z**5 = 0. Calculate z.
-2, -1, 1
Let n(w) = 7*w**5 + 12*w**4 + 28*w**3 + 37*w**2 + 23*w + 4. Let y(z) = 3*z**5 + 6*z**4 + 14*z**3 + 18*z**2 + 11*z + 2. Let p(t) = 4*n(t) - 10*y(t). Factor p(s).
-2*(s + 1)**4*(s + 2)
Let q be (-30)/(-12)*((-14)/10 - -1). Let t be q/4 + (-195)/(-300). Factor -7/5*j + j**2 + t.
(j - 1)*(5*j - 2)/5
Let h(g) be the second derivative of -1/30*g**3 + 0 + 1/100*g**5 - 1/10*g**2 + 1/60*g**4 - 26*g. Factor h(o).
(o - 1)*(o + 1)**2/5
Let l = -2643 - -2645. Factor 3/2*t + 3/4*t**l - 6.
3*(t - 2)*(t + 4)/4
Let p(m) = m**2 - 3. Let v be p(-3). Factor -3*d**5 - v*d**2 + 6*d**4 - 4*d + 7*d + 0*d.
-3*d*(d - 1)**3*(d + 1)
Suppose -5 = -x + 4. Suppose 4*l - x - 1 = r, -4*r = 4*l - 20. Let -1/3*w**l + 2/3*w**2 - 1/3*w + 0 = 0. Calculate w.
0, 1
Let b(p) be the first derivative of -p**6/51 + 11*p**4/34 - 4*p**3/17 - 28*p**2/17 + 48*p/17 - 51. Suppose b(m) = 0. What is m?
-3, -2, 1, 2
Let i(u) be the second derivative of u**7/14 + 3*u**6/10 - 3*u**5/2 + 26*u + 4. Factor i(a).
3*a**3*(a - 2)*(a + 5)
Let y = 15 - -67. Let a = y + -80. Factor 4/9*j**4 + 0 + 0*j**a + 0*j**3 + 0*j - 2/9*j**5.
-2*j**4*(j - 2)/9
Let c = 3370 - 3370. Factor 0 - 3/4*v**2 + 1/2*v + 1/4*v**4 + c*v**3.
v*(v - 1)**2*(v + 2)/4
Let x = 2 + 0. Let m = -15 - -18. Factor 14*l - l**x + 4*l**2 + 12*l**4 + 22*l + 12 - 36*l**m.
3*(l - 2)**2*(2*l + 1)**2
Solve -2/11*i**5 + 10*i - 108/11*i**3 - 150/11 + 26/11*i**4 + 124/11*i**2 = 0.
-1, 1, 3, 5
Let m be (-192)/(-160)*(-5)/(-9). Let a(q) be the first derivative of -10 - m*q**2 - 10/9*q**3 + 0*q - 2/15*q**5 - 2/3*q**4. Factor a(v).
-2*v*(v + 1)**2*(v + 2)/3
Let k = -57/50 + 871/150. Let c = 56/51 + 4/17. Suppose -4/3 + c*n**2 - 14/3*n + k*n**3 = 0. What is n?
-1, -2/7, 1
Let m(b) be the third derivative of 0*b + 0*b**3 + 7*b**2 - 1/150*b**5 + 0 + 1/300*b**6 + 0*b**4. Find d, given that m(d) = 0.
0, 1
Suppose -5*y + 32 = 2. Let i(m) be the third derivative of -5*m**2 + 0*m + 0 - 2/15*m**5 + 0*m**4 + 1/30*m**y + 0*m**3. Solve i(f) = 0 for f.
0, 2
Let k(m) be the second derivative of -1/8*m**5 + 35/36*m**3 - 35/36*m**4 + 2*m - 11 + 25/6*m**2. Factor k(p).
-5*(p - 1)*(p + 5)*(3*p + 2)/6
Let h = -2 + 1. Let m(f) = f**2 - f + 1. Let v(g) = 4*g**3 - 12*g + 28. Suppose 14*a = -16*a + 360. Let j(y) = a*m(y) + h*v(y). Suppose j(w) = 0. What is w?
-1, 2
Suppose -4*l - c + 3 = -4, 4*l - 12 = 4*c. Factor 1/5*h**l + 5 + 2*h.
(h + 5)**2/5
Let f(q) = -15*q**3 + 81*q. Let i be -63 - ((-3)/(-3) + 2). Let l = i - -33. Let s(d) = -d**3 + 5*d. Let o(h) = l*s(h) + 2*f(h). Determine m so that o(m) = 0.
-1, 0, 1
Let q(y) be the third derivative of 0*y + 1/21*y**3 + 11*y**2 + 1/210*y**6 + 0 - 4/105*y**5 + 1/42*y**4 - 1/294*y**8 + 1/105*y**7. Solve q(z) = 0 for z.
-1, -1/4, 1
Let l = 165 + -47. Factor -7 + 0*r**2 - l + 50*r - 5*r**2.
-5*(r - 5)**2
Let l(b) = b**2 + 7*b + 12. Let z be l(-6). Suppose 15*s**2 - 22*s**3 + 42*s**2 - 37*s**2 - z*s + 8*s**4 = 0. What is s?
0, 3/4, 1
Let m be 4 - 8 - -1 - (-282)/(-208). Let k = m - -41/8. Suppose -k*g**2 + 2/13*g**3 - 8/13 + 16/13*g = 0. Calculate g.
1, 2
Suppose 5*x + 15 = 0, -3*q - 3*x + 7 - 4 = 0. Let h(v) be the second derivative of -3/4*v**2 - 5*v + 0 + 0*v**q + 1/20*v**6 - 1/2*v**3 + 3/20*v**5. Factor h(i).
3*(i - 1)*(i + 1)**3/2
Solve -1/4*o**2 + 7/2*o + 0 = 0 for o.
0, 14
Suppose -1/3*l**2 + 0 - 13*l = 0. What is l?
-39, 0
Let j(b) be the third derivative of -b**5/90 - b**4/6 + 7*b**3/9 - 142*b**2. Find f, given that j(f) = 0.
-7, 1
Let a(m) be the first derivative of -m**8/28 + 4*m**7/21 - 2*m**5/3 + m**4/2 + 2*m**2 - 6. Let s(w) be the second derivative of a(w). Let s(d) = 0. What is d?
-1, 0, 1/3, 1, 3
Let p be -3 - 4/(-1) - 62/(-2). Factor -2*r**3 + 33*r**2 - 3*r**4 - p*r**2 + 4*r**4.
r**2*(r - 1)**2
Let z(g) be the third derivative of g**5/180 - g**4/72 - 2*g**3/3 - 14*g**2 + 5. Factor z(t).
(t - 4)*(t + 3)/3
Determine p so that -88*p**2 - 384*p + 6*p**4 - 32*p**3 - 377 - 88*p**2 + 4*p**4 - 12*p**4 + 89 = 0.
-6, -2
Let k(p) = 2*p**2 + 141*p + 657. Let m be k(-5). Solve 4/3*x**m + 16/3 + 20/3*x = 0 for x.
-4, -1
Factor 16*p - 315 + 315 - 2*p**2 - 2*p**2.
-4*p*(p - 4)
Factor 294 + 2/3*f**4 - 80/3*f**3 + 716/3*f**2 + 560*f.
2*(f - 21)**2*(f + 1)**2/3
Let a(m) be the first derivative of 2*m**3/3 + 19*m**2/2 + 9*m - 18. Let a(j) = 0. What is j?
-9, -1/2
What is n in -5/2*n**2 - 3/2*n**3 + 161/6*n + 49 + 1/6*n**4 = 0?
-3, -2, 7
Factor 0 - 1/11*l**2 - 2*l.
-l*(l + 22)/11
Let k(f) = f**2 - 11 + f**3 - f**4 - f**5 + 12 - 1. Let m(l) = -28*l**5 - 44*l**4 - 16*l**3 - 16*l**2 - 20*l - 4. Let y(h) = 24*k(h) - m(h). Factor y(v).
4*(v + 1)**5
Let r = -12 - 0. Let x(t) = t**2 + 9*t - 34. Let g be x(r). Factor 1/4*o**3 + 1/4*o**g + 0 + 0*o - 1/4*o**5 - 1/4*o**4.
-o**2*(o - 1)*(o + 1)**2/4
Let a(r) be the first derivative of -r**6/450 - r**5/25 - 11*r**3/3 + 1. Let p(c) be the third derivative of a(c). Factor p(j).
-4*j*(j + 6)/5
Suppose -38 = -4*s + 402. Let r = 113 - s. Factor 4/5*i**r - 4/5*i - 4/5*i**2 + 4/5.
4*(i - 1)**2*(i + 1)/5
Let k(a) be the second derivative of a**8/840 + a**7/420 - a**6/45 - a**5/15 + 11*a**3/6 + 9*a - 4. Let r(o) be the second derivative of k(o). Factor r(w).
2*w*(w - 2)*(w + 1)*(w + 2)
Let x(i) be the first derivative of i**4/6 + 10*i**3/9 - 4*i**2 - 24*i - 18. Factor x(t).
2*(t - 3)*(t + 2)*(t + 6)/3
Let q = -90667/4 + 22668. Factor 0 - q*p**4 + 1/2*p + 1/4*p**5 + 9/4*p**3 - 7/4*p**2.
p*(p - 2)*(p - 1)**3/4
Factor -25175/4*s**3 - 26875/4*s**4 + 200*s - 5 - 9245/4*s**5 - 6725/4*s**2.
-5*(s + 1)**3*(43*s - 2)**2/4
Let h(p) be the second derivative of -1/3*p**3 - 1/3*p**4 + 15*p + 0*p**2 + 0 - 1/10*p**5. Let h(g) = 0. What is g?
-1, 0
Let l(a) be the third derivative of -a**8/112 - a**7/70 + a**6/8 - 3*a**5/20 - a**2 - 56. Factor l(t).
-3*t**2*(t - 1)**2*(t + 3)
Let w(o) be the third derivative of -1/330*o**5 - 21*o**2 + 2/11*o**3 + 0 - 1/132*o**4 + 0*o. What is d in w(d) = 0?
-3, 2
Let j(y) be the second derivative of 0 + 0*y**2 + 0*y**4 + 9*y + 3/2*y**3 - 1/1440*y**6 + 0*y**5. Let o(n) be the second derivative of j(n). Factor o(g).
-g**2/4
Let u(r) be the first derivative of -1/15*r**3 - 7/20*r**4 - 4/5*r - 22 - 1/30*r**6 + 1/5*r**5 + 4/5*r**2. Solve u(h) = 0 for h.
-1, 1, 2
Let j(k) be the third derivative of -k**7/378 + 17*k**6/1080 - 4*k**5/135 + k**4/54 - 283*k**2. Determine m, given that j(m) = 0.
0, 2/5, 1, 2
Suppose 7 - 11 = -g. Factor 6*k**2 + 1 + 0 + 0 + g*k**3 + 15*k**4 - 14*k**4 + 4*k.
(k + 1)**4
Let f(p) be the second derivative of -p**7/42 - p**6/30 + 3*p**5/20 + p**4/12 - p**3/3 + 113*p. Solve f(n) = 0.
-2, -1, 0, 1
Let -62*h + 22/3*h**2 + 102 + 2/3*h**3 = 0. Calculate h.
-17, 3
Let y = 27 + -20. Let v = 6 - 4. Factor 3*n**3 + 9*n - 3 - 5*n**2 - y*n**v + 3*n**2.
3*(n - 1)**3
Let t(n) be the first derivative of 0*n + 4/11*n**2 - 7/22*n**4 - 8/11*n**3 + 6. Find m, given that t(m) = 0.
-2, 0, 2/7
Suppose -4*a - 18*n = -23*n - 37, a = -4*n - 17. Factor 0 + 16/3*h**2 + 4/3*h + 7/3*h**a.
h*(h + 2)*(7*h + 2)/3
Suppose -y - 4*y + 12 = j, 5*y - 10 = 0. Let v = -488/7 - -70. Find f, given that -2/7*f + 2/7*f**3 + 2/7*f**j - v = 0.
-1, 1
Let a(i) = 2*i - 97*i**2 + 1 + 98*i**2 - i. Let r(z) = 14*z**2 + 46*z + 42. Let f(v) = -10*a(v) + r(v). Factor f(h).
4*(h + 1)*(h + 8)
Let a(s) be the third derivative of s**7/945 + 4*s**6/135 + 26*s**5/135 + 4*s**4/9 + 130*s**2. Factor a(f).
2*f*(f + 2)**2*(f + 12)/9
Let k be 10 + (-19)/(247/104). Solve 1/4*d - 1/4*d**3 - 3/4 + 3/4*d**k = 0 for d.
-1, 1, 3
Suppose 0 = 48*f - 61*f + 52. Solve 2/5*i - 2/5*i**2 + 0 + 2/5*i**f - 2/5*i**3 = 0.
-1, 0, 1
Suppose 210*i - i**2 - 432*i - 2 + 233*i + 7*i**2 = 0. What is i?
-2, 1/6
Suppose 12 = 3*h, 2*b - 2*h - h + 14 = 0. Let y be b + (-3)/(1 + -2). Factor -o**4 + 6*o - o**3 - 7*o**4 - o**4 + 9*o**y - 5*o**3.
-3*o*(o - 1)*(o + 1)*(3*o + 2)
Let b(h) be the first derivative of 3/8*h**2 - 1/2*h**3 - 12 + 0*h + 3/16*h**4. Factor b(s).
3*s*(s - 1)**2/4
Suppose 7*a + 5*a - 72 = 0. Let j be 8/12 - a/9. Find y, given that -6/7*y**2 - 9/7*y**3 + 3/7*y**5 + 0*y**4 + 0 + j*y = 0.
-1, 0, 2
Let j = 8 - 6. Suppose 0 = -4*