. Let w(n) = -n**4 - n**3 - n**2 - n. Let k(m) = d(m) + 6*w(m). Factor k(s).
3*s*(s - 1)**2*(s + 1)
Suppose -7*s + 1 + 13 = 0. Factor 1/2*h**s - 1 + 1/2*h.
(h - 1)*(h + 2)/2
Let d be (4 - 1)/(3/2). Factor -28*r**2 + 4 - 6*r + 24*r**4 + 14*r**5 - 5*r**3 + 0*r + d*r**3 - 5*r**3.
2*(r - 1)*(r + 1)**3*(7*r - 2)
Let b(x) be the second derivative of 4*x**2 - 16/3*x**3 - 19/10*x**5 - 1/21*x**7 + 25/6*x**4 + 7/15*x**6 + 7*x + 0. Factor b(d).
-2*(d - 2)**2*(d - 1)**3
Let t(b) be the first derivative of 28*b**5/5 + 30*b**4 + 48*b**3 + 16*b**2 + 32. Factor t(g).
4*g*(g + 2)**2*(7*g + 2)
Suppose -32 = -2*v + 4. Let j = v - 12. Let -j*a - 3*a**2 + 6*a = 0. Calculate a.
0
Let n(k) be the first derivative of -k**6/21 - 8*k**5/35 - 3*k**4/7 - 8*k**3/21 - k**2/7 - 4. Determine t so that n(t) = 0.
-1, 0
Suppose 5 = 5*d - 10. Suppose n = d*n - 4. Factor 18/5*y**3 - 4/5*y + 0 - 6/5*y**n.
2*y*(3*y - 2)*(3*y + 1)/5
Suppose 0 = -2*h - 2*h. Let b(x) be the first derivative of 2 + 0*x**4 - 2/5*x**5 + 2/3*x**3 + 0*x + h*x**2. Factor b(j).
-2*j**2*(j - 1)*(j + 1)
Let t = 3/962 - -3247/38480. Let h(a) be the second derivative of 0*a**2 + 0*a**3 + t*a**5 + 0 - a - 1/24*a**4. Factor h(z).
z**2*(7*z - 2)/4
Let t be (18/(-16)*4/3)/(-2). Suppose 3*f - 5*o = 26, 32 + 36 = 5*f + 4*o. Determine s, given that 30*s**3 + 99/4*s**2 + f*s**4 + 15/2*s + t = 0.
-1, -1/4
Let n(r) be the first derivative of 14*r**3/9 + 3*r**2 + 4*r/3 + 9. Factor n(w).
2*(w + 1)*(7*w + 2)/3
Let y(r) be the third derivative of 4*r**7/105 - r**6/30 - 7*r**5/120 - r**4/48 - 6*r**2. Factor y(k).
k*(k - 1)*(4*k + 1)**2/2
Let s(a) be the first derivative of -2*a**5/25 + 2*a**3/15 - 6. Suppose s(k) = 0. What is k?
-1, 0, 1
Solve -36/7*h**3 + 0 - 24/7*h**2 - 4/7*h = 0.
-1/3, 0
Let d(f) = 52*f**3 - f**2 + 1. Let h be d(-1). Let v = -101/2 - h. Let 9/2*y**3 - 4*y + 2 - v*y**2 = 0. Calculate y.
-1, 2/3
Let m(c) be the third derivative of -5*c**8/112 + 8*c**7/21 - c**6 + 10*c**4/3 + 21*c**2. Factor m(b).
-5*b*(b - 2)**3*(3*b + 2)
Let w(p) = 3*p**4 + p**3 + 2*p**2 + 2*p. Let l(j) = -10*j**4 - 3*j**3 - 7*j**2 - 7*j. Let u(d) = 2*l(d) + 7*w(d). What is f in u(f) = 0?
-1, 0
Let r(y) be the first derivative of -y**5/45 + 5*y**4/36 - y**3/3 + 7*y**2/18 - 2*y/9 - 20. Suppose r(m) = 0. What is m?
1, 2
Let y(j) be the third derivative of 2/21*j**3 + 0*j + 0 - 1/84*j**4 - 1/210*j**5 - 3*j**2. Factor y(c).
-2*(c - 1)*(c + 2)/7
Determine d, given that 3/7 + 4/7*d**3 + 17/7*d**2 + 16/7*d = 0.
-3, -1, -1/4
Let i(p) be the second derivative of p**7/4620 - p**6/1980 + p**3/6 + p. Let n(d) be the second derivative of i(d). Let n(y) = 0. Calculate y.
0, 1
Suppose 21*t - 3 = 20*t. Factor 2*y - 4*y**2 + 0 + 5/2*y**t - 1/2*y**4.
-y*(y - 2)**2*(y - 1)/2
Determine v, given that -22/5*v**2 + 18/5*v**4 + 12/5*v**3 + 8/5 - 8/5*v = 0.
-1, 2/3
Let u(a) be the second derivative of 1/90*a**6 - 2*a + 0 + 0*a**3 - 1/36*a**4 + 0*a**5 + 0*a**2. Find k, given that u(k) = 0.
-1, 0, 1
Let w(c) = -c**3 - 2*c**2 + 9*c + 3. Let s(b) be the second derivative of b**5/20 + b**4/6 - 5*b**3/3 - b**2 - 6*b. Let r(a) = -5*s(a) - 6*w(a). Factor r(n).
(n - 2)*(n + 2)**2
Let q = -13 - -15. Determine i, given that -2*i + 0*i + 0*i + i**q = 0.
0, 2
Let d(o) be the first derivative of 0*o + 1/540*o**6 - 1/18*o**4 + 0*o**2 - 1/180*o**5 + 1/3*o**3 + 2. Let m(a) be the third derivative of d(a). Factor m(i).
2*(i - 2)*(i + 1)/3
Let n = 49 - 46. Let i(v) be the second derivative of 3*v + 0 + 0*v**2 - 1/60*v**5 + 1/126*v**7 + 1/90*v**6 + 0*v**n - 1/36*v**4. Factor i(q).
q**2*(q - 1)*(q + 1)**2/3
Let w be ((-6)/15)/((-1)/10). Determine t so that 6*t**3 + 5/2*t**2 - 6*t - 9/2*t**w + 2 = 0.
-1, 2/3, 1
Let y(p) = p**3 - 3*p**2 + 2. Let r be y(2). Let f(a) = -a**3 - 3*a**2 - 4*a - 2. Let l be f(r). Suppose -2/5*i**3 - l*i**2 - 8/5 - 16/5*i = 0. Calculate i.
-2, -1
Let f(t) be the third derivative of -t**7/350 - t**6/40 - 3*t**5/100 + 9*t**4/40 - 29*t**2. Let f(m) = 0. Calculate m.
-3, 0, 1
Let c(w) be the second derivative of -2/5*w**2 - 3/25*w**6 + 0 + 2*w - 7/50*w**5 + 7/15*w**3 + 11/30*w**4. Determine p so that c(p) = 0.
-1, 2/9, 1
Let t(o) be the first derivative of o**5/10 - o**4/6 + 3*o - 2. Let n(k) be the first derivative of t(k). Factor n(p).
2*p**2*(p - 1)
Let i(c) be the first derivative of 1/12*c**4 + 0*c + 1/3*c**3 + 1/3*c**2 - 3. Factor i(b).
b*(b + 1)*(b + 2)/3
Let a(f) be the third derivative of f**7/1050 - 3*f**6/50 + 81*f**5/50 - 243*f**4/10 + 2187*f**3/10 + 22*f**2. Factor a(w).
(w - 9)**4/5
Let h(v) = -5*v**2 + 24*v - 45. Let u(z) = 55*z**2 - 265*z + 495. Let q(k) = 65*h(k) + 6*u(k). Factor q(a).
5*(a - 3)**2
Let d = -3 + 7. Let i(x) be the first derivative of 7/6*x**d - 4/3*x + 4/9*x**3 - 7/3*x**2 - 1. Determine y so that i(y) = 0.
-1, -2/7, 1
Let i(z) be the second derivative of -z**6/50 - 3*z**5/100 + z**4/5 + 2*z**3/5 - 19*z. Factor i(c).
-3*c*(c - 2)*(c + 1)*(c + 2)/5
Let j be 8/6*9/(-2). Let q = j - -8. Factor -3 + w**2 + 5 - 4*w + w**q.
2*(w - 1)**2
Let n(f) be the first derivative of 5*f**4/4 + 25*f**3/3 + 35*f**2/2 + 15*f + 31. Let n(j) = 0. What is j?
-3, -1
Let g(r) be the second derivative of -r**7/3780 + r**6/1080 + r**4/6 + r. Let q(v) be the third derivative of g(v). Let q(b) = 0. What is b?
0, 1
Factor 1/5*g**2 + 8/5*g + 7/5.
(g + 1)*(g + 7)/5
Let w(b) be the third derivative of -b**5/210 - b**4/84 + 2*b**3/21 - 10*b**2. Factor w(f).
-2*(f - 1)*(f + 2)/7
Let r = -138 + 277/2. Factor -1/4*l**2 - 1/4 - r*l.
-(l + 1)**2/4
Let l = -45 - -243/5. Factor 0*w + 2/5*w**2 - 8/5*w**5 + l*w**4 + 0 - 12/5*w**3.
-2*w**2*(w - 1)**2*(4*w - 1)/5
Let m(n) be the second derivative of -1/12*n**3 + 0*n**6 + 1/20*n**5 + 0*n**4 - 1/84*n**7 + 0*n**2 + 0 + n. Factor m(h).
-h*(h - 1)**2*(h + 1)**2/2
Let a(v) be the first derivative of 44*v**3/3 + 8*v**2 - 62. Factor a(b).
4*b*(11*b + 4)
Let d(r) be the first derivative of 0*r**2 + 3/5*r**5 + r**3 - 3/2*r**4 + 0*r + 5. Factor d(z).
3*z**2*(z - 1)**2
Let v(x) be the first derivative of -1/5*x**2 + 1/10*x**4 + 0*x + 0*x**3 + 10. Factor v(d).
2*d*(d - 1)*(d + 1)/5
Let 0*p - 1/4*p**4 - p**2 + 0 + p**3 = 0. What is p?
0, 2
Let h = 3160 + -947999/300. Let d(f) be the third derivative of -f**2 + 1/60*f**4 + 0 + 1/15*f**3 + 0*f - h*f**6 - 1/150*f**5. Determine o, given that d(o) = 0.
-1, 1
Let i(h) be the first derivative of -h**8/8400 + h**6/1800 - h**3 - 2. Let d(r) be the third derivative of i(r). Factor d(o).
-o**2*(o - 1)*(o + 1)/5
Suppose 4*w = 4*f - 8, -3 - 3 = -3*f + 4*w. Suppose v - 1 - 2 = 0. Factor -1/2 - v*d**2 + f*d - 1/2*d**4 + 2*d**3.
-(d - 1)**4/2
Let g(y) = -5*y**2 + 2*y - 3 - y**3 + 5*y - y - y**2. Let r be g(-7). Factor -5*b**5 - 11*b**2 - 7*b**4 - 4*b**r - 21*b**3 - 2*b - 6*b**4.
-b*(b + 1)**3*(5*b + 2)
Factor -4/9*i**2 - 2/9*i**3 - 2/9*i + 0.
-2*i*(i + 1)**2/9
Suppose -8*t + 19*t = 22. Factor 0 - 1/2*u - 1/4*u**t.
-u*(u + 2)/4
Let c be 11/(-3) + -1 + 5. Let f(j) be the first derivative of 2/3*j - c*j**4 + 2/3*j**2 - 2 + 0*j**3 - 2/15*j**5. Factor f(i).
-2*(i - 1)*(i + 1)**3/3
Let b = -54 + 494/9. Factor -b*o + 2/3*o**2 + 2/9.
2*(o - 1)*(3*o - 1)/9
Let w(n) be the first derivative of -n**7/42 - n**6/15 + n**5/20 + n**4/6 - 8*n + 6. Let v(p) be the first derivative of w(p). Factor v(l).
-l**2*(l - 1)*(l + 1)*(l + 2)
Factor 6/7 - 5/7*t - 8/7*t**2 + 3/7*t**3.
(t - 3)*(t + 1)*(3*t - 2)/7
Let z(y) be the second derivative of -y**5/5 + y**4/3 + 10*y**3/3 + 6*y**2 + 4*y. Factor z(p).
-4*(p - 3)*(p + 1)**2
Let y(m) be the third derivative of m**6/30 - 2*m**5/15 - m**4/6 + 4*m**3/3 - 41*m**2. Determine d, given that y(d) = 0.
-1, 1, 2
Let a = 0 - -4. Factor -2*j + j**a - j + 2*j**3 - j**2 - j**5 - j**2 + 2*j + 1.
-(j - 1)**3*(j + 1)**2
Let l be (-1)/(2/(-6)) + -1. Factor 0*g**3 - 3*g**3 + 3*g**2 - l*g**3 + 3*g**4 - g**3.
3*g**2*(g - 1)**2
Let y = -5 - 2. Let w = y - -10. Factor -2 + 5*j - 2*j + 7*j**3 - 8*j**w.
-(j - 1)**2*(j + 2)
Let r be 102/(-63) - (-4 - -2). Let d = r - -2/7. Determine l, given that -3*l + 10/3*l**2 + d - l**3 = 0.
1/3, 1, 2
Suppose -4*i + 28 = 5*s + 5, -4*s - i = -14. Suppose -5*a + 67 = 57. Factor a*u**3 + 4*u**2 + 4*u**s + 2*u**4 - 4 + 4.
2*u**2*(u + 1)*(u + 2)
Suppose -8 = -3*z - 2. Let v(y) = -y**3 - 3*y**2 - y - 1. Let j(l) = l**3 + 4*l**2 + 2*l + 2. Let o(i) = z*j(i) + 3*v(i). Factor o