or t(h).
2*(h - 2)*(h + 1)*(h + 4)/15
Let o(c) be the first derivative of -c**4/4 + 5*c**3/9 + 11*c**2/6 + c - 24. Find h, given that o(h) = 0.
-1, -1/3, 3
Let c(q) = 33*q**2 - 12*q. Let y(d) = -4*d**2. Let z(h) = 3*c(h) + 24*y(h). Solve z(l) = 0 for l.
0, 12
Let g(u) be the third derivative of -5*u**8/28 + 194*u**7/105 - 53*u**6/9 + 182*u**5/45 + 5*u**4/6 - 2*u**3 + 25*u**2 - 7. Solve g(s) = 0 for s.
-1/5, 1/3, 3
Let w be (-2 + (-42)/(-9))*15/10. Factor -103*z + 2*z**4 + 103*z + 3*z**w - 5*z**2.
5*z**2*(z - 1)*(z + 1)
Let g(y) be the first derivative of y**4/5 + 12*y**3/5 + 225. What is s in g(s) = 0?
-9, 0
Factor -45*k**4 + 11*k**4 + 30*k**4 - 4*k**2 + 20*k**2.
-4*k**2*(k - 2)*(k + 2)
Let h(c) be the first derivative of c**5/60 - c**3/6 + c**2/3 - 15*c - 3. Let t(b) be the first derivative of h(b). Factor t(d).
(d - 1)**2*(d + 2)/3
Let a(g) be the first derivative of g**7/280 + g**6/40 + g**5/20 + g**3 + 14. Let o(y) be the third derivative of a(y). Determine i so that o(i) = 0.
-2, -1, 0
Let m(p) be the second derivative of 2*p**6/15 - 3*p**5/5 + p**4/3 + 2*p**3 - 4*p**2 - p + 17. Factor m(v).
4*(v - 2)*(v - 1)**2*(v + 1)
Let g(h) be the second derivative of 0 + 2/5*h**5 - 4/3*h**3 + 0*h**2 - 1/3*h**4 + 2/15*h**6 + 9*h. Solve g(x) = 0.
-2, -1, 0, 1
Solve 52*g**2 - 4*g**3 - 2386*g - 126 - 82 + 2402*g = 0 for g.
-2, 2, 13
Suppose 4*l + 48 = -0*l. Let j(y) = -y**3 - 12*y**2 + y + 14. Let g be j(l). Factor -9*w**g + 3*w - 3*w + 6*w**2.
-3*w**2
Let s(p) be the first derivative of -p**4/4 + p**3/3 - p**2/2 - 1. Let b be s(0). Factor b + 2/7*j - 2/7*j**2.
-2*j*(j - 1)/7
Suppose 0 = -2*f + 3 + 1. Suppose f*i + 3*x - 13 = 0, i - 8 = 5*x + 5. Find b such that 10 + 12 - 3 + 18*b + i + 3*b**2 = 0.
-3
Let z(t) = -4*t**2 - 32*t - 111. Let w(p) = -p**2 + 2*p - 2. Let n(a) = 6*w(a) - 2*z(a). Factor n(v).
2*(v + 3)*(v + 35)
Factor 247/6*u - 7/6*u**2 - 35/3.
-(u - 35)*(7*u - 2)/6
Factor 0 - 5/4*f**3 - 1/4*f**4 + 1/4*f**2 + 5/4*f.
-f*(f - 1)*(f + 1)*(f + 5)/4
Let g be 4 + (-1 - -3) + -1 + (-8820)/2268. Suppose 8/9*p + 2/9*p**4 - 10/9*p**2 + 8/9 + 2/9*p**5 - g*p**3 = 0. What is p?
-2, -1, 1, 2
Let b = 14825/88914 - 1/14819. Factor 1/2*p**3 + 1/3*p**2 + b*p**4 + 0*p + 0.
p**2*(p + 1)*(p + 2)/6
Let r = -459 - -464. Let q(s) be the third derivative of 0 - 7/270*s**r + 1/27*s**4 + 0*s + s**2 + 1/9*s**3. Factor q(x).
-2*(x - 1)*(7*x + 3)/9
Factor 108/7*d - 1458/7 - 2/7*d**2.
-2*(d - 27)**2/7
Let o(s) be the first derivative of 6*s**5/85 + 11*s**4/17 + 110*s**3/51 + 52*s**2/17 + 24*s/17 - 14. Find p, given that o(p) = 0.
-3, -2, -1/3
Let s(b) be the first derivative of -2*b**3/21 - 5*b**2/7 - 12*b/7 + 167. Factor s(n).
-2*(n + 2)*(n + 3)/7
Let f(s) = -6*s**2 - 86*s + 256. Let d(m) = 17*m**2 + 256*m - 767. Let l(j) = -4*d(j) - 11*f(j). Let l(w) = 0. What is w?
-42, 3
Let c(t) be the third derivative of -10/3*t**3 + 0*t - 1/12*t**6 + 0 + 29*t**2 - 5/6*t**4 + 7/12*t**5. Factor c(h).
-5*(h - 2)**2*(2*h + 1)
Let y(c) be the first derivative of -5*c**6/6 - 19*c**5 + 115*c**4/4 + 275*c**3/3 - 245*c**2 + 200*c + 48. Find r such that y(r) = 0.
-20, -2, 1
Let x = -6 + 9. Let s be (-8)/28 - 32/(-14). Factor -5*c**s - 81 + 4*c**x + 83 - c**2.
2*(c - 1)**2*(2*c + 1)
Suppose -5*a - 216*b = -215*b - 28, -3*b + 19 = 2*a. Let z(l) be the third derivative of -1/24*l**4 - 5*l**2 - 1/60*l**a + 0 + 0*l**3 + 0*l. Factor z(c).
-c*(c + 1)
Let j(w) be the third derivative of 1/3*w**5 + 0 - 1/3*w**7 - 7/48*w**8 + 1/40*w**6 + 8*w**2 + 0*w - 1/6*w**4 + 0*w**3. Let j(r) = 0. What is r?
-1, 0, 2/7
Let w be ((-8)/2)/2 - -34. Let h be 1/(w/(-11) - -3). Suppose -2 + 4 + h*v**3 - 4*v**3 - 12*v**2 + 4*v - v = 0. Calculate v.
-2/7, 1
Let q = -104 + 49. Let z be 4/22 + ((-60)/q)/(-6). Find g, given that z + 2/3*g - g**3 - 1/3*g**2 = 0.
-1, 0, 2/3
Let j = -14147/3 + 4716. Factor 1/3*i**2 - j*i + 0.
i*(i - 1)/3
Let d(t) be the second derivative of t**5/20 - 7*t**4/12 - 4*t**3 + 90*t**2 + 125*t + 1. Determine v, given that d(v) = 0.
-5, 6
Let l(m) be the first derivative of 5*m**8/336 - m**7/42 - m**6/24 + m**5/12 + 4*m**2 - 6. Let c(j) be the second derivative of l(j). Factor c(i).
5*i**2*(i - 1)**2*(i + 1)
Let b(u) be the third derivative of u**6/660 - 17*u**5/165 - u**4/132 + 34*u**3/33 + 193*u**2. Let b(x) = 0. Calculate x.
-1, 1, 34
Suppose 2*w - 21 = -7*s + 2*s, 3*s = w + 17. Let v(x) be the first derivative of x - 3/2*x**2 + 1/2*x**4 - 4 + 1/6*x**6 + 2/3*x**3 - 3/5*x**s. Factor v(u).
(u - 1)**4*(u + 1)
Let c(q) = q**3 - q**2 - 1. Let h(m) = -4*m**4 - 7*m**3 - 13*m**2 - 5. Let b be (-1 - 2) + (3 + -7)*-2. Let u(d) = b*c(d) - h(d). Solve u(i) = 0 for i.
-2, -1, 0
Find d such that 3/2 + 29/8*d**2 - 13/8*d**4 + 21/8*d**3 - 5/8*d**5 - 11/2*d = 0.
-3, -2, 2/5, 1
Suppose 0 = -4*x + 5*x + 3*x. Let q = 66/7 - 184/21. Find f, given that 0*f + x - 2/3*f**2 + q*f**4 - 2/3*f**3 + 2/3*f**5 = 0.
-1, 0, 1
Let s = -489 - -489. Let c(g) be the second derivative of 0*g**4 - 1/42*g**7 + 0*g**3 - g - 1/15*g**6 + 0*g**2 + s + 0*g**5. Factor c(n).
-n**4*(n + 2)
Let c = 814 - 10580/13. Determine q so that 4/13*q**2 + 2/13*q + 0 + c*q**3 = 0.
-1, 0
Let s(b) = -3*b**4 - 6*b**3 + 3. Let a(i) = 6*i**4 + 11*i**3 - i**2 - i - 5. Let w = -1 - -4. Let x(t) = w*a(t) + 5*s(t). Factor x(d).
3*d*(d - 1)*(d + 1)**2
Suppose -2*z = 1923 - 1927. Factor -4/3 + 1/3*n**z - 5/6*n**3 + 10/3*n.
-(n - 2)*(n + 2)*(5*n - 2)/6
Solve -4/15*m**3 - 8/15*m**4 + 2/5*m - 2/15*m**5 + 8/15*m**2 + 0 = 0.
-3, -1, 0, 1
Let d(s) be the first derivative of -s**6/2 + 6*s**5/5 + 33*s**4/4 - 12*s**3 - 54*s**2 + 35. Suppose d(m) = 0. What is m?
-2, 0, 3
Let j(t) = -t**2 - 8*t + 1. Let k be j(-8). Suppose 0 = -8*m + k + 23. Suppose 2/7 + 4/7*r**m - 2/7*r**4 - 4/7*r + 0*r**2 = 0. Calculate r.
-1, 1
Let a = -249 - -748/3. Let d(k) be the third derivative of -4*k**2 + 1/120*k**6 + 1/30*k**5 - a*k**3 + 0 - 1/24*k**4 + 0*k. Let d(i) = 0. Calculate i.
-2, -1, 1
Let b = 19657/42 + -468. Let i(x) be the third derivative of b*x**4 - 7*x**2 + 0*x + 0 + 0*x**3 - 1/70*x**5 + 1/420*x**6. Factor i(f).
2*f*(f - 2)*(f - 1)/7
Let j(b) be the first derivative of 4*b**5/5 + 2*b**4 - 16*b**3/3 - 4*b**2 + 12*b - 235. Factor j(o).
4*(o - 1)**2*(o + 1)*(o + 3)
Let n(k) = k**3 - 18*k**2 + k - 15. Let y be n(18). Suppose 3*o - 4*o + 2*r - 7 = 0, -2*r + 13 = o. Solve y*z - o - 3/4*z**2 = 0 for z.
2
Suppose 19*t = 16*t + 9. Let z(b) be the first derivative of -2/27*b**t - 2/9*b + 3 + 2/9*b**2. Factor z(i).
-2*(i - 1)**2/9
Let l = 3 + 15. Find r, given that -l*r**2 - 18 - 4*r + 10 + 68*r**2 - 20*r**3 + 6*r**2 - 24*r**4 = 0.
-2, -1/3, 1/2, 1
Let z be 4/(-12)*(-60)/5. Let o be z/6*(-90)/(-20). Suppose -4/3*r**5 + 0 + 16/3*r**o + 4/3*r**4 + 0*r - 16/3*r**2 = 0. What is r?
-2, 0, 1, 2
Let b(o) be the first derivative of -4*o + 1/36*o**4 + 0*o**3 + 0*o**2 - 3. Let c(f) be the first derivative of b(f). Let c(k) = 0. What is k?
0
Suppose -3*f + 141*y = 144*y - 21, -y + 5 = 0. Let c(d) be the second derivative of -1/4*d**f + 0 + 1/24*d**4 + 6*d + 0*d**3. Let c(t) = 0. Calculate t.
-1, 1
Factor 384 - 189/8*b**2 + 360*b + 3/8*b**3.
3*(b - 32)**2*(b + 1)/8
Suppose -2*d + 4 + 4 = 0. Suppose -5*x - 12 = -5*w + 8, 16 = d*w. Factor -1/3*a**2 + 1/3*a + x.
-a*(a - 1)/3
Let -72/11*i**2 + 128/11 - 2/11*i**4 + 32/11*i + 2*i**3 = 0. What is i?
-1, 4
Let t = -19 - -33. Let k = -14 + t. Factor o**3 + 0*o**4 + k*o**2 + o**2 - 4*o**5 - o**4 + 3*o**5.
-o**2*(o - 1)*(o + 1)**2
Let r = 27 + -20. Suppose 4*k + 5*f + r = -10, -2*k + 2*f = -14. Factor -4*w**k + w + 6*w**2 - w.
2*w**2
Suppose -11*a - 12 + 34 = 0. Factor 5/3*r - 1/2 + r**3 - 1/6*r**4 - a*r**2.
-(r - 3)*(r - 1)**3/6
Factor -4/3*h**3 - 11/3*h**2 - 4/3 + 19/3*h.
-(h - 1)*(h + 4)*(4*h - 1)/3
Let y(c) be the third derivative of -35*c**6/48 + 71*c**5/24 - 29*c**4/6 + 4*c**3 - 308*c**2. Let y(w) = 0. Calculate w.
3/7, 4/5
Let s(z) be the first derivative of -z**5/45 + 55*z**4/36 + 56*z**3/27 + 631. Factor s(b).
-b**2*(b - 56)*(b + 1)/9
Factor 20*s**2 + 5*s - 45*s + 14*s**3 - 4*s**3 - 5*s**4.
-5*s*(s - 2)**2*(s + 2)
Factor 32/13 - 2/13*h**2 + 12/13*h.
-2*(h - 8)*(h + 2)/13
Suppose -512*k - 9 + 464*k - 27 - 13*k**2 + 0 - k**3 = 0. What is k?
-6, -1
Suppose 2*m = 2 + 6. Suppose 17 = m*c + 1. What is u in -4*u**3 + 12*u**3 - 3*u**3 - 2*u**2 + 7*u**c = 0?
-1, 0, 2/