18 - -18. Let i(z) = -z**3 - z. Let b be i(w). Suppose 4/9*h**2 - 2/9*h**4 + 0*h - 2/9 + b*h**3 = 0. What is h?
-1, 1
Let g(i) = i**3 + 11*i**2 + 9*i - 8. Let d be g(-10). Let u(x) be the second derivative of -1/36*x**4 + 0 + 2/9*x**3 - 2/3*x**d + x. Factor u(q).
-(q - 2)**2/3
Suppose 0 = -9*d + 4*d + 25. Suppose 0 = 5*y - c + 2*c - 25, -2*y = -5*c + 17. Find j such that 2*j**d - 4*j**5 + y*j**5 = 0.
0
Let p(b) be the third derivative of -2/75*b**5 + 0*b + 8/15*b**3 - 1/75*b**6 + 1/1680*b**8 + 4*b**2 + 2/15*b**4 + 0 + 1/1050*b**7. Solve p(y) = 0.
-2, -1, 2
Let f(n) be the first derivative of 0*n**3 + 2 - 1/7*n**4 + 0*n + 2/7*n**2. Determine q so that f(q) = 0.
-1, 0, 1
Let i(w) be the first derivative of -w**4/6 - 2*w**3/9 + w**2/3 + 2*w/3 + 4. Factor i(l).
-2*(l - 1)*(l + 1)**2/3
Let p = -610 - -3052/5. Determine g, given that 0*g + 4/5*g**2 + 0*g**3 - 2/5 - p*g**4 = 0.
-1, 1
Let b(c) be the first derivative of 0*c**2 + 2 + 0*c + 2/3*c**3 - 1/2*c**4. Factor b(d).
-2*d**2*(d - 1)
Let k(m) = 8*m**4 + 6*m**3 - 12*m**2 + 2*m + 2. Let d(n) = 25*n**4 + 19*n**3 - 35*n**2 + 5*n + 7. Let w(t) = -4*d(t) + 14*k(t). Factor w(r).
4*r*(r - 1)*(r + 2)*(3*r - 1)
Let l be -1*(74/(-26) - 26/169). Find k such that -4/3 - 20/3*k - 13*k**2 - 37/3*k**l - 17/3*k**4 - k**5 = 0.
-2, -1, -2/3
Let -2/5*s**2 + 18/5*s - 16/5 = 0. Calculate s.
1, 8
Suppose -4*q - y = 5, 5 + 15 = -4*y. Factor q*o + 1/4 + 0*o**3 - 1/2*o**2 + 1/4*o**4.
(o - 1)**2*(o + 1)**2/4
Let l(x) be the first derivative of -x**4/36 + x**3/9 - x**2/6 - 3*x - 1. Let a(g) be the first derivative of l(g). Solve a(t) = 0.
1
Let d(m) be the first derivative of 3 - m + 1/6*m**3 + 1/10*m**5 + 3/4*m**2 - 3/8*m**4. Factor d(j).
(j - 2)*(j - 1)**2*(j + 1)/2
Let r(y) = -6*y**3 + 3*y**2 + 21*y - 12. Suppose 6*q + 18 = 3*q. Let v(f) = -f**2 - f + 1. Let w(c) = q*v(c) - r(c). Factor w(h).
3*(h - 1)*(h + 2)*(2*h - 1)
Let a be 1/((1/5)/((-256)/(-480))). Factor 8/3*z**2 + 2/3*z**5 + a*z - 2*z**3 + 0 - 4/3*z**4.
2*z*(z - 2)**2*(z + 1)**2/3
Let a = -26 - -79/3. Factor 1/3*s**3 + 0 + 0*s - a*s**2.
s**2*(s - 1)/3
Let n(x) = x**3 - 5*x**2 - 6*x + 2. Let i be (0 + -3)*-1 - -3. Let s be n(i). Factor -1/2*d**s - 1/2*d**3 + 0 + 0*d.
-d**2*(d + 1)/2
Let m(t) be the first derivative of t**3/6 + t**2/4 + 18. Factor m(b).
b*(b + 1)/2
Let f(u) be the second derivative of u**5/20 - u**4/12 - 6*u. Determine h, given that f(h) = 0.
0, 1
Let y(x) be the first derivative of -x**3/9 - x**2/3 - x/3 + 12. Suppose y(s) = 0. What is s?
-1
Let u = 12 - 17. Let c = u - -8. Solve -1 - h**c - h + 5*h - 6*h - 3*h**2 - h = 0 for h.
-1
Let i(h) be the second derivative of h**7/56 + 11*h**6/120 + 7*h**5/40 + h**4/8 - h**3/24 - h**2/8 + 10*h. Suppose i(b) = 0. Calculate b.
-1, 1/3
Factor 9/8*r + 3/8*r**2 - 9/8*r**3 + 3/8*r**4 - 3/4.
3*(r - 2)*(r - 1)**2*(r + 1)/8
Let y = 6/11 - 7/33. Let v(z) be the third derivative of -y*z**3 + 1/30*z**5 + 0*z**4 + 0*z + 0 + 2*z**2. Find f, given that v(f) = 0.
-1, 1
Let c(p) be the third derivative of p**6/60 - p**5/9 - p**4/4 + 4*p**3/9 + 5*p**2. Factor c(l).
2*(l - 4)*(l + 1)*(3*l - 1)/3
Suppose 0 = 19*u - 25*u. Suppose 1/4*j**2 + u*j - 1/4 = 0. What is j?
-1, 1
Let x(b) be the third derivative of -5*b**2 + 0*b**3 + 0*b**5 + 0*b - 1/80*b**6 + 1/16*b**4 + 0. Factor x(k).
-3*k*(k - 1)*(k + 1)/2
Let 2/11*v**2 + 6/11*v**3 - 4/11*v**5 + 0 - 2/11*v**4 - 2/11*v = 0. Calculate v.
-1, 0, 1/2, 1
Let k(a) = a - 3. Let d be k(3). Let t(b) be the first derivative of 1/6*b**3 + 0*b**2 - 5/8*b**4 + 7/10*b**5 + 3 - 1/4*b**6 + d*b. Factor t(c).
-c**2*(c - 1)**2*(3*c - 1)/2
Let w(v) be the third derivative of 1/6*v**3 + 0*v + 1/12*v**4 - 1/210*v**7 + 0*v**5 - 1/60*v**6 + 2*v**2 + 0. What is z in w(z) = 0?
-1, 1
Let 0*b**2 - 1/2*b**4 - 2*b + 3/2*b**3 + 0 = 0. What is b?
-1, 0, 2
Let m(t) be the third derivative of -6*t**2 + 3/20*t**5 + 0*t**4 + 0*t + 0 + 1/40*t**6 - 2*t**3. What is n in m(n) = 0?
-2, 1
Let r be 8/12 + (-48)/(-9). Factor 4*d**3 - d**5 + 4*d**2 - 2*d + r - 8 - 2*d**4 - d**5.
-2*(d - 1)**2*(d + 1)**3
Let x(i) = -i**2 + 2*i - 2. Let k(b) be the second derivative of b**4/4 - 7*b**3/6 + 7*b**2/2 - b. Let j(z) = -2*k(z) - 7*x(z). Factor j(m).
m**2
Suppose 0 = 2*r + 2*r. Let d(t) = t + 3. Let w be d(r). Factor -o - 7*o**2 + 9*o**2 - 4*o**3 + 3*o**w.
-o*(o - 1)**2
Suppose -4*o - 2*o**2 - 1/3*o**3 - 8/3 = 0. Calculate o.
-2
Let x = -49 + 17. Let i = -158/5 - x. Solve -2/5*o**2 + 0 + i*o = 0.
0, 1
Suppose 4*c - 4*o = 4, c + 26 = 3*c + 4*o. Factor -3 + 6*d**3 - c*d + 3*d + 3*d**4 - 4*d.
3*(d - 1)*(d + 1)**3
Let p(g) be the third derivative of -g**7/84 - g**6/12 - g**5/8 - 12*g**2. Find h, given that p(h) = 0.
-3, -1, 0
Let o = -227/4 - -57. Factor 1/4*m**4 + 0*m**3 - o*m**2 + 0 + 0*m.
m**2*(m - 1)*(m + 1)/4
Suppose 28 + 2 = 4*j - 3*s, -j + s = -8. Suppose 6*r - 3*r = j. Factor 3*c + 0*c**2 + 2*c**2 - 2 + 2*c - r*c**3 - 3*c.
-2*(c - 1)**2*(c + 1)
Factor 2/5 - 2/5*d - 2/5*d**2 + 2/5*d**3.
2*(d - 1)**2*(d + 1)/5
Let y = -84 + 256/3. Suppose -2/3*z**3 + y*z**2 + 0 - 2/3*z = 0. Calculate z.
0, 1
Let j(k) = -7*k**4 + 19*k**3 - 27*k**2 + 19*k - 7. Let o(g) = -76*g**4 + 208*g**3 - 296*g**2 + 208*g - 76. Let d(f) = 32*j(f) - 3*o(f). Let d(r) = 0. What is r?
1
Let t(m) = -m**2 - 1. Let k(i) = 3*i**3 - i**2 + 5. Let w(n) = k(n) + 5*t(n). Determine o so that w(o) = 0.
0, 2
Factor -8/7*k**3 + 0 + 6/7*k + 2/7*k**2.
-2*k*(k - 1)*(4*k + 3)/7
Let x = -15 + 17. Solve 2*m**2 + 4*m - 8*m**2 + 4*m**3 - x*m**2 = 0 for m.
0, 1
Factor -8 + 4*m**2 - 4*m - m + m.
4*(m - 2)*(m + 1)
Let 3/4*q**2 + 3/4*q + 0 = 0. What is q?
-1, 0
Let d(g) = 15*g**5 + 21*g**4 + 6*g**3 - 6*g**2 - 9*g - 15. Suppose 0 = -0*p - p - 12. Let l(m) = m**5 + m**4 - 1. Let x(b) = p*l(b) + d(b). Solve x(a) = 0.
-1, 1
Let c = 13 - 16. Let v be (-18)/12*c/18. Determine y, given that y - y**3 - 1/4 + v*y**2 = 0.
-1, 1/4, 1
Let o(f) be the second derivative of 1/3*f**3 + 0 + 0*f**4 + 0*f**2 - 1/10*f**5 - 2*f. Factor o(u).
-2*u*(u - 1)*(u + 1)
Let d(s) be the third derivative of -s**5/240 - s**4/16 - 5*s**3/24 - 12*s**2 + s. Let d(v) = 0. Calculate v.
-5, -1
Factor 61*y**2 - 16*y**2 + 2*y**2 + 37*y**2 + 135*y**3 + 12*y.
3*y*(5*y + 2)*(9*y + 2)
Let u(f) = -f**3 + 5*f**2 - f + 3. Let p be u(5). Let l = p - -4. Let -y**l + y - y**4 - y**3 + 0*y**2 + 2*y**4 = 0. Calculate y.
-1, 0, 1
Factor o**2 - 3/5*o - 2/5.
(o - 1)*(5*o + 2)/5
Suppose -2 + 22 = -m - 5*i, 3*m - 3*i = -6. Let v be (4/m)/((-32)/80). Factor 0 - 2/11*j - 2/11*j**v.
-2*j*(j + 1)/11
Let c(p) be the first derivative of 1/8*p**2 + 2 - p + 1/12*p**3 + 1/48*p**4. Let y(m) be the first derivative of c(m). Factor y(v).
(v + 1)**2/4
Factor -5/6 + y - 1/6*y**2.
-(y - 5)*(y - 1)/6
Suppose 2*z + 5 = -1. Let m be (-2)/z + (-26)/(-15). What is t in 2/5*t**2 + m*t + 18/5 = 0?
-3
Let m = 5632/7 - 802. Factor 8/7*i + 16/7*i**2 - m*i**4 + 0 - 6/7*i**3.
-2*i*(i - 1)*(3*i + 2)**2/7
Factor -2*p**3 - 4*p**3 + p**3 + p**2 + 5*p + 3*p**3 + 2.
-(p - 2)*(p + 1)*(2*p + 1)
Let b(x) be the first derivative of -x**7/3780 + x**6/405 - x**5/108 + x**4/54 + x**3/3 + 3. Let m(k) be the third derivative of b(k). Solve m(g) = 0.
1, 2
Let q(d) be the second derivative of d**5/80 + d**4/48 - d**3/12 - 21*d. Factor q(y).
y*(y - 1)*(y + 2)/4
Let d(z) = -2*z**3 + 26*z**2 + 150*z + 254. Let u(x) = -x**3 - x**2 + 1. Let p(a) = -d(a) + 4*u(a). Factor p(v).
-2*(v + 5)**3
Let b(r) be the third derivative of r**8/560 + r**7/175 - 3*r**6/200 - r**5/25 + r**4/10 + r**2. Factor b(p).
3*p*(p - 1)**2*(p + 2)**2/5
Let o(t) = t**3 + 20*t**2 - 22*t - 21. Let y be o(-21). Let z(v) be the first derivative of -1 + 0*v + 2/3*v**3 + y*v**2. Factor z(c).
2*c**2
Suppose 3*s = 5*p - 11, -6*s + 8*s - 5*p = -14. Factor -1/3 + m - m**2 + 1/3*m**s.
(m - 1)**3/3
Factor -4*r**2 + 8 + 1/2*r**4 + 0*r + 0*r**3.
(r - 2)**2*(r + 2)**2/2
Let h(m) be the first derivative of -m**7/70 + m**6/40 + m**5/10 - 7*m**2/2 + 1. Let p(v) be the second derivative of h(v). Solve p(d) = 0.
-1, 0, 2
Let j(i) = -5*i**3 - 6*i**2 + 11. Let p be 4 - (1 + 0/(-2)). Let t(z) = -11*z**3 - 12*z**2 + 23. Let m(o) = p*t(o) - 7*j(o). Factor m(x).
2*(x - 1)*(x + 2)**2
Factor -268*a**2 + a + 6*a**4 + 6*a**4 - 49*a + 284*a**2 + 76*a**3.
4*a*(a + 1)*(a + 6)*(3*a - 2)
Solve 7*p**3 - 55*p**2 - 72 - 70*p**2 + 276*p + 39*p**2 = 0 for 