(h) = 7*h**2 - 5*h - 13. Let p(m) = -3*m**2 + 2*m + 6. Suppose b + 6 - 1 = 0. Let n(c) = b*p(c) - 2*j(c). Factor n(o).
(o - 2)*(o + 2)
Let z(t) = t**3 - 7*t**2 + 5. Let g be z(7). Let m be -2 - -3*(1 + 0). Factor n**3 + 1 - n**g - m.
-n**3*(n - 1)*(n + 1)
Let l = 1 + 1. Factor 0*s**3 + s + s**2 + 0*s - 2*s**l + s**4 - s**3.
s*(s - 1)**2*(s + 1)
Solve 5 + 35 - 78*u**2 + 28*u - 40*u**3 - 118*u**2 = 0.
-5, -2/5, 1/2
Let u(n) be the second derivative of -n**7/231 - 2*n**6/165 + 6*n**5/55 - 7*n**4/33 + 5*n**3/33 - 18*n. Let u(p) = 0. What is p?
-5, 0, 1
Let x(n) = n**2 - n - 1. Let p(y) = 3*y - 2. Let h(r) = 3*r - 1. Let f(c) = 3*h(c) - 2*p(c). Let z(k) = 3*f(k) + 6*x(k). Let z(m) = 0. Calculate m.
-1, 1/2
Suppose 2 = v - 5*o, 4*v + 2*o = -0*o + 8. Suppose -20 = -3*c - c + 4*b, -v*b + 5 = 3*c. Determine s so that 9*s**2 + c*s + 5 + 9*s**3 - 5 + 3*s**4 = 0.
-1, 0
Determine k, given that 4/7*k**2 + 0 - 8/7*k + 8/7*k**3 - 4/7*k**4 = 0.
-1, 0, 1, 2
Let y(j) be the third derivative of j**8/5040 - j**7/2520 + j**6/2880 + j**5/30 + 10*j**2. Let w(f) be the third derivative of y(f). Factor w(a).
(4*a - 1)**2/4
Let b(k) be the first derivative of -5*k**4/26 - 44*k**3/39 - 28*k**2/13 - 16*k/13 - 19. Determine h, given that b(h) = 0.
-2, -2/5
Let o(y) be the first derivative of y**5/5 - 3*y**4/2 + 4*y**3 - 4*y**2 + 8. Factor o(i).
i*(i - 2)**3
Let k(g) = -2*g**4 - 6*g**3 + 5*g**2. Let z(u) = -7*u**3 + 5*u**2 + 2*u**4 - 5*u**4 + u**2. Let a(r) = -4*k(r) + 3*z(r). Find m, given that a(m) = 0.
0, 1, 2
Let q = 85/147 - 1/147. Factor -2/7*f**2 + 0*f + 0 - q*f**3.
-2*f**2*(2*f + 1)/7
Let h(o) be the third derivative of 1/40*o**6 + 0 + 0*o**7 + 0*o**5 + 0*o + 0*o**4 + 0*o**3 - 2*o**2 - 1/112*o**8. Solve h(p) = 0 for p.
-1, 0, 1
Let f(z) be the second derivative of -1/70*z**5 + 0*z**2 + 0 - 3*z + 2/21*z**3 + 1/42*z**4. Factor f(w).
-2*w*(w - 2)*(w + 1)/7
Let n(p) = p**3 + 5*p**2 - 7*p + 3. Let d be n(-6). Factor d*k**2 - 6*k**2 - 3*k + k**3 + 2*k**3 - 3.
3*(k - 1)*(k + 1)**2
Let k = 364 - 1804/5. Solve 2/5*f - k*f**4 - 4/5 + 8/5*f**3 - 2*f**5 + 4*f**2 = 0 for f.
-1, 2/5, 1
Suppose -15/4*d**2 - 5/4*d**3 - 5/2*d + 0 = 0. Calculate d.
-2, -1, 0
Factor -2/3*x + 0 - 2/3*x**3 + 4/3*x**2.
-2*x*(x - 1)**2/3
Let z(n) = n + 11. Let k be z(-8). Find v, given that -v**3 + 19*v + 2 + 30*v**2 + 19*v**k - 5*v = 0.
-1, -1/3
Let m(d) be the second derivative of 0 + 0*d**2 - 4*d + 0*d**3 - 1/4*d**4. Factor m(o).
-3*o**2
Let s be 1 - 1*3/6. Let p = 0 - -3. Factor 0*o - 3/2*o**p + 1/2*o**2 + 0 + 3/2*o**4 - s*o**5.
-o**2*(o - 1)**3/2
Find i, given that -4 + 885*i**5 + 1615*i**5 - 20*i - 221*i**2 - 2584*i**3 + 104*i + 225*i**4 = 0.
-1, -1/4, 2/25, 1
Let m(y) = -6*y**2 + 6*y - 3. Let c(w) = -w**2 - 10*w - 8. Let i be c(-9). Let j(f) = f**2. Let v(u) = i*m(u) + 3*j(u). Factor v(n).
-3*(n - 1)**2
Let w(z) = -z - 1. Let s be w(-5). Suppose p = s - 1. Suppose -b**3 + 0*b**5 - b**5 - p*b**4 + b**4 = 0. Calculate b.
-1, 0
Let n = -11 - -6. Let c = 7 + n. Determine z so that -2/5*z**c + 0 + 2/5*z - 2/5*z**3 + 2/5*z**4 = 0.
-1, 0, 1
Suppose -13*v + 10*v - 6 = -5*x, 2*v - 4*x = -6. Find c such that -2/9*c**4 - 4/9 + 2/9*c + 2/3*c**2 - 2/9*c**v = 0.
-2, -1, 1
Let z = 49/20 - 11/5. Factor -z*o**2 - 1 + o.
-(o - 2)**2/4
Let t(g) be the third derivative of -g**8/36960 + g**7/6930 - g**6/3960 - g**4/24 + 2*g**2. Let o(c) be the second derivative of t(c). Factor o(p).
-2*p*(p - 1)**2/11
Suppose n = 2*n - 9. Let l be 1/2*(13 - n). Solve 0 - 1/4*v**l + 0*v = 0 for v.
0
Let p(h) = 5*h**2 + 8*h - 9. Let g(j) = -6*j**2 - 9*j + 9. Let r(x) = 2*g(x) + 3*p(x). Factor r(o).
3*(o - 1)*(o + 3)
Let v(s) = s**3 + 3*s**2 - 3*s + 4. Let n be v(-4). Let w(k) be the second derivative of 2*k + n + 0*k**3 - 1/9*k**2 + 1/54*k**4. Solve w(o) = 0 for o.
-1, 1
Let l(v) = 40*v. Let o be l(1). Let g be 4/(-18) - o/(-18). Factor 4*z + z - 3 - z + 0*z**g - z**2.
-(z - 3)*(z - 1)
Let g(q) = -4*q**2 + q**2 + 5*q**2. Let a(y) = -y**2. Let v(z) = -11*a(z) - 6*g(z). Factor v(j).
-j**2
Let m(g) be the second derivative of -g**7/735 + 3*g**2/2 + g. Let x(k) be the first derivative of m(k). Factor x(h).
-2*h**4/7
Suppose -28*q + 20*q = -16. Suppose -4/9 + 2/9*u**q + 2/9*u = 0. Calculate u.
-2, 1
Suppose -4*d + n - 5*n = 0, -d - 2*n - 2 = 0. Let 4/9 - 2/3*m**d + 2/9*m**4 + 2/9*m**3 - 2/9*m = 0. Calculate m.
-2, -1, 1
Let n be (4 + -10)*(2 + -3). Factor n*q + q + 2 - q + 2*q**2 - 2*q.
2*(q + 1)**2
Let j(t) be the second derivative of -t**4/3 - 8*t**3/3 + 10*t**2 - 27*t. Let j(y) = 0. What is y?
-5, 1
Let p(m) = -15*m**3 + 15*m**2 + 12. Let t(i) = i**3 - i**2 - 1. Let q(s) = -p(s) - 12*t(s). Factor q(f).
3*f**2*(f - 1)
Let z(n) be the third derivative of -n**9/15120 + n**8/6720 + n**7/2520 - n**6/720 - n**4/8 + 2*n**2. Let s(c) be the second derivative of z(c). Solve s(t) = 0.
-1, 0, 1
Let i be ((-3)/4)/((-13)/156). Determine s, given that 3*s**5 - 10*s**2 + 17*s**4 - 12*s + i*s**3 - 2*s**2 - 5*s**4 = 0.
-2, -1, 0, 1
Factor 6/5*q - 4/5 - 2/5*q**2.
-2*(q - 2)*(q - 1)/5
Let o(a) be the second derivative of -1/5*a**5 + 3*a + 0 + 2/3*a**3 + 2/3*a**4 - 4*a**2. Factor o(c).
-4*(c - 2)*(c - 1)*(c + 1)
Suppose 9 = 3*l - 6. Solve -2*c**2 - l + 5 - 2 + 0*c - 4*c = 0 for c.
-1
Let p(v) be the third derivative of -v**6/540 + v**5/30 - 5*v**4/36 + 7*v**3/27 + 59*v**2. Solve p(x) = 0.
1, 7
Let a(s) = -s**3 + 1. Let h(z) = -3*z**3 - 6*z**2 + 3*z + 6. Let w(g) = 6*a(g) - h(g). Factor w(y).
-3*y*(y - 1)**2
Let g(v) = v**3 - v**2 + v - 1. Let t be g(1). Let a(l) be the second derivative of -1/6*l**4 + 0 + t*l**2 + l + 1/3*l**3. Solve a(w) = 0.
0, 1
Let p = 16 + -12. Factor -q + 4*q**3 - 15*q**3 + q**p + 3*q**2 + 8*q**3.
q*(q - 1)**3
Let h(v) be the first derivative of -v**3 - 3*v**2 - 3*v - 1. Solve h(d) = 0 for d.
-1
Let d(f) be the first derivative of 0*f**4 - 3 + 0*f + 2/3*f**3 - 1/2*f**2 + 1/6*f**6 - 2/5*f**5. Find w such that d(w) = 0.
-1, 0, 1
Let m = -2 - -7. Suppose m*k - 4 = 11. Let 0*i**k - 4/9*i**2 + 2/9*i**5 - 2/9*i + 4/9*i**4 + 0 = 0. Calculate i.
-1, 0, 1
Let y(u) be the first derivative of -2*u**4 + 6*u**3 - 2*u**2 + 8. Factor y(x).
-2*x*(x - 2)*(4*x - 1)
Factor -68*w**2 - 6 - 16*w + 33*w**3 + 107*w**3 + 20*w**5 + 22 - 92*w**4.
4*(w - 2)*(w - 1)**3*(5*w + 2)
Let t be (7*3/210)/(21/5). Let y(u) be the second derivative of t*u**7 - 3*u + 1/6*u**3 - 1/10*u**5 + 0*u**4 + 0 + 0*u**6 + 0*u**2. Factor y(z).
z*(z - 1)**2*(z + 1)**2
Let a be (3/(-3))/(2/(-8)). Suppose -2*w + 3*b - 9 = 0, 2*b - 3 - 3 = 0. Factor 2/5*x**a - 2/5*x**3 + 0*x + w*x**2 + 0.
2*x**3*(x - 1)/5
Suppose 3*x + 3 = 4*f, -2*f + 3 - 2 = -x. Let a = f - -3. Determine g, given that -6*g + 5*g - 2*g**4 - 12*g**2 - 7*g - 8*g**a - 2 = 0.
-1
Let f(t) be the second derivative of 0*t**2 + 1/12*t**3 - 1/24*t**4 - t + 0. Let f(h) = 0. What is h?
0, 1
Let y(d) be the third derivative of d**8/168 - d**7/35 + d**6/20 - d**5/30 - 4*d**2. Factor y(n).
2*n**2*(n - 1)**3
Let k(t) be the second derivative of t**4/30 + t**3/15 - 2*t**2/5 - 5*t. Let k(p) = 0. Calculate p.
-2, 1
Let f(t) = -4*t**3 + 132*t**2 - 1452*t + 5324. Let p(i) = -8*i**3 + 264*i**2 - 2904*i + 10648. Let b(h) = 9*f(h) - 4*p(h). Determine x so that b(x) = 0.
11
Let d(y) = -y**2 - 10*y + 2. Let c be d(-10). Let i be 3/(-6) + 7/c. Find r such that -4*r**3 + 2*r**3 - 2*r**i - 3*r**2 + 6*r + r**3 = 0.
-2, 0, 1
Let f = -4 - 0. Let p = f - -6. Factor 1/2*b**4 - 1/2*b + 3/2*b**p + 0 - 3/2*b**3.
b*(b - 1)**3/2
Let y = -7/5 + 47/30. Let w(n) be the third derivative of 1/120*n**5 - y*n**3 + 0 + 1/48*n**4 + 3*n**2 + 0*n. Solve w(k) = 0.
-2, 1
Let y(b) be the first derivative of -16*b**5/35 + 3*b**4/7 + 20*b**3/21 - 6*b**2/7 - 4*b/7 + 8. Solve y(n) = 0.
-1, -1/4, 1
Let t(o) be the first derivative of -3/4*o**4 + 0*o**3 - 6*o - 2 + 9/2*o**2. Solve t(m) = 0 for m.
-2, 1
Let t = 3 + -1. Let g be 3 + -1 + 0 + -2. Suppose 0 - 1/3*f**t + g*f = 0. What is f?
0
Let n(u) = -u**3 - 12*u**2 + 5. Let g be n(-12). Find o, given that 6/5*o**4 + 2/5*o**3 + 8/5 - 14/5*o**2 - 2/5*o**g + 0*o = 0.
-1, 1, 2
Let q(z) be the second derivative of -z**6/75 - z**5/25 + z**4/30 + 2*z**3/15 + 2*z. Factor q(w).
-2*w*(w - 1)*(w + 1)*(w + 2)/5
Suppose 0 = 5*y - 2*h - 11, -4*h + 5 = -7*y + 6*y. Factor 13/2*f**2 - 3/2*f**4 + 1 - 9/2*f - 5/2*f**y + f**5.
(f - 1)**3*(f + 2)*(