**3 + 4*d**2 - 4. Let k(a) = a**4 + a**2 - 1. Let n(t) = 4*k(t) - p(t). Find g, given that n(g) = 0.
-1, 0
Let p(b) be the first derivative of b**3/3 + 3*b**2/16 - 22. Find f such that p(f) = 0.
-3/8, 0
Let d be (-8)/(240/(-126)) - (1 + 3). Solve -1/5*n**2 + 2/5 + d*n = 0.
-1, 2
Let m(c) be the second derivative of -3*c**5/35 - 11*c**4/28 - 5*c**3/7 - 9*c**2/14 + 7*c. Factor m(a).
-3*(a + 1)**2*(4*a + 3)/7
Find f, given that 5*f**4 + 2*f**3 - 3*f**3 + f**3 + 10*f**5 = 0.
-1/2, 0
Let j(n) = n**3 + 3*n**2 + 2*n + 2. Let x be j(-2). Suppose x*y + 2*a - 6 = -a, y = -2*a + 4. Factor -2/7*z + y - 2/7*z**4 + 2/7*z**2 + 2/7*z**3.
-2*z*(z - 1)**2*(z + 1)/7
Let s = 2/45 + 37/180. Factor 0*l**2 + 0 + 1/4*l**5 + 0*l**4 + 0*l - s*l**3.
l**3*(l - 1)*(l + 1)/4
Let b(v) = 4*v**3 - 2*v**2 - 2. Suppose 7 = -3*m + p, m = p - 3*p. Let i(o) = 13*o**3 - 6*o**2 - 7. Let d(g) = m*i(g) + 7*b(g). Factor d(x).
2*x**2*(x - 1)
Determine a, given that -2*a**2 - 8 + 11*a - 2*a**2 - 7*a + 8*a = 0.
1, 2
Let j(v) = -v**3 + 14*v**2 - 13*v + 2. Let g be j(13). Factor 3*h**2 + 5*h - 9*h - h**g.
2*h*(h - 2)
Let i(b) be the third derivative of -b**7/105 + b**6/30 + 2*b**5/15 - b**4/6 - b**3 + 20*b**2. Find p such that i(p) = 0.
-1, 1, 3
Let j(t) be the third derivative of t**6/24 + 7*t**5/12 + 25*t**4/8 + 15*t**3/2 - 24*t**2. Find i such that j(i) = 0.
-3, -1
Let i(h) = h**3 - 8*h**2 - 11*h + 21. Let t be i(9). Let p(n) be the third derivative of -2/3*n**t + 2*n**2 - 11/30*n**5 - 13/12*n**4 + 0 + 0*n. Factor p(w).
-2*(w + 1)*(11*w + 2)
What is x in -5 + 8*x + 3 - x**2 - 5*x = 0?
1, 2
Let y(m) be the second derivative of m**7/63 + m**6/45 - m**5/5 + m**4/9 + 5*m**3/9 - m**2 - 7*m. Suppose y(h) = 0. Calculate h.
-3, -1, 1
Let 16/23 - 4/23*z - 2/23*z**2 = 0. What is z?
-4, 2
Let b be 1 - (1 + (-9)/3). Factor 2*a**3 + 2*a**2 - a**4 + 5*a**4 - 6*a**b - 2*a**4.
2*a**2*(a - 1)**2
Factor 0*n**2 + 0 - 1/6*n**3 + 1/6*n.
-n*(n - 1)*(n + 1)/6
Let t = 308 + -916/3. Solve 10/3*o**2 + 4/3*o + 0 + t*o**3 + 2/3*o**4 = 0 for o.
-2, -1, 0
Let z be 3 + (1 - -1)/2. Let y(g) = g**3 + 6*g**2 - g - 4. Let u be y(-6). Suppose t**u + z*t - 3 + t**2 + 5 = 0. What is t?
-1
Let p(i) be the second derivative of 1/40*i**5 + 0*i**4 + 0*i**3 + 0 - 3*i + 0*i**2 + 1/60*i**6. Solve p(z) = 0.
-1, 0
Let y(q) be the third derivative of -q**8/1176 - q**7/420 - q**6/630 + q**3/6 - 4*q**2. Let k(h) be the first derivative of y(h). Factor k(u).
-2*u**2*(u + 1)*(5*u + 2)/7
Determine g, given that 24*g**5 - 9*g + 2*g**2 + 9*g + 16*g**3 + 38*g**4 = 0.
-1, -1/3, -1/4, 0
Factor -3*l**3 + 2*l**3 - 19*l**2 + 3*l**2 - 6*l + 9*l**2.
-l*(l + 1)*(l + 6)
Let v(w) be the first derivative of 0*w - 8 - 3/5*w**5 + 3*w**3 + 3*w**2 + 0*w**4. Solve v(d) = 0 for d.
-1, 0, 2
Let z(l) be the second derivative of 0 - 1/15*l**6 - 1/21*l**7 + 0*l**2 + 3/10*l**5 + 5/6*l**4 + 2*l + 2/3*l**3. Factor z(f).
-2*f*(f - 2)*(f + 1)**3
Determine p so that 14*p + 5 + 7 - p**2 - 18 - 7*p = 0.
1, 6
Let d(z) = 5*z**5 + 2*z**4 - 11*z**3 - 2*z**2 - 6*z + 6. Let j(b) = b**5 + b**4 - b**3 - b + 1. Let g(q) = d(q) - 6*j(q). Factor g(s).
-s**2*(s + 1)**2*(s + 2)
Factor 6*u**2 - 14*u**2 + 3*u**2.
-5*u**2
Let w(z) be the first derivative of 3*z**6/4 - 9*z**5/2 + 33*z**4/4 - 58*z**3/9 + 2*z**2 - 35. Solve w(g) = 0.
0, 2/3, 3
Let i be (7 - 0 - 7) + (-4)/(-14). Let j(d) be the second derivative of -3/14*d**4 + 0 - 1/3*d**3 + i*d**2 - 3*d. Factor j(o).
-2*(o + 1)*(9*o - 2)/7
Let u(m) = m**3 - 10*m**2 + m - 10. Let d be u(10). Let a(f) be the first derivative of 0*f**2 - 2/9*f**3 - 1 + d*f. Factor a(k).
-2*k**2/3
Suppose 4*a + 8 - 92 = 0. Let d = -15 + a. Factor -h**3 - d*h**2 + 8*h**2 - 4*h**2.
-h**2*(h + 2)
Factor -18*x + 3/2*x**2 + 0.
3*x*(x - 12)/2
Let b(c) be the second derivative of -2*c**6/15 + 2*c**5/5 - 4*c**3/3 + 2*c**2 - 6*c. Factor b(i).
-4*(i - 1)**3*(i + 1)
Solve 0*l**2 + 0 - 2/5*l**4 + 2/5*l**5 + 0*l - 4/5*l**3 = 0 for l.
-1, 0, 2
Solve -109*l - 6*l**2 + 121*l + 3*l**2 = 0 for l.
0, 4
Factor 56*w - 56*w + w**2.
w**2
Let n be 7/(3/1 + -2). Let s = -5 + n. Factor -2*l**3 - 4*l + 2*l + 6*l**2 - s*l**2.
-2*l*(l - 1)**2
Let z(k) = k**3 + 3*k**2 + k - 3. Let u(c) = -c**3 - c**2 + 1. Let t = 0 - 2. Let l(q) = t*u(q) - z(q). What is i in l(i) = 0?
-1, 1
Let f(d) = 3*d - 7. Suppose 6*j = 9 + 9. Let z be f(j). Factor 0 + 0*m**z + 0*m - 1/6*m**3 + 1/6*m**4.
m**3*(m - 1)/6
Let j = -22 - -25. Let s(n) be the first derivative of -1/5*n**5 + 0*n**2 + 1 - 1/18*n**6 + 0*n - 1/9*n**j - 1/4*n**4. Find c, given that s(c) = 0.
-1, 0
Let h = 216 - 213. Find f, given that 1/2*f**2 + 9/2 + h*f = 0.
-3
Determine x, given that 0 - 4/3*x**2 - 4/3*x = 0.
-1, 0
Determine z so that 0*z - 2/7*z**3 - 2/7*z**4 + 0 + 0*z**2 = 0.
-1, 0
Let j(g) be the second derivative of -g**7/147 - 2*g**6/105 + g**4/21 + g**3/21 + 8*g. Factor j(d).
-2*d*(d - 1)*(d + 1)**3/7
Factor 32*z**3 + 9*z**2 + 21*z**4 - 136*z**3 + 68*z**3 + 6*z.
3*z*(z - 1)**2*(7*z + 2)
Let s(t) = t**3 + 6*t**2 + 2. Let f be s(-6). Let h(d) = -d**3 + 2*d + 1. Let p be h(-2). Factor 4*a**4 + a - 3*a**p - 2*a + 3*a**3 + 2 - 6*a**f + a**3.
-(a - 1)**3*(a + 1)*(3*a + 2)
Suppose 0 = -i + 3*c + 1, 2*i + 6 = -c + 3*c. Let y = i - -9. Factor 5*o**3 - 7*o**4 + 2 - o + 4*o**3 + 5*o**2 - y*o - 4*o.
-(o - 1)**2*(o + 1)*(7*o - 2)
Let t(n) be the second derivative of 5*n - 3/2*n**2 + 0 - 1/36*n**4 + 1/3*n**3. Solve t(u) = 0.
3
Suppose v + 2*n - 11 + 2 = 0, 0 = 3*v + n - 12. Let l = 8 - v. Factor -3*k**5 + l*k**5 - 2 + 4*k**2 - k**3 - 2*k**4 + 2*k - 3*k**3.
2*(k - 1)**3*(k + 1)**2
Let o(k) = -k**3 - 6*k**2 - 4*k + 7. Let b be o(-5). Solve 2*h**2 + h**b - 4*h + 3 - 2*h = 0 for h.
1
Let a(v) be the second derivative of 2*v**7/231 - 3*v**6/55 + 8*v**5/55 - 7*v**4/33 + 2*v**3/11 - v**2/11 + v. Factor a(h).
2*(h - 1)**4*(2*h - 1)/11
Let m(k) be the second derivative of 0*k**2 - 1/48*k**4 + 0 + 1/80*k**5 - 2*k - 1/12*k**3. Factor m(x).
x*(x - 2)*(x + 1)/4
Let i be (-24)/16 + 15/2. Let k(o) be the second derivative of -3/10*o**5 + 1/15*o**i + 1/2*o**4 + 0 + 0*o**2 - 1/3*o**3 - 2*o. Solve k(t) = 0 for t.
0, 1
Let k(l) = l**2 + 27*l + 28. Let u be k(-26). Find g, given that -21/5*g**4 + 69/5*g**3 - 6/5 - 81/5*g**u + 39/5*g = 0.
2/7, 1
Let h(q) be the second derivative of 0*q**2 + 2/135*q**6 - 1/27*q**4 + 1/189*q**7 - 1/27*q**3 - 4*q + 0*q**5 + 0. Factor h(g).
2*g*(g - 1)*(g + 1)**3/9
Suppose 25*l + l**2 + 20 + 0*l**2 + 4*l**2 = 0. Calculate l.
-4, -1
Let p(n) be the second derivative of -n**6/90 + n**4/6 - 2*n**3/3 - 3*n. Let z(d) be the second derivative of p(d). What is g in z(g) = 0?
-1, 1
Let c(x) = -3*x + 3. Let p(n) = n**2 - 1. Let w(j) = -c(j) + p(j). Let z be (4 + -1)*6/6. Let g(t) = 3*t - 5. Let q(o) = z*g(o) - 4*w(o). Factor q(k).
-(k + 1)*(4*k - 1)
Let y(o) be the first derivative of -o**3/3 - 5*o**2/2 - 4*o - 2. Factor y(x).
-(x + 1)*(x + 4)
Let p(m) be the first derivative of m**6/60 + m**5/10 + m**4/4 + m**3/3 + m**2 - 3. Let z(s) be the second derivative of p(s). Suppose z(y) = 0. What is y?
-1
Let h(f) be the third derivative of f**6/120 + f**5/15 - 5*f**4/24 + f**3/3 - 3*f**2. Let a be h(-5). Factor -18*j + 20*j - 2 + 3*j**a + j**2.
2*(j + 1)*(2*j - 1)
Let k be (4/24)/(18/4). Let q(o) be the third derivative of -2*o**2 + k*o**3 - 1/54*o**4 + 0 + 1/270*o**5 + 0*o. Factor q(g).
2*(g - 1)**2/9
Suppose -s - o + 2 = 0, 2*s - 5*o = -o - 8. Suppose s = -z - 4*z + 20. Suppose 5*d**4 + 9*d**4 + z*d**5 + 6*d**5 + 4*d**3 = 0. Calculate d.
-1, -2/5, 0
Factor -8/17 - 2/17*b**2 + 8/17*b.
-2*(b - 2)**2/17
Suppose 5*v - 3*m - 9 = 0, m = 3*v - 3 - 4. Let q be v - ((-4)/(-1))/2. Determine c, given that 5*c**2 - q - 3*c**2 + c**5 - 2*c**3 + c - c**4 + 0*c = 0.
-1, 1
Let m(w) be the second derivative of 1/4*w**4 - 1/20*w**5 + 0 - 1/3*w**3 - 11*w + 0*w**2. Factor m(b).
-b*(b - 2)*(b - 1)
Let p = 27 + -27. Let w(c) be the third derivative of -1/6*c**3 + 0*c**6 - 1/210*c**7 + p*c**4 + 1/30*c**5 + 0*c - 2*c**2 + 0. Factor w(v).
-(v - 1)**2*(v + 1)**2
Let o be ((-24)/(-25))/(-8)*-5. Factor -2/5 - 1/5*s**4 - 1/5*s + 1/5*s**3 + o*s**2.
-(s - 2)*(s - 1)*(s + 1)**2/5
Let h(a) be the second derivative of 0 + 1/45*a**6 + 1/18*a**3 + 0*a**2 - 3*a - 1/126*a**7 - 1/18*a**4 + 0*a**5. Let h(q) = 0. What is q?
-1, 0, 1
Let i be 5/20*(-6)/(-9). Factor -1/6*w**2 + i*w**4 + 1/6