p such that x(p) = 0.
-2, 1
Let j(a) be the second derivative of -a**5/60 + a**4/24 + a**3/3 - a**2 + 4*a. Let h(c) be the first derivative of j(c). Factor h(n).
-(n - 2)*(n + 1)
Let f(o) be the second derivative of 11/4*o**4 - 5/2*o**3 - 3/5*o**5 - o + 0 - 3*o**2. Factor f(m).
-3*(m - 2)*(m - 1)*(4*m + 1)
Let k be (-10)/(-6) + 1 + -2. Let m = 28/33 - 2/11. Factor 0 - k*n + m*n**2.
2*n*(n - 1)/3
Let -14/13*h**2 - 22/13*h - 2/13*h**3 - 10/13 = 0. Calculate h.
-5, -1
Let w be ((-2)/(-5))/(1/10). Suppose 5*g = 14 + 1. Factor 4*n**3 - 5*n**3 - 2*n**w + 4*n**4 + n**2 + 4*n**g.
n**2*(n + 1)*(2*n + 1)
Let h(p) be the second derivative of 0 + 1/54*p**4 - 1/27*p**3 + 1/2*p**2 - 2*p - 1/270*p**5. Let f(a) be the first derivative of h(a). Factor f(n).
-2*(n - 1)**2/9
Let o(q) be the third derivative of -q**5/60 + q**4/8 + 5*q**2. Determine f, given that o(f) = 0.
0, 3
Suppose 9 = -3*p - 6*c + c, 2*p = c + 7. Find l such that -4/3 + 2*l + 4/3*l**p = 0.
-2, 1/2
Let c(g) be the second derivative of -g**8/1680 - g**7/525 - g**6/600 - 3*g**2/2 + 4*g. Let d(t) be the first derivative of c(t). Factor d(n).
-n**3*(n + 1)**2/5
Let v(m) = -m**3 + m. Let c be v(0). Find j, given that 1/2*j + c - 9/4*j**2 + 7/4*j**3 = 0.
0, 2/7, 1
Let i(s) = s - 8. Let p be i(8). Let h = 0 - p. Solve -3/5*y**3 - 1/5*y**4 + h - 1/5*y - 3/5*y**2 = 0.
-1, 0
Let h be -7 - -3 - -1 - -3. Let z(b) be the first derivative of h*b + 0*b**2 + 2/21*b**3 + 2 + 2/35*b**5 - 1/7*b**4. Solve z(m) = 0 for m.
0, 1
Let n(h) be the second derivative of h**4/30 - h**3/15 - 2*h**2/5 + 30*h. Factor n(j).
2*(j - 2)*(j + 1)/5
Let g(a) be the second derivative of 1/8*a**5 + 5*a + 0*a**2 + 0 + 5/24*a**4 - 5/6*a**3. Suppose g(z) = 0. What is z?
-2, 0, 1
Let c(a) be the second derivative of -a**6/6 + 5*a**4/12 + 15*a. Factor c(u).
-5*u**2*(u - 1)*(u + 1)
Let s be (2/(4/(-5)))/(23 + -28). Factor -1/4 + 1/4*i + s*i**2.
(i + 1)*(2*i - 1)/4
Factor 6*t**2 + 4*t**3 - 16*t**3 + 3*t**5 + 3*t**3.
3*t**2*(t - 1)**2*(t + 2)
Solve 8/5*s - 12/5 + 4/5*s**2 = 0 for s.
-3, 1
Let p = -5 + 3. Let s(f) = -2*f - 2. Let q be s(p). Factor q*o - 3*o**4 - 2*o - o**3 + 4*o**4 - 2*o**2.
o**2*(o - 2)*(o + 1)
Let o(x) be the third derivative of -3*x**7/70 - x**6/20 + x**5/20 + 5*x**2. Let o(k) = 0. What is k?
-1, 0, 1/3
Find s, given that 0 + 8/3*s**3 + 4/9*s + 28/9*s**2 = 0.
-1, -1/6, 0
Let n(x) = x**2. Let z(a) = 2*a**2 + 5*a - 2. Let f be (-1 - 1) + -3 + 3. Let g(r) = f*z(r) + 10*n(r). Solve g(d) = 0 for d.
2/3, 1
Suppose 3*p + 4*a - 15 = 0, 3*p - 3*a - 15 = -a. Let h(g) be the third derivative of 0*g - 1/48*g**4 + 1/120*g**p + 0 + 2*g**2 + 0*g**3. Factor h(t).
t*(t - 1)/2
Let w(c) = -c**3 - 1. Let a(k) be the second derivative of k**6/15 + 3*k**5/10 + k**4/12 + 3*k**2/2 + 8*k. Let v(s) = a(s) + 3*w(s). Factor v(t).
t**2*(t + 1)*(2*t + 1)
Let c = 5 + -17. Let j be 0 + -1*8/c. Factor 0 + 2/3*q**3 - 2/3*q + 2/3*q**2 - j*q**4.
-2*q*(q - 1)**2*(q + 1)/3
Let c be (-2 + 0)/(9/72*-20). Factor 0 - 2/5*x**2 - c*x.
-2*x*(x + 2)/5
Let f = -2 - -4. Factor 2*t + 0*t - 21*t**f + 20*t**2.
-t*(t - 2)
Let z(x) be the first derivative of -x**3/21 + x/7 + 1. Suppose z(s) = 0. What is s?
-1, 1
Suppose 138 = 4*q + 130. Let d be 39/9 + (-2)/2. Factor -2/3*w**q + 4/3*w**3 - d*w - 4/3.
2*(w - 2)*(w + 1)*(2*w + 1)/3
Suppose -4 = -8*o + 28. Let i(v) be the third derivative of 3*v**2 + 0*v + 0 - 1/8*v**3 - 1/80*v**5 + 1/16*v**o. Suppose i(m) = 0. What is m?
1
Let s be 1 + (-4)/3 + 9/3. Find t such that 8/3 - s*t + 2/3*t**2 = 0.
2
Let m be ((-14)/(-42))/((-1)/(-1)). Find x such that 1/3 + m*x**2 - 2/3*x = 0.
1
Factor 0 + 0*o - 4/3*o**2 + 10/3*o**3 - 8/3*o**4 + 2/3*o**5.
2*o**2*(o - 2)*(o - 1)**2/3
Let n(w) be the second derivative of 2*w**7/63 - 4*w**6/45 - w**5/20 + 7*w**4/36 - w**3/9 - 7*w. What is k in n(k) = 0?
-1, 0, 1/2, 2
Let t(b) be the third derivative of -b**6/10 + 11*b**5/15 + 2*b**4/3 - 24*b**2. Factor t(n).
-4*n*(n - 4)*(3*n + 1)
Let f = -51 - -53. Factor 2/7*c + 0*c**f + 0*c**4 + 2/7*c**5 + 0 - 4/7*c**3.
2*c*(c - 1)**2*(c + 1)**2/7
Let s(d) = 3*d**2 - 2*d + 3. Let i(k) = k**2 - k. Let g(u) = -4*u. Let c be g(1). Let r(y) = c*i(y) + s(y). Factor r(b).
-(b - 3)*(b + 1)
Suppose -3*n + 7 = -8, -n + 29 = 4*o. Let l be (o/12)/((-2)/(-16)). Factor 2*i**2 + 0*i**2 - i**4 - i**l.
-2*i**2*(i - 1)*(i + 1)
Let d be (2 - -2)*2/8. Let a(v) = -4*v**2 - 5*v + 5. Let p(f) = f**2 + f - 1. Let i(l) = d*a(l) + 5*p(l). Suppose i(k) = 0. Calculate k.
0
Let x be (-2)/(-16)*-2*-4. Let r(b) be the first derivative of -1/4*b**4 + 1/6*b**3 - x + 1/10*b**5 + 0*b**2 + 0*b. Let r(v) = 0. What is v?
0, 1
Let z = 2/41 + 119/82. Factor -z*v**2 + 1/2*v**4 - 1 - 1/2*v**3 + 5/2*v.
(v - 1)**3*(v + 2)/2
Let f(i) be the third derivative of -1/180*i**5 - 2/9*i**3 + 1/18*i**4 + 0*i - 2*i**2 + 0. Factor f(g).
-(g - 2)**2/3
Let y be (8/(-10))/((-7)/35). Let 4*h + 6*h**2 - 6*h**4 + 9 - y*h**3 - 9 = 0. Calculate h.
-1, -2/3, 0, 1
Suppose 1 = 2*v - 11. Factor -4*s + v + 6*s - 2*s**2 + s - s**2.
-3*(s - 2)*(s + 1)
Let y(q) = 9*q**2 - 23*q - 7. Let k be y(3). Factor -2/15*a**k + 2/5*a**3 - 4/15*a**2 + 0*a**4 + 0*a + 0.
-2*a**2*(a - 1)**2*(a + 2)/15
Let 1/3*s + 1/3*s**4 - 1/3*s**2 - 1/3*s**3 + 0 = 0. What is s?
-1, 0, 1
Let u be (-26)/42 - (-6)/9. Let t(s) be the second derivative of u*s**7 + 0*s**2 + s - 1/5*s**6 - 1/6*s**4 + 3/10*s**5 + 0 + 0*s**3. Factor t(l).
2*l**2*(l - 1)**3
Let -1/4*s**3 - 3/4 - 7/4*s - 5/4*s**2 = 0. What is s?
-3, -1
Factor 0*m**2 + 8/3*m**3 + 4*m**4 + 0 + 4/3*m**5 + 0*m.
4*m**3*(m + 1)*(m + 2)/3
Let y = -479 + 1441/3. Solve y*w**2 - 2/3*w**5 + 0*w**3 + 0 + 2/3*w - 4/3*w**4 = 0 for w.
-1, 0, 1
Let c(q) = -2*q**3 - 8*q**2 + 4*q + 8. Let i(a) = 2*a**3 + 9*a**2 - 5*a - 9. Let z(o) = -3*c(o) - 2*i(o). Suppose z(j) = 0. What is j?
-3, -1, 1
Let s(o) be the third derivative of o**6/540 + o**5/90 + o**4/54 + 9*o**2. Factor s(x).
2*x*(x + 1)*(x + 2)/9
Let x be (24/6)/(4/2). Factor -3*a**3 - 2 + 3*a - 3*a**2 + 2*a**4 + a**4 + x.
3*a*(a - 1)**2*(a + 1)
Let p(x) be the first derivative of 1/18*x**3 - 1/12*x**2 + 1/24*x**4 + 2 + 0*x - 1/30*x**5. Factor p(r).
-r*(r - 1)**2*(r + 1)/6
Let g(y) = y**3 + 5*y**2 - 9*y - 18. Let b be g(-6). Factor 8/7*o**2 + 8/7*o + b + 2/7*o**3.
2*o*(o + 2)**2/7
Let y = 8 - 6. Let v be y/6*(-3)/(-3). Factor 1/3*a**5 + 0*a**3 + 2/3*a**2 + 0 - v*a - 2/3*a**4.
a*(a - 1)**3*(a + 1)/3
Let p(r) be the second derivative of r**8/1680 + r**7/210 + r**6/90 + r**4/3 + 6*r. Let q(x) be the third derivative of p(x). Factor q(k).
4*k*(k + 1)*(k + 2)
Factor 0*a + 3/2*a**2 - 1/4 + 3/4*a**4 - 2*a**3.
(a - 1)**3*(3*a + 1)/4
Let x be -1*(2 + 120/(-28) + 0). Factor 6/7*p**2 + x*p - 18/7*p**3 - 8/7.
-2*(p + 1)*(3*p - 2)**2/7
Let j(v) be the first derivative of 2*v**3/3 - 6*v**2 + 16*v - 3. Factor j(r).
2*(r - 4)*(r - 2)
Let u(t) = -10*t**4 - 30*t**3 - 14*t**2 + 6*t. Let g(x) = 2*x**4 + 6*x**3 + 3*x**2 - x. Let f = -11 + 14. Let d(y) = f*u(y) + 16*g(y). Solve d(z) = 0 for z.
-1, 0
Let a be 1*(4/1)/2. Determine m, given that 1/3 - 1/3*m**a + 0*m = 0.
-1, 1
Suppose 0 = -5*y + 8 + 2. Let k(u) be the second derivative of -2/3*u**3 + 1/6*u**4 - 2*u + u**y + 0. Determine z, given that k(z) = 0.
1
Let w(o) be the third derivative of 1/10*o**5 - 3/70*o**7 - 3/8*o**4 + 1/112*o**8 + 1/20*o**6 + 1/2*o**3 + 0 + 5*o**2 + 0*o. Factor w(x).
3*(x - 1)**4*(x + 1)
Let f(v) be the first derivative of v**4/8 - v**3/3 - v**2/4 + v + 6. Factor f(a).
(a - 2)*(a - 1)*(a + 1)/2
Let n(k) be the first derivative of -k**7/280 + 3*k**5/40 + k**4/4 + k**3/3 + 5. Let j(a) be the third derivative of n(a). Determine d so that j(d) = 0.
-1, 2
Let r(l) be the third derivative of l**5/300 - l**4/30 + l**3/10 + 6*l**2. Determine b, given that r(b) = 0.
1, 3
Suppose 11 = 3*j + 5*y - 8, -5*y = 2*j - 16. Solve -2/7 + 2/7*m**4 + 0*m**2 - 4/7*m**j + 4/7*m = 0 for m.
-1, 1
Let y = -711/8 - -89. Let j(a) be the first derivative of -2 - 1/10*a**5 + 1/24*a**6 - y*a**2 + 0*a + 0*a**4 + 1/6*a**3. Factor j(h).
h*(h - 1)**3*(h + 1)/4
Suppose -5*i + 20 = -i. Let u(n) = n**2 + n - 1. Let l be u(-3). What is k in l*k**i - 2*k**3 - 3*k**5 - 4*k**4 + 4*k**3 = 0?
0, 1
Let 39*h**2 + 179*h**5 - 18 + 11*h - 167*h**5 - 21*h**4 - 27*h**3 + 4*h = 0. What is h?
-1, 3/4, 1, 2
Let m(l) be the third derivative of 1/160*l**6 - 1/8*l**3 + 0*