(v) = v**2 + 1. Let z be p(1). Solve 5*q - 10*q**z - q**3 + 11*q + 4*q**3 - q**3 - 8 = 0 for q.
1, 2
Let f(i) be the third derivative of -1/18*i**4 + 0*i + 2/27*i**3 - 7/540*i**5 - 3*i**2 + 0. Factor f(t).
-(t + 2)*(7*t - 2)/9
Let r(n) = 3*n**3 - 33*n**2 - 105*n - 75. Let x(z) = 4*z**3 - 33*z**2 - 105*z - 75. Let p(s) = -7*r(s) + 6*x(s). What is j in p(j) = 0?
-5, -1
Let w(g) be the third derivative of 0*g + 1/630*g**7 - g**2 + 0*g**3 + 0 - 1/180*g**5 + 1/36*g**4 - 1/180*g**6. Find o, given that w(o) = 0.
-1, 0, 1, 2
Let g(w) be the second derivative of -w**7/98 + w**6/35 + 9*w**5/140 - 2*w**4/7 + 2*w**3/7 - 3*w. Find b such that g(b) = 0.
-2, 0, 1, 2
Suppose -2*a - 4*d + 12 = 0, d = -4*a + 5*d. Let c(h) be the first derivative of 0*h**a + 8/3*h - 1/6*h**4 - 4 - 2/3*h**3. Solve c(u) = 0 for u.
-2, 1
Let h(g) be the second derivative of -g**9/15120 - g**8/2240 - g**7/1260 + 5*g**4/12 + 4*g. Let w(i) be the third derivative of h(i). Factor w(x).
-x**2*(x + 1)*(x + 2)
Let m(t) = -6*t**2 - 18*t - 17. Let q(a) = 9*a**2 + 27*a + 26. Let g(w) = -8*m(w) - 5*q(w). Factor g(f).
3*(f + 1)*(f + 2)
Let p be 3 + (-3)/(-2) + (-12)/3. Let i(o) be the first derivative of p*o - 9/16*o**4 + o**3 - 1 + 11/8*o**2. Determine n so that i(n) = 0.
-1/3, 2
Let h(c) = 5*c**3 + 5*c**2 - 14*c - 10. Let v(q) = 66*q**3 + 66*q**2 - 183*q - 129. Let f(d) = 27*h(d) - 2*v(d). Factor f(y).
3*(y - 2)*(y + 1)*(y + 2)
Let b(d) be the second derivative of d**7/42 + d**6/30 - d**5/10 - d**4/6 + d**3/6 + d**2/2 + 9*d. Determine f, given that b(f) = 0.
-1, 1
Let t(x) be the third derivative of x**7/350 + x**6/50 - x**5/50 - 3*x**4/10 + 9*x**3/10 + 15*x**2 - 1. Factor t(c).
3*(c - 1)**2*(c + 3)**2/5
Let t(q) = 28*q - 12. Let l be t(5). Let y = 642/5 - l. Factor -4/5*i**2 + 2/5*i + 2/5*i**5 - 4/5*i**3 + 2/5*i**4 + y.
2*(i - 1)**2*(i + 1)**3/5
Let x be (-2)/6*(-126)/(-6). Let d be ((-24)/(-42))/((-2)/x). What is v in 3*v**2 + d*v**3 + 5*v + v - 5*v**3 = 0?
-1, 0, 2
Let v = -127/4 - -133/4. Factor 0*y**2 + 3/2*y**4 + 0 + 0*y + v*y**3.
3*y**3*(y + 1)/2
Let l(d) = d. Let b be l(-5). Let z(f) = 10*f**2 - 13*f - 4. Let a(r) = -5*r**2 + 9*r - r**2 - r**2 + 3. Let y(x) = b*z(x) - 7*a(x). Solve y(n) = 0 for n.
1
Let j(v) = -v**2 + 5*v + 3. Let c be j(4). Let 5*n**4 + 0*n**5 - 2*n**2 - c*n**5 + n**5 + 3*n**3 = 0. What is n?
-2/3, 0, 1/2, 1
Determine f, given that 2/5*f**3 + 2/5*f**2 - 8/5*f - 8/5 = 0.
-2, -1, 2
Let t(s) = 39*s**3 + 45*s**2 + 9*s. Let x(c) be the second derivative of c**5/2 + 11*c**4/12 + c**3/3 - 9*c. Let f(w) = 4*t(w) - 15*x(w). Solve f(d) = 0.
-2, -1/2, 0
Suppose 0*d + 1/3*d**3 - 2/3*d**2 + 0 + 1/3*d**4 = 0. What is d?
-2, 0, 1
Let b(y) be the second derivative of y**9/1008 - y**8/560 - y**7/280 + y**6/120 + 2*y**3/3 - 3*y. Let m(u) be the second derivative of b(u). Factor m(n).
3*n**2*(n - 1)**2*(n + 1)
Let r(y) = 2*y**2 + 2*y - 1. Let n be r(1). Suppose -n*a = a - 12. Let -l**2 - 5 - l**a + 5 = 0. Calculate l.
-1, 0
Let y(b) = b**3 + b**2. Let d be (2 - 1) + 1 + 0. Let a(w) be the second derivative of w**5/10 + w**4/4 + 5*w. Let i(k) = d*a(k) - 5*y(k). Factor i(x).
-x**2*(x - 1)
Let s(o) = -5*o - o**2 - 7 - 4*o - 2*o + o. Let c be s(-9). Factor c*t - t + 0*t**3 - t**3.
-t*(t - 1)*(t + 1)
Let r = 93 - 91. Let 1/2*q**4 + 0 + 0*q**3 + 0*q - 1/2*q**r = 0. What is q?
-1, 0, 1
Suppose 0 = -130*i + 112*i. Find b, given that i*b + 1/4*b**2 + 0 - 3/4*b**3 - b**4 = 0.
-1, 0, 1/4
Find u such that 4/9 + 10/9*u + 8/9*u**2 + 2/9*u**3 = 0.
-2, -1
Let l(x) = -6*x**5 + 4*x**4 + 6*x**3 + x**2 - 5. Let w(h) = -h**5 - h**4 + 2*h**4 + h**3 + 0*h**4 - 1. Let k(m) = -l(m) + 5*w(m). Factor k(j).
j**2*(j - 1)*(j + 1)**2
Let y be ((-8)/(-3))/((-35)/(-21)). Let -y*k**2 + 0*k - 42/5*k**5 + 32/5*k**3 - 2/5*k**4 + 0 = 0. What is k?
-1, 0, 2/7, 2/3
Let l = 1178 - 5886/5. Solve -6/5*j**4 + 0 + l*j**3 - 4/5*j + 6/5*j**2 = 0 for j.
-1, 0, 2/3, 1
Suppose -2*y + 1 = -1, -2*c = -5*y + 1. Determine d, given that -2/9*d**c + 2/9*d + 2/9 - 2/9*d**3 = 0.
-1, 1
Factor 1/3*p**4 + 0 + 2/3*p**3 - 2/3*p - 1/3*p**2.
p*(p - 1)*(p + 1)*(p + 2)/3
Let l = -725 - -725. Factor 4/5*v**2 + 4/5*v**3 + 1/5*v**4 + l + 0*v.
v**2*(v + 2)**2/5
Let k(y) be the third derivative of 1/300*y**5 + 2*y**2 + 0*y**4 - 1/1050*y**7 + 0*y**3 + 0*y + 1/600*y**6 - 1/1680*y**8 + 0. Let k(i) = 0. Calculate i.
-1, 0, 1
Let c(m) be the first derivative of 1/12*m**3 + 0*m**2 + 0*m + 2. Factor c(p).
p**2/4
Let q(y) = -y**3 - 4*y**2 + 2. Let v be q(-4). Let u be v - (-2 + 2 - -1). Factor -2*a**3 + u - 2 - 2*a**4 + 1.
-2*a**3*(a + 1)
Let u(h) = -50*h**2 + 24*h + 26. Let r(q) = 17*q**2 - 8*q - 9. Let p(k) = -14*r(k) - 5*u(k). Suppose p(m) = 0. Calculate m.
-1/3, 1
Let q be ((-5)/(-3))/((-2)/(-6)). Suppose j + 2*j = 0. Determine v so that 0*v**2 + 2/3*v**3 + 4/3*v**4 + j*v + 0 + 2/3*v**q = 0.
-1, 0
Let o(r) be the second derivative of 0 - 1/3*r**3 + 1/21*r**7 + 0*r**5 + 0*r**2 - 7*r + 1/3*r**4 - 2/15*r**6. Find s such that o(s) = 0.
-1, 0, 1
Let n(s) = 7*s**2 + s - 2. Let q(l) = -8*l**2 + 3. Suppose 0 = 2*a + 4*f - 10, 0 = 4*a - 0*a + 5*f - 20. Let r(j) = a*n(j) + 4*q(j). Factor r(i).
(i + 1)*(3*i + 2)
Let f(s) be the second derivative of 0*s**6 + 0 + 1/63*s**7 + 0*s**3 + 3*s - 1/9*s**4 + 0*s**2 - 1/10*s**5. Determine z so that f(z) = 0.
-1, 0, 2
Let v(d) = -53*d + 214. Let y be v(4). Determine z, given that -y + 3/2*z**2 - 2*z**3 + 1/2*z**4 + 2*z = 0.
-1, 1, 2
Find j, given that -6*j - 24 - 3*j**3 + 0*j**3 + 24*j + 9*j**2 = 0.
-2, 1, 4
Let j(g) be the first derivative of -3*g**5 + 5*g**4 - 5*g**3/3 - 12. Factor j(x).
-5*x**2*(x - 1)*(3*x - 1)
Factor -4/3*q - 2/3*q**2 + 2.
-2*(q - 1)*(q + 3)/3
Factor 7*j - j**2 + 3*j**2 - 20*j + 7*j.
2*j*(j - 3)
Let d(v) be the second derivative of -2*v + 4*v**2 + 27/2*v**4 + 12*v**3 + 0. Let d(s) = 0. What is s?
-2/9
Suppose -g - 7 = -12. Let z(h) be the second derivative of -2/3*h**3 + 0 + 1/2*h**4 + 0*h**2 + h - 1/10*h**g. Suppose z(y) = 0. What is y?
0, 1, 2
Let b(y) be the third derivative of y**5/50 + y**4/10 + y**3/5 + 20*y**2. Factor b(l).
6*(l + 1)**2/5
Let h = 36 - 33. Let p(b) be the second derivative of -1/60*b**4 - 1/100*b**5 + 0 - 3*b + 1/30*b**h + 1/150*b**6 + 0*b**2. Factor p(u).
u*(u - 1)**2*(u + 1)/5
Let b be ((-16)/(-8))/((-1)/(-2)). Suppose -b*w = w. Factor -1/4*h**2 + 1/2*h**3 - 1/4*h**4 + 0*h + w.
-h**2*(h - 1)**2/4
Let w(i) = -1 + 0*i - 2*i + 4*i**2 - 6*i**2 - i. Let q(z) = z**2 + 2*z + 1. Let c(h) = -3*q(h) - 2*w(h). Determine j, given that c(j) = 0.
-1, 1
Let r(i) be the third derivative of -i**7/1260 - i**6/180 - i**5/60 + i**4/24 + 4*i**2. Let w(x) be the second derivative of r(x). Factor w(j).
-2*(j + 1)**2
Let j = -1039/6 - -171. Let u = 8/3 + j. Factor -1/2*a**4 + 0*a - u + 0*a**3 + a**2.
-(a - 1)**2*(a + 1)**2/2
Suppose -19*z + 21*z = 6. Let a(p) be the second derivative of 1/15*p**6 + 1/10*p**5 + 0 + z*p - 1/6*p**4 + 0*p**2 - 1/21*p**7 + 0*p**3. Factor a(v).
-2*v**2*(v - 1)**2*(v + 1)
Let f(k) be the first derivative of 2*k**4/9 - 28*k**3/27 + 14*k**2/9 - 8*k/9 + 1. Factor f(u).
4*(u - 2)*(u - 1)*(2*u - 1)/9
Suppose 2/11*r**3 - 14/11*r - 4/11*r**2 - 8/11 = 0. What is r?
-1, 4
Let t be (-5292)/66 + 4/22. Let w be (-232)/t - 4/10. Let 1/2 + w*b**4 - 1/2*b**5 - 5*b**3 - 5/2*b + 5*b**2 = 0. What is b?
1
Let h be 2/6*2 - (-168)/(-441). Factor -1/7*m**4 - 1/7 + 0*m**3 + 0*m + h*m**2.
-(m - 1)**2*(m + 1)**2/7
Let l(a) be the second derivative of a**4/30 - a**3/15 - 24*a. Suppose l(f) = 0. What is f?
0, 1
Let i(j) be the second derivative of 0 + 3*j + 1/15*j**6 + 7/12*j**3 + 13/40*j**5 + 1/4*j**2 + 5/8*j**4. Find q, given that i(q) = 0.
-1, -1/4
Determine c so that 6*c**3 + 4*c**2 - 11*c + 1 + 2*c**3 - 5 + 3*c = 0.
-1, -1/2, 1
Factor 4/5 + 1/5*p**2 + 4/5*p.
(p + 2)**2/5
Factor -4*u + 0 - 4/3*u**4 - 4/3*u**3 + 20/3*u**2.
-4*u*(u - 1)**2*(u + 3)/3
Factor -1/4 + 3/2*j - 3/2*j**3 - 2*j**2 + 9/4*j**4.
(j - 1)*(j + 1)*(3*j - 1)**2/4
Suppose 10*q = 3*q + 14. Let g(t) be the first derivative of 1/3*t - 2 + 1/3*t**q + 1/9*t**3. Suppose g(n) = 0. What is n?
-1
Suppose -4*o - 9 = -5*r, -5*r + 5 + 0 = -5*o. Suppose -r*v = -0*v - 10. Solve -v*a + a**2 + a + 0*a = 0.
0, 1
Let c(h) be the first derivative of -4*h**3/27 + 4*h/9 + 11. Factor c(s).
-4*(s - 1)*(s + 1)/9
Let d(c) be the third derivative of c**6/20 - 4