 the second derivative of p(i). Suppose r(b) = 0. What is b?
-2, 0, 1
Let z(x) be the second derivative of x**5/4 + 25*x**4/12 + 5*x**3/2 - 45*x**2/2 + 2*x. Factor z(a).
5*(a - 1)*(a + 3)**2
Let k be (-4)/(-14) + 10/(-35). Let y = 3 - k. Determine q so that q**3 - q - 3*q**3 + q**y + 2*q**2 = 0.
0, 1
Let o(t) = -t**2. Let c(r) = -5*r**2 + 5*r + 3. Let z(i) = -2*c(i) + 6*o(i). Factor z(s).
2*(s - 3)*(2*s + 1)
Factor -46*n**2 + 5*n**3 + 10*n**2 + 80*n - 4*n**2.
5*n*(n - 4)**2
Let r = 1741/3 + -575. Determine n so that 140/3*n**3 - 88/3*n**2 + 0 + r*n - 50/3*n**4 = 0.
0, 2/5, 2
What is c in -17*c**3 - 1/3 + c + 12*c**4 + 13/3*c**2 = 0?
-1/4, 1/3, 1
Suppose 4*c + 6 = c. Let l be (3/3)/((-1)/c). Solve l*q - 4/7 - 16/7*q**2 + 6/7*q**3 = 0 for q.
2/3, 1
Let t(g) = g**3 - 1. Let m(j) = 53*j**3 - 12*j**2 - 8*j + 3. Let k(d) = m(d) + 3*t(d). Solve k(s) = 0.
-2/7, 0, 1/2
Let -15*d**5 + 3*d**4 - 11*d**2 - 12*d - d**3 + 32*d**5 - 16*d**5 - 4 = 0. Calculate d.
-2, -1, 2
Let g = -88 + 90. Let x be (-5)/(-6)*(-2)/(-5). Factor -5/3*m - 4/3*m**g - x.
-(m + 1)*(4*m + 1)/3
What is o in 0 + 4*o**2 - 4/7*o**5 + 20/7*o**4 + 0*o + 52/7*o**3 = 0?
-1, 0, 7
Let z be (3 - 15/6)*(-84)/(-35). Solve -32/5*l**3 + 112/5*l**2 + z - 10*l = 0 for l.
1/4, 3
Let r = -2/85 - -89/170. Let n be (((-14)/6 + 3)*3)/1. Factor -r*i**n + 0 + 0*i + 1/4*i**3.
i**2*(i - 2)/4
Let r(p) be the second derivative of p**7/168 - p**6/24 + p**5/40 + 7*p**4/24 - p**3/8 - 9*p**2/8 + 36*p. What is b in r(b) = 0?
-1, 1, 3
Let k(t) be the first derivative of 0*t + 0*t**3 + 1 + 1/2*t**2 + 1/270*t**5 + 0*t**4. Let r(a) be the second derivative of k(a). Find q, given that r(q) = 0.
0
Suppose -4*o + 7 = -5. Factor 4*m**4 + 8*m**5 - 2*m**4 - 5*m**5 - 2*m**o - m**4.
m**3*(m + 1)*(3*m - 2)
Let l(s) = -2*s**3 + 6*s**2 + 6*s - 10. Let d(r) = r - 1. Let n(x) = -4*d(x) + l(x). Factor n(k).
-2*(k - 3)*(k - 1)*(k + 1)
Let h(c) be the first derivative of -c**3/2 + 39*c**2/2 - 507*c/2 + 6. Factor h(n).
-3*(n - 13)**2/2
Let o(f) = f**3 - f**2 + f. Let r(s) = -6*s**3 + 7*s**2 - 7*s. Suppose 5*u = 2*l - 22, 0*l - 12 = 3*l. Let c(a) = u*r(a) - 34*o(a). Factor c(j).
2*j*(j - 2)**2
Let u be -2 - 74/(-18) - (3 + -1). Let v(y) be the first derivative of 1 + 2/45*y**5 - u*y**2 + 2/9*y**3 - 1/6*y**4 + 0*y. Determine z so that v(z) = 0.
0, 1
Let d(l) be the third derivative of -l**8/840 + l**7/210 - l**6/180 - l**3 + 3*l**2. Let t(i) be the first derivative of d(i). Find h, given that t(h) = 0.
0, 1
Let r(a) be the third derivative of -a**7/4200 + a**6/300 - 3*a**5/200 - a**4/24 + 6*a**2. Let v(s) be the second derivative of r(s). Factor v(n).
-3*(n - 3)*(n - 1)/5
Let n(t) be the first derivative of -5 + 2*t**2 - 2*t - 2/3*t**3. Factor n(x).
-2*(x - 1)**2
Suppose -2*b - 2 = 3*c, 0 = b + c + 1. Let x be b/((-3 - -2)/5). Let 1 + v**4 + 3*v**3 - x*v**3 + 2*v - 2 = 0. Calculate v.
-1, 1
What is k in -9 - 6*k + 5*k**3 + k + 19 - 10*k**2 = 0?
-1, 1, 2
Suppose -2*v - 3*v + 70 = 0. Suppose 0 = 4*n - 5*d - 11, -d + v = 2*n + 5. Let -i**3 + n*i - 3*i - i + i**5 + i**4 - i**2 = 0. Calculate i.
-1, 0, 1
Solve 0*m - 1/7*m**4 + 1/7*m**2 + 0 - 3/7*m**3 + 3/7*m**5 = 0.
-1, 0, 1/3, 1
Let l = -77/3 - -26. Suppose 2*j + 6 = 4*b + 2, -j - 3*b = -3. Factor -1/3*w + j - l*w**2.
-w*(w + 1)/3
Let n(w) be the first derivative of -w**5/15 + w**4/6 + 4*w**3/9 - w**2/3 - w + 5. Suppose n(y) = 0. Calculate y.
-1, 1, 3
Let j(c) = c**2 + 11*c - 42. Let d be j(-14). Find p, given that 0*p**4 + d + 0*p + 1/3*p**5 - 1/3*p**3 + 0*p**2 = 0.
-1, 0, 1
Solve -4*d**5 + 2*d**5 - d + 4*d**3 - d = 0.
-1, 0, 1
Let w(r) be the second derivative of -27*r**5/40 - 9*r**4/8 - 3*r**3/4 - r**2/4 + 5*r. Solve w(y) = 0.
-1/3
Suppose -5*l + 2 = -18. Factor 0*n + 0*n**l + 0 + 2/7*n**5 - 2/7*n**3 + 0*n**2.
2*n**3*(n - 1)*(n + 1)/7
Let l(g) be the second derivative of -g**6/6 + 3*g**5/2 - 5*g**4 + 25*g**3/3 - 15*g**2/2 - 26*g. Factor l(u).
-5*(u - 3)*(u - 1)**3
Let o(p) be the first derivative of -p - p**3 - 3/2*p**2 - 3 - 1/4*p**4. Factor o(x).
-(x + 1)**3
Determine y so that -4*y**5 + 32*y**2 + y**5 - 9*y + 20*y**4 - y**5 - 4*y - 37*y**3 + 2 = 0.
1/2, 1, 2
Let y(h) be the second derivative of h**5/210 + 2*h**4/21 + 16*h**3/21 + 5*h**2/2 + 3*h. Let z(q) be the first derivative of y(q). Factor z(v).
2*(v + 4)**2/7
Let x = 12 + -6. Factor -3*a**5 - 3 + 9*a**4 - x*a**2 + 6*a - a - 6*a**3 + 4*a.
-3*(a - 1)**4*(a + 1)
Suppose -2*r = 3*r. What is y in 0 + r*y - 3/5*y**2 = 0?
0
Let h(t) be the third derivative of -t**6/300 + t**4/60 - 5*t**2. Determine c so that h(c) = 0.
-1, 0, 1
Suppose -5*c + 18 - 8 = 0, 0 = -v + 2*c + 7. Factor 10*z**2 + 2*z - v*z**2 - z.
-z*(z - 1)
Let q be 1/(-3)*(6 + -18). Factor 0 + 3/4*k - 3/4*k**5 + 0*k**3 - 3/2*k**2 + 3/2*k**q.
-3*k*(k - 1)**3*(k + 1)/4
Suppose -5*j + 0*j + 20 = 0. Find w such that 3*w**2 + 0*w**j + 0*w + 24*w**3 - 6*w + 6*w**4 + 9*w**4 = 0.
-1, 0, 2/5
Let c(u) = -u + 1. Let i be c(4). Let j = 0 - i. Factor j + 0 - w**2 + w - 3.
-w*(w - 1)
Let v = -2 + 4. Factor 6*p - 10*p**3 - 6*p**2 + 2*p**4 + v*p + 8 + 6*p**3.
2*(p - 2)**2*(p + 1)**2
Let x(b) be the first derivative of -b**4/30 + b**2/15 + 11. Factor x(g).
-2*g*(g - 1)*(g + 1)/15
Let d(o) = -o**3 - 4*o**2 - 4*o - 5. Let z be d(-3). Let x(m) = -2*m - 4. Let k be x(z). Factor 1/2*a**3 - 1/4*a**4 + 0 + k*a - 1/4*a**2.
-a**2*(a - 1)**2/4
Let z(o) be the first derivative of -2*o**3/15 + o**2/5 - 21. Factor z(m).
-2*m*(m - 1)/5
Let i = 1933/20 - 482/5. Find u such that 0 + i*u**2 - 1/2*u = 0.
0, 2
Let c = 17 - 14. Factor -2 + 2 - 10*x**4 + c*x**3 + x**3 - 14*x**5.
-2*x**3*(x + 1)*(7*x - 2)
Let l = -13/7 + 53/21. Find g, given that -4/3*g**2 - 1/3*g + l + g**3 = 0.
-2/3, 1
Suppose 2*f = -0*f + 4. Suppose 0 = 2*t + 5*b - 14, 14 = 5*t - 0*t + f*b. What is j in -1/2*j**t + 1/2*j - 1/2*j**3 + 1/2 = 0?
-1, 1
Let -5/6 + 1/6*y**2 + 2/3*y = 0. What is y?
-5, 1
Let q(w) = -w**2 + 6*w. Let j be q(6). Let c be (-4 - -6) + j/(-3). Factor 0*t + 1/4*t**3 + 0 - 1/4*t**c.
t**2*(t - 1)/4
Let q(l) = -3*l**2 + 3*l. Let u(m) = -4*m**2 + 2*m. Let y(w) = 13*w**2 - 6*w. Let i(x) = -14*u(x) - 4*y(x). Let r(f) = -4*i(f) - 6*q(f). Factor r(o).
2*o*(o - 1)
Let n(d) = 10*d**2 - 10*d + 4. Let u(g) be the second derivative of g**5/20 + 31*g**4/12 - 5*g**3 + 6*g**2 - 3*g. Let b(a) = 7*n(a) - 2*u(a). Factor b(c).
-2*(c - 2)*(c - 1)**2
Let v(d) be the third derivative of d**7/10 - 23*d**6/40 + 3*d**5/10 - 25*d**2. Factor v(j).
3*j**2*(j - 3)*(7*j - 2)
Let f(t) be the first derivative of -4/9*t + 14/27*t**3 - 4 - 5/9*t**2. Let f(h) = 0. Calculate h.
-2/7, 1
Let i(f) be the second derivative of 0 - 1/3*f**3 - 1/10*f**5 - 1/3*f**4 - 7*f + 0*f**2. Suppose i(y) = 0. What is y?
-1, 0
Let o(z) = -z**3 - z**2. Suppose -1 = u - 0. Let w(h) = -5*h**3 - 3*h**2 + 3*h + 1. Let q(j) = u*w(j) + 6*o(j). Factor q(t).
-(t + 1)**3
Let g(k) = k**3 - k**2 - 4*k + 3. Let s be g(3). Let f = s + -5. Factor 48*z + f + 3*z**4 - 18*z + 15*z**4 + 58*z**3 + 66*z**2.
2*(z + 1)**3*(9*z + 2)
Suppose 0 = a - 3 - 0. Factor a*h**3 + 5*h**2 + 3*h**4 - 7*h**4 - 3 - 3*h + 2.
-(h - 1)**2*(h + 1)*(4*h + 1)
Let n = 7 - 10. Let z be ((18/(-8))/3)/n. Factor z*a**4 - 1/4 - 1/2*a**3 + 0*a**2 + 1/2*a.
(a - 1)**3*(a + 1)/4
Suppose -2*d = d - 21. Let j = d - 7. Factor t**2 + 0*t**3 - t**4 + j - 1/2*t**5 + 1/2*t.
-t*(t - 1)*(t + 1)**3/2
Suppose -o + 13 = 4*u - 8, -2*u + 28 = 4*o. Let v(m) be the second derivative of -3/2*m**2 - 3/5*m**o - 2*m**3 + 3*m - 1/10*m**6 + 0 - 3/2*m**4. Factor v(r).
-3*(r + 1)**4
Suppose -4*u + 2*t = 0, -12*u + 5*t = -10*u + 16. Solve 0 + 2/11*f**u + 0*f = 0.
0
Let f(t) be the first derivative of 2*t**5/25 - 7*t**4/10 + 6*t**3/5 + 27*t**2/5 - 108*t/5 - 26. Let f(w) = 0. What is w?
-2, 3
Let t be (1/2)/(-1*1/(-4)). Factor -1/4*j**3 - 1/4*j**4 + 1/4*j + 1/4*j**t + 0.
-j*(j - 1)*(j + 1)**2/4
Suppose 14 = -b - n + 5*n, 0 = -4*b + 2*n. Let 0*u**b + 1/4*u**3 + 0*u + 1/4*u**4 + 0 = 0. What is u?
-1, 0
Let f(c) be the first derivative of 2*c**3/21 + 10*c**2/7 + 50*c/7 - 6. Factor f(r).
2*(r + 5)**2/7
Let b(s) = 2*s**3 - 6*s + 4. Let m(g) = g**3 - 3*g + 2. Let z(a) = -4*b(a) + 7*m(a). Suppose z(l) = 0. Calculate l.
-2, 1
Factor -7/8*y**4 + 1/8*y**5 - 1/2 + 2*y - 25/8*y**2 + 19/8*y**3.
(y - 2)**2*(y - 1)**3/8
Suppose -3*c = 2*c. Let u = c + 2. Let 0*q**u - 1/2*q