g + 2)
Let o(q) = q**2 + 3*q + 2. Let s(p) = -1 + 2*p**2 + 4 + 5*p + p + 1. Let d(u) = -5*o(u) + 3*s(u). Solve d(b) = 0 for b.
-2, -1
Factor 0 - 1/3*m**3 + m**2 - 2/3*m.
-m*(m - 2)*(m - 1)/3
Let c(b) be the first derivative of b**3/12 + b**2/8 - b/2 + 18. Factor c(q).
(q - 1)*(q + 2)/4
Solve -12*c**4 + c**4 + 8*c**4 + 3*c**3 = 0.
0, 1
Let q = 4 - 0. Suppose 5*i - 25 = -q*d, -i + 3*i - 4 = -d. Factor 0 + d*x**4 + 2*x**3 - 32/5*x**2 + 8/5*x.
2*x*(x + 1)*(5*x - 2)**2/5
Let k(t) be the third derivative of 0*t**4 + 0 - 2/105*t**7 - 1/20*t**6 + 0*t**3 - 1/30*t**5 - t**2 + 0*t. Factor k(o).
-2*o**2*(o + 1)*(2*o + 1)
Let a = -1 + 8. Factor 9*k - 2*k**2 + 0*k**2 - a*k.
-2*k*(k - 1)
Suppose 2*h - 3*d + 3 = -6, -4*d + 12 = -5*h. Factor -p**2 + h + 0 - p.
-p*(p + 1)
Let p(l) = 2*l. Let i be p(1). Let u(g) be the second derivative of g**3 - i*g**2 + 0 - 1/6*g**4 - 3*g. Find n, given that u(n) = 0.
1, 2
Let d = -8 + 13. Let p = 5/11 - 4/33. Let 0*a - 2/3*a**4 - 1/3*a**d + 0 - p*a**3 + 0*a**2 = 0. What is a?
-1, 0
Let n(k) = 7*k - k**3 - 5*k**2 + 7 - k + k**2. Let a be n(-5). Factor a*p**2 + p + p + 0*p.
2*p*(p + 1)
Factor -8*s - 6*s + 3*s**3 + 2*s**2 + s**2 - 3 + 11*s.
3*(s - 1)*(s + 1)**2
Let x(q) = -q**2 - 2*q + 3. Let n(k) be the third derivative of -1/60*k**5 + 2*k**2 - 1/8*k**4 + 2/3*k**3 + 0 + 0*k. Let b(z) = 3*n(z) - 4*x(z). Factor b(a).
a*(a - 1)
Let b(x) be the second derivative of 1/10*x**5 + 1/30*x**6 - 1/3*x**3 + 6*x + 0 - 1/12*x**4 + 0*x**2. Suppose b(t) = 0. What is t?
-2, -1, 0, 1
Find y such that 6*y**3 + 46*y**2 + 3 - 3*y**4 - 6*y - 46*y**2 = 0.
-1, 1
Suppose 3*n - i - 5 = 0, n + 5*i + 25 = -n. Let c(o) be the third derivative of 0 - 1/48*o**5 + n*o + 1/12*o**3 + 4*o**2 - 1/32*o**4. Factor c(f).
-(f + 1)*(5*f - 2)/4
Let j = 4 - 11. Let h(n) = 2*n**4 + 2*n**3 + 5*n**2 - 2*n - 7. Let r(c) = c**4 + c**3 + 2*c**2 - c - 3. Let t(a) = j*r(a) + 3*h(a). Factor t(x).
-x*(x - 1)*(x + 1)**2
Let q(h) be the first derivative of -1/14*h**4 + 0*h**3 + 3/7*h**2 - 4/7*h + 4. What is y in q(y) = 0?
-2, 1
Let u(t) = t**2 - t - 1. Let g be u(-2). Determine d so that d + 45*d**g - 7*d - d**3 - 15*d**2 + 87*d**4 + 34*d**3 = 0.
-1, -1/3, 0, 2/5
Let r be ((-55)/(-15) - 3) + 0. Let k(o) be the second derivative of -r*o**3 + 2*o**2 + o + 0 + 1/12*o**4. Factor k(c).
(c - 2)**2
Let g = -139/15 - -53/5. Factor -8/3*s - g*s**5 - 28/3*s**3 - 1/3 - 22/3*s**2 - 17/3*s**4.
-(s + 1)**4*(4*s + 1)/3
Let h = 1 - -2. Let d be 1/((-1)/4*-2). Suppose w - w + 2*w**d + 2*w**h = 0. What is w?
-1, 0
Let v(w) be the first derivative of w**3/3 + 2*w + 1. Let s be v(0). Solve -10*h**4 + h**s + 4*h**2 + 5*h**4 + 4*h**5 - h - 3*h**3 = 0 for h.
-1, 0, 1/4, 1
Let i(z) = 7*z**2 + z. Let m be i(-1). Let o = 76 - 72. Let -4*g**5 - g**5 + 2*g**5 - m*g**o + 2*g + g + 6*g**2 = 0. What is g?
-1, 0, 1
Let d(c) be the first derivative of 0*c + 0*c**2 + 0*c**3 - 3 + 1/16*c**4. Factor d(q).
q**3/4
Let o(b) = b**3 + 2*b**2 + 2*b - 2. Let a be o(-2). Let u be 16/4 + 21/a. Determine j, given that u*j**3 + 1/4 + 0*j - 3/4*j**2 = 0.
-1/2, 1
Let s(i) be the second derivative of -i**6/1440 + i**5/120 - i**4/32 + i**3/6 - 4*i. Let k(p) be the second derivative of s(p). Factor k(q).
-(q - 3)*(q - 1)/4
Let x = -61 - -91. Let u be ((-6)/20)/(x/(-40)). Factor -u*i**2 + 0*i - 2/5*i**3 + 2/5*i**5 + 0 + 2/5*i**4.
2*i**2*(i - 1)*(i + 1)**2/5
Let t = 3 - -3. Let j = t - 4. Factor -2*r + 0*r + 9*r**j - r**4 - 6*r**2.
-r*(r - 1)**2*(r + 2)
Let v(h) = -h**5 - 4*h**4 + 4*h**3 - 2*h**2. Let j(y) = y**4 + y**3 + y**2. Let w(x) = -18*j(x) - 2*v(x). Determine k so that w(k) = 0.
-1, 0, 7
Let m(d) be the third derivative of -d**7/595 - d**6/1020 + 4*d**5/255 - d**4/51 - 49*d**2. Let m(x) = 0. Calculate x.
-2, 0, 2/3, 1
Let z(d) = 2*d**3 + 5 + 2*d**3 - 15*d**4 - 5*d**3 + 4*d**2. Let n(j) = 7*j**4 + j**3 - 2*j**2 - 2. Let w(r) = 5*n(r) + 2*z(r). Factor w(v).
v**2*(v + 1)*(5*v - 2)
Suppose 3*t + 2*t = 4*q + 96, 2*q + 48 = 4*t. Let m be (-4)/(-12)*q/(-9). Factor -10/9*u - 2/9 - m*u**2.
-2*(u + 1)*(4*u + 1)/9
Let y(l) be the third derivative of -l**8/2240 + l**7/420 - l**6/240 - l**5/12 + l**2. Let a(s) be the third derivative of y(s). Let a(r) = 0. What is r?
1/3, 1
Let i(x) = 0*x**2 - x + 0*x**2 - 2*x**2 + 1 + 5*x**2. Let w be i(1). Factor 0*z + 0 + 1/5*z**w - 1/5*z**2.
z**2*(z - 1)/5
Let y(t) be the third derivative of -t**9/7560 + t**7/1260 + t**4/12 + 3*t**2. Let w(p) be the second derivative of y(p). What is a in w(a) = 0?
-1, 0, 1
Factor -2/7*c**2 + 2/7*c**3 + 0*c + 0.
2*c**2*(c - 1)/7
Suppose 2*f - 5*f = -15. Suppose 2*l = 8 - 0. Determine m, given that l*m - f + 14*m**2 + 0*m**2 + 5 = 0.
-2/7, 0
Determine m so that 5*m**3 - m**3 - 2*m**3 - 2*m**2 - 2*m**2 = 0.
0, 2
Let d(t) be the first derivative of t**6/6 + 4*t**5/5 + t**4/2 - 4*t**3/3 - 3*t**2/2 + 50. Factor d(x).
x*(x - 1)*(x + 1)**2*(x + 3)
Factor 28*b**2 + 16*b + 16/7.
4*(7*b + 2)**2/7
Factor 2/9 + 4/9*i - 2/9*i**4 - 4/9*i**3 + 0*i**2.
-2*(i - 1)*(i + 1)**3/9
Let p(l) = l**4 - l**3 + l**2 - 1. Let x(t) = t**5 + 8*t**4 - 9*t**3 + 2*t**2 + 4*t - 6. Let k(s) = -6*p(s) + x(s). Factor k(r).
r*(r - 1)**2*(r + 2)**2
Let s(z) be the second derivative of z**3/6 + 2*z**2 - z. Let v be s(0). Factor -g**4 + 0*g**3 - v*g**3 + 4*g**3 - 2*g**3 - g**2.
-g**2*(g + 1)**2
Let n(i) = -2*i**5 - 4*i**4 + 10*i**3 + 12*i + 12. Let r(f) = f**3 + f + 1. Let z(q) = -n(q) + 12*r(q). Factor z(w).
2*w**3*(w + 1)**2
Let j(c) be the second derivative of c**7/3360 + c**6/480 + c**5/240 - c**3/6 - 3*c. Let z(p) be the second derivative of j(p). Let z(g) = 0. What is g?
-2, -1, 0
Let a(d) be the first derivative of d**4/10 - d**2/5 - 11. Find h, given that a(h) = 0.
-1, 0, 1
Let m(b) be the first derivative of -b**4/14 - 2*b**3/21 - 2. Factor m(y).
-2*y**2*(y + 1)/7
Let n = 9633/4 + -2390. Let h = -18 + n. Find u, given that -h*u**2 + 0*u + 0 = 0.
0
Let s(x) = 2*x - 7. Let v be s(5). Suppose 3*d**2 + 0*d**2 - 2*d**3 - d**3 + v*d + 0 - 3 = 0. Calculate d.
-1, 1
Let o(r) = r. Let a be o(2). Factor 0*g**2 + 6*g + 0*g**2 - 6*g**a + 3 - 3*g**2.
-3*(g - 1)*(3*g + 1)
Let g(m) = 19*m**2 + 12*m + 6. Let j(k) = -3*k**2 - 2*k - 1. Let v(h) = 6*g(h) + 39*j(h). What is s in v(s) = 0?
-1
Let l = 3 + -7. Let h be (8/24)/((-6)/l). Let -2/9*q - h*q**2 + 0 = 0. What is q?
-1, 0
Let i(u) = 3*u - 33. Let m be i(11). Find o such that -2/7*o**4 - 2/7*o**2 + 4/7*o**3 + m + 0*o = 0.
0, 1
Let z(i) be the third derivative of 0 - 3/20*i**5 - 2/3*i**3 - i**2 + 1/2*i**4 + 0*i. Factor z(f).
-(3*f - 2)**2
Let x(i) be the second derivative of -2*i**5/5 + i**4/3 + 10*i**3/3 + 4*i**2 + 7*i. Factor x(n).
-4*(n - 2)*(n + 1)*(2*n + 1)
Let l(u) be the second derivative of u**7/189 - u**6/45 + u**5/45 + u**4/27 - u**3/9 + u**2/9 - u. Find a, given that l(a) = 0.
-1, 1
Let t(h) = -5*h**4 + h**3 + 4*h**2 + 6*h - 6. Let z(s) = -55*s**4 + 10*s**3 + 45*s**2 + 65*s - 65. Let c(i) = -65*t(i) + 6*z(i). Factor c(x).
-5*x**2*(x - 1)*(x + 2)
Factor -f**2 + f**3 - 1/2*f - 1/2*f**5 + 1/2 + 1/2*f**4.
-(f - 1)**3*(f + 1)**2/2
Let i(h) be the third derivative of -35*h**6/24 + 13*h**5/3 - 95*h**4/24 + 5*h**3/3 + 9*h**2. Let i(d) = 0. Calculate d.
1/5, 2/7, 1
Let d = -33 + 36. Suppose 1/4*y + 1/2 + 19/4*y**d - 7/4*y**4 - 15/4*y**2 = 0. What is y?
-2/7, 1
Let j(f) = -250*f**4 + 464*f**3 - 226*f**2 + 54*f - 14. Let i(o) = -50*o**4 + 93*o**3 - 45*o**2 + 11*o - 3. Let a(m) = 28*i(m) - 6*j(m). Factor a(r).
4*r*(r - 1)*(5*r - 2)**2
Let b(c) be the second derivative of c**8/6720 - c**7/840 + c**6/360 - c**4/3 + 2*c. Let n(f) be the third derivative of b(f). Factor n(w).
w*(w - 2)*(w - 1)
Factor -3*k**2 + 11*k - 2*k - 4 - 2.
-3*(k - 2)*(k - 1)
Suppose -t - 5 = 3*r - 2, -t + 2*r + 2 = 0. Let w(f) be the second derivative of t + 2/3*f**3 + 1/12*f**4 - 3*f + 2*f**2. Find q, given that w(q) = 0.
-2
Factor 16/7*n**3 - 4*n**2 - 12/7 - 8*n.
4*(n - 3)*(n + 1)*(4*n + 1)/7
Let v(s) be the first derivative of 1 + 1/3*s**3 + 0*s - 1/2*s**2. Let o(k) = -10*k**2 + 12*k - 2. Let m(z) = o(z) + 12*v(z). Determine c, given that m(c) = 0.
-1, 1
Factor 18 - 2/3*d**3 - 18*d + 6*d**2.
-2*(d - 3)**3/3
Let z = 41 + -39. Let n(u) be the second derivative of -1/20*u**5 + 1/10*u**6 + 1/6*u**3 + 0 + u**z - 3*u - 5/12*u**4. Let n(h) = 0. Calculate h.
-1, -2/3, 1
Let u(l) = -2*l**3 + 8*l**2