t a = 3 - 4. Let q(f) = 2*f**5 - 2*f**4 - 18*f**3 - 8*f**2 + 14*f + 8. Let u(l) = a*q(l) + 2*o(l). Factor u(z).
-4*(z - 2)*(z - 1)*(z + 1)**3
Factor -7*l**4 - 4*l**3 + 16*l - 11*l**2 + 7*l**4 + 4*l**4 - 5*l**2.
4*l*(l - 2)*(l - 1)*(l + 2)
Let a(m) be the first derivative of -m**6/21 - 2*m**5/35 + m**4/7 + 4*m**3/21 - m**2/7 - 2*m/7 + 8. Find g such that a(g) = 0.
-1, 1
Let u be 3/4*-1*4. Let a = u - -6. Let 2/7*j + 0 + 6/7*j**4 - 10/7*j**a + 2/7*j**2 = 0. Calculate j.
-1/3, 0, 1
Let n(j) be the second derivative of 3*j**7/14 - 11*j**6/10 + 9*j**5/4 - 9*j**4/4 + j**3 - 28*j. Determine u so that n(u) = 0.
0, 2/3, 1
Find l such that -2*l**3 - 2/7*l - 10/7*l**2 - 6/7*l**4 + 0 = 0.
-1, -1/3, 0
Let s(q) be the third derivative of -2*q**5/315 + q**4/36 - q**3/21 + 10*q**2. Determine l so that s(l) = 0.
3/4, 1
Factor 2/5*n**2 + 2/5*n**3 + 0 - 2/5*n**4 - 2/5*n.
-2*n*(n - 1)**2*(n + 1)/5
Let n(v) be the first derivative of 0*v + 32/3*v**3 - 6 + 96/5*v**5 + 22*v**4 + 2*v**2 + 6*v**6. What is z in n(z) = 0?
-1, -1/3, 0
Let i = 5 - 6. Let f be (i + 2)*(2 + 2). Suppose 3*j + 3*j**5 - 12*j**2 + 0*j**3 + 2*j**3 + 8*j**3 - 12*j**f + 8*j**3 = 0. Calculate j.
0, 1
Let x(g) be the third derivative of g**5/330 - g**4/66 - g**3/11 + 23*g**2. Factor x(k).
2*(k - 3)*(k + 1)/11
Let t = 3 + 4. Let v(g) = -g**2 + 6*g + 9. Let w be v(t). Solve -l**4 + w*l - l**3 - l**4 - l**3 + 2*l**2 = 0 for l.
-1, 0, 1
Factor 6*t**3 - 2*t**2 - 3*t**5 - 3*t + 0*t**5 + 2*t**2.
-3*t*(t - 1)**2*(t + 1)**2
Let n(d) = 3*d**2 + 6*d + 3. Let x(p) = 30*p**2 + 60*p + 30. Let m(k) = -21*n(k) + 2*x(k). Factor m(q).
-3*(q + 1)**2
Let l(h) be the first derivative of -h**6/360 - h**5/15 - 2*h**4/3 + 10*h**3/3 - 8. Let v(i) be the third derivative of l(i). Find q such that v(q) = 0.
-4
Suppose -l = -10*l. Let m(k) be the third derivative of 1/120*k**6 + 0*k + 2*k**2 + 0 + 0*k**3 + l*k**4 + 0*k**5. Find f, given that m(f) = 0.
0
Let z(l) = -l**2 + 4. Let j be z(-2). Let s(r) be the second derivative of -2*r + j + 0*r**3 + 1/30*r**4 - 1/5*r**2. Find k such that s(k) = 0.
-1, 1
Let z(t) be the third derivative of t**5/80 - t**4/48 - 24*t**2. Factor z(o).
o*(3*o - 2)/4
Let n be 2/((-252)/(-125) - 2). Let x = n - 1123/9. Determine l so that 2/3*l + x - 8/9*l**2 = 0.
-1/4, 1
Suppose -j - z = 3*j - 7, -4*j + 12 = -4*z. Let t be 1/(j/(-16)*-2). What is l in 4*l**4 - 6*l**3 - 3*l**5 - l**2 + 9*l**3 - 3*l**t = 0?
-1, 0, 1/3, 1
Factor -2/9*z**2 + 8/9 + 0*z.
-2*(z - 2)*(z + 2)/9
Let w(m) be the third derivative of -1/160*m**6 + 0*m + 1/40*m**5 - 4*m**2 + 0 - 1/4*m**3 + 1/32*m**4. Factor w(z).
-3*(z - 2)*(z - 1)*(z + 1)/4
Let m(n) be the first derivative of n**3/15 + n**2/10 + 35. Find j, given that m(j) = 0.
-1, 0
Let b(i) = -i**5 - 11*i**4 + i**3 + i**2 - 5. Let p(x) = 6*x**4 + 3. Let u(y) = -3*b(y) - 5*p(y). Factor u(k).
3*k**2*(k - 1)*(k + 1)**2
Let i(z) = z**2 - 8*z - 6. Let p(t) = -2*t - 5. Let f be p(-4). Let c(g) = 2*g**2 - 9*g - 5. Let v(q) = f*c(q) - 2*i(q). Factor v(w).
(w - 3)*(4*w + 1)
Let o(h) = 7*h - 8. Let w(q) = 3*q - 4. Let n(i) = 2*o(i) - 5*w(i). Let p be n(2). Suppose -3*m**3 + p*m**5 + m**2 - 2*m**4 + m**2 + m**3 = 0. What is m?
-1, 0, 1
Let m be (-4)/(-12)*(5 - -1). Factor -m*l**4 + 384*l**2 + 42*l + 6*l**4 + 982*l - 27*l**3 + 91*l**3 + 1024.
4*(l + 4)**4
Suppose 0 = 3*d - 34 + 28. Factor -2/11*p**d - 8/11 + 8/11*p.
-2*(p - 2)**2/11
Factor 0 - 3/5*d - 4/5*d**2 - 1/5*d**3.
-d*(d + 1)*(d + 3)/5
Suppose 5 + 3 = 4*z. Suppose -22 = -5*d + 4*x, -2*d - x = 1 - z. Determine a, given that -d*a**3 + 2*a**5 + 4*a**4 - a**3 + 5*a**3 = 0.
-1, 0
Let h(q) = -30*q**2 - 55*q - 20. Let s(a) = -29*a**2 - 56*a - 20. Let t(r) = 4*h(r) - 5*s(r). Suppose t(p) = 0. What is p?
-2, -2/5
Let n(u) = -u**3 - u**2 - 2*u + 2. Let p be n(0). Let z(w) be the first derivative of -1/4*w**4 - 1/5*w**5 + 0*w + 0*w**p - 3 + 0*w**3. Factor z(i).
-i**3*(i + 1)
Let v be ((-3)/8*2)/(45/(-40)). Factor -8/3*y**3 - 4*y**2 - 8/3*y - 2/3 - v*y**4.
-2*(y + 1)**4/3
Let t(z) be the second derivative of z**4/36 - z**3/9 + 12*z. Factor t(x).
x*(x - 2)/3
Let i be 53/(-371) + ((-17)/(-21) - 0). Find o such that 2*o + 4/3*o**2 + 0 - i*o**3 = 0.
-1, 0, 3
Let j(i) be the first derivative of -i**7/252 - i**6/90 - i**5/120 + 8*i + 7. Let k(m) be the first derivative of j(m). Factor k(o).
-o**3*(o + 1)**2/6
Let p(z) = z + 4. Let h be p(-4). Let m be 1*(1 - 1) + h. Factor 1/4*u**3 + 1/2*u**4 + 1/4*u**5 + 0*u + m + 0*u**2.
u**3*(u + 1)**2/4
Let p(w) = 2*w - 1. Let z be p(3). Suppose -2 = 2*v + v + 4*l, z*v + 2*l = 6. Suppose 4*a - 1 - 1 - a**2 - a**v = 0. Calculate a.
1
Let c(b) = 2*b + 2 - 1 - 1. Let v be c(1). Factor -5*a + 8 + 4*a**2 - a - 4 - 2*a**v.
2*(a - 2)*(a - 1)
Let a(g) be the first derivative of g**2/2 - 5*g - 3. Let w be a(7). Determine i so that 4*i + 4 + w*i**3 - 4*i**3 + 2*i = 0.
-1, 2
Factor 2/7*p**2 + 0 - 4/7*p.
2*p*(p - 2)/7
Let n(f) = 22*f**3 - f**4 + f**4 - 17*f**2 + 4 - 3*f**4 - 9*f + 3*f**3. Let k(t) = t**4 - 13*t**3 + 9*t**2 + 5*t - 2. Let v(b) = 5*k(b) + 3*n(b). Factor v(x).
-2*(x - 1)**3*(2*x + 1)
Let v(r) = -15*r + 30. Let d(h) = -5*h**2 - 59 + 18*h + 4*h**2 + 13*h + 0*h**2. Let l(m) = -3*d(m) - 5*v(m). Determine o so that l(o) = 0.
3
Let k = -209 - -212. Let 24/5*f**2 + 4/5 - 18/5*f - 2*f**k = 0. Calculate f.
2/5, 1
Let c(w) be the second derivative of -w**7/42 + 3*w**5/80 - w**4/48 + 9*w. Factor c(o).
-o**2*(o + 1)*(2*o - 1)**2/4
Let g(z) be the first derivative of -2 + 0*z + 2/3*z**3 + 2*z**2. Suppose g(w) = 0. Calculate w.
-2, 0
Let i be (-1)/3 - (-14)/42. Let g(u) be the third derivative of -1/36*u**4 + 1/180*u**6 + 0*u**3 - 3*u**2 + 0*u + i + 0*u**5. Factor g(r).
2*r*(r - 1)*(r + 1)/3
Let c(x) = 4*x**3 + 3*x**2 - x + 5. Suppose -5*f = -7*f + 10. Let p(r) = -2*r**3 - r**2 + r - 3. Let t(g) = f*p(g) + 3*c(g). Solve t(z) = 0.
-1, 0
Let k(y) be the second derivative of y**7/252 + y**6/45 - y**5/60 - y**4/9 + y**3/36 + y**2/3 - 3*y. Determine c so that k(c) = 0.
-4, -1, 1
Let d(w) be the third derivative of -1/120*w**6 + 5*w**2 - 5/24*w**4 + 0*w + 0 + 1/3*w**3 + 1/15*w**5. Let d(x) = 0. Calculate x.
1, 2
Let b = -114 + 50. Let x = -446/7 - b. Factor 2/7*a**2 - x*a + 0.
2*a*(a - 1)/7
Suppose -a = -5*x + 19, -x - 2*x + 5*a + 7 = 0. Determine g so that -50/7*g**2 + 38/7*g**3 - 2*g**x + 32/7*g + 2/7*g**5 - 8/7 = 0.
1, 2
Suppose 15 + 33 = 24*t. Factor -2/7*o**4 + 0 - 2/7*o**t + 4/7*o**3 + 0*o.
-2*o**2*(o - 1)**2/7
Suppose 33 = 3*f + 8*f. Let u(w) be the third derivative of 0*w**4 + 0*w**f + 3*w**2 + 0 + 0*w - 1/210*w**5. Factor u(k).
-2*k**2/7
Let h(q) be the third derivative of -q**5/30 + 5*q**4/12 - 4*q**3/3 + 11*q**2. Factor h(t).
-2*(t - 4)*(t - 1)
Suppose 4 = y + y. Solve 0*r - 3*r**2 + 4*r**2 - y*r = 0.
0, 2
Let h(l) be the second derivative of -l**5/50 + l**4/30 - 5*l. Let h(x) = 0. What is x?
0, 1
Let q be -3 + (3 - 1/(-12)). Let w(z) be the first derivative of 2 - q*z**3 - 1/2*z - 3/8*z**2. Determine g, given that w(g) = 0.
-2, -1
Suppose -41*y = -44*y. Let 2/7 - 4/7*v + y*v**2 + 4/7*v**3 - 2/7*v**4 = 0. What is v?
-1, 1
Factor d**2 + 4*d**3 - 2*d**2 + 0*d**2 - 15*d**2.
4*d**2*(d - 4)
Let n(u) = -7*u**2 + 10*u. Let p(i) = 11*i**2 - 25*i + 4. Let x(g) = 10*g**2 - 26*g + 5. Let d(m) = 5*p(m) - 4*x(m). Let s(a) = -4*d(a) - 9*n(a). Factor s(t).
3*t*(t - 2)
Let m(s) = -3*s + 3 + 2*s - 3*s**2 - s**3 - 2*s + 0. Let j(h) = 2*h**3 + 4*h**2 + 4*h - 4. Let l(p) = -3*j(p) - 4*m(p). Find k such that l(k) = 0.
0
Let f = -7/18 + 53/90. Suppose -f*l**2 + 1/5 + 0*l = 0. What is l?
-1, 1
Let o(u) = u**3 + 7*u**2 + 4*u - 7. Let p be o(-6). Suppose 4*s - 3*j = -0 + 5, p*j - 7 = -s. Factor 0 + 2/5*v + 12/5*v**s + 18/5*v**3 + 8/5*v**4.
2*v*(v + 1)**2*(4*v + 1)/5
Suppose -1/3 - 5/6*k - 1/6*k**3 - 2/3*k**2 = 0. Calculate k.
-2, -1
Let p be (-6)/27 + (-141)/(-27). Solve p*n**3 + 8*n**5 + 11*n**3 - 4*n**5 + 16*n**4 = 0.
-2, 0
Let f = 56 - 166/3. Factor f*g**3 + 0 + 0*g + 4/3*g**4 + 0*g**2 + 2/3*g**5.
2*g**3*(g + 1)**2/3
Let u = -36 + 28. Let b(t) = 2*t + 16. Let h be b(u). Determine o, given that 3/2*o**2 + 3/2*o**3 + h*o - 3/2*o**5 - 3/2*o**4 + 0 = 0.
-1, 0, 1
Let h(f) = -2*f**4 + f**3 + 2*f**2 - 4. Let v(q) = 6*q**4 - 2*q**3 - 6*q**2 + 11. Let z(b) = 11*h(b) + 4*v(b). Let z(a) = 0. Calculate a.
-2, 0, 1/2
Let r(u) be the second derivative o