3*t**3 + j*t**2 + 20*t**4 - 3*t**2.
t**2*(4*t - 1)*(5*t + 2)
Let l(f) be the second derivative of -f**7/12600 + f**6/1200 - f**5/300 - f**4/6 - 2*f. Let w(d) be the third derivative of l(d). Let w(s) = 0. Calculate s.
1, 2
Solve -50/3 - 20/3*d - 2/3*d**2 = 0 for d.
-5
Suppose -2 = u - 5. Determine q, given that 0*q + 2*q - 3 - 9*q**2 + 7*q + u*q**3 = 0.
1
Suppose -3*j - k + 0*k = -16, -20 = -2*j + 4*k. Determine q, given that 8 + 3*q**4 - j*q**2 - 5 + 0 = 0.
-1, 1
Find g, given that 0*g + 2/3*g**3 + 0 - 4/3*g**2 = 0.
0, 2
Let x = 6 - 6. Determine m so that -3*m + 3*m**2 - 6*m**2 + x*m + 0*m**2 = 0.
-1, 0
Let a be 0*(1 + 1/(-2)). Suppose a = -3*t - 12, -3*o = t + 4*t + 14. Factor 3/2*q**4 + q**3 - 2*q**o + 1/2 - q.
(q - 1)*(q + 1)**2*(3*q - 1)/2
Suppose 2*w - 13 = -3. Factor -23 - v**w + v**3 + 23.
-v**3*(v - 1)*(v + 1)
Factor -27/2 - 12*o + 3/2*o**2.
3*(o - 9)*(o + 1)/2
Let o(n) = -4*n**4 + 5*n**3 + 4*n**2. Suppose 6 = 2*x + 20. Let q(i) = -6*i**4 + 7*i**3 + 6*i**2. Let l(c) = x*o(c) + 5*q(c). Factor l(p).
-2*p**2*(p - 1)*(p + 1)
Let b(g) = g**5 - g**3 + g**2 - g. Let p(j) = -22*j**5 + 111*j**4 - 197*j**3 + 131*j**2 - 23*j. Let u(h) = -b(h) - p(h). What is i in u(i) = 0?
0, 2/7, 1, 2
Let q(z) be the second derivative of -z**4/48 + 11*z**3/12 - 121*z**2/8 + 28*z - 1. Factor q(i).
-(i - 11)**2/4
What is g in -84/5*g**2 - 1176/5*g - 2/5*g**3 - 5488/5 = 0?
-14
Let q be 21/(-70) + 92/40. Factor 0 - p**q + 1/2*p**5 + p**4 + 0*p**3 - 1/2*p.
p*(p - 1)*(p + 1)**3/2
Let d(u) be the first derivative of u**7/84 + u**6/45 - u**5/60 - u**4/18 - u**3/36 + 2*u - 4. Let t(z) be the first derivative of d(z). Solve t(v) = 0 for v.
-1, -1/3, 0, 1
Let z(w) = w**5 - w**2 - 1. Let p(o) = 6*o**5 + 10*o**4 + 12*o**3 + 3*o**2 + o - 3. Let r(x) = -p(x) + 3*z(x). Find f such that r(f) = 0.
-1, -1/3, 0
Let k = 6 - 3. Suppose -k*a - 2*z + 3*z + 2 = 0, -10 = -5*a + 5*z. Factor 0 + a + y**4 - 2*y**3 + 2*y - 5*y**4 + 4*y**2.
-2*y*(y - 1)*(y + 1)*(2*y + 1)
Let v(a) be the second derivative of 3*a**5/50 - 7*a**4/5 + 49*a**3/5 - 7*a. Suppose v(t) = 0. Calculate t.
0, 7
Suppose 0 = q + 2*r - 4, q - 2*q + 3*r - 1 = 0. Suppose -q = -t - 0. Factor x**t - 2*x**3 + 5*x**3 - 2*x**3 - x**4 - x.
-x*(x - 1)**2*(x + 1)
Let q(y) be the third derivative of y**8/1008 - y**6/180 + y**4/72 - 35*y**2. Suppose q(l) = 0. What is l?
-1, 0, 1
Suppose 5*t - 4 = -2*d + 3*t, -3*d + 2*t = -11. Factor -d*z**2 + 4*z**3 - 3/2*z**4 + 0*z + 1/2.
-(z - 1)**3*(3*z + 1)/2
Find r such that 2/9*r - 1/9*r**3 - 1/3*r**2 + 0 + 1/3*r**4 - 1/9*r**5 = 0.
-1, 0, 1, 2
Let w(o) = -4*o**4 + 4*o**3 - 6*o**2 - 4*o - 2. Let v(d) = -3*d**4 + 4*d**3 - 5*d**2 - 4*d - 2. Let q(i) = 6*v(i) - 5*w(i). Factor q(h).
2*(h - 1)*(h + 1)**3
Let o be 4 - 13/35 - (-3)/(-15). Factor 4/7 - 10/7*t**3 + o*t**2 - 18/7*t.
-2*(t - 1)**2*(5*t - 2)/7
Let z(o) = o**3 - o - 2. Let l(n) = -3*n**3 + 2*n + 6. Let w(a) = -4*l(a) - 14*z(a). Determine m, given that w(m) = 0.
-1, 2
Let b = -4 + 7. Factor -4*k - 3*k**2 - k + 4 + 4*k - k**4 - 4*k**b + 5*k.
-(k - 1)*(k + 1)*(k + 2)**2
Let v(d) = -4*d**2 + 4*d**2 + 3*d**3 - d**2 - 2*d**3. Let k(b) = -6*b**3 + 6*b**2 + b - 1. Let r(l) = -k(l) - 5*v(l). Factor r(n).
(n - 1)**2*(n + 1)
Suppose 0 = 5*u + 2*g - 8, 0 = -2*u - 9*g + 4*g + 20. Let r be (1 + u)/6*8. Factor 2/3*b**3 + 2/3*b + 0 + r*b**2.
2*b*(b + 1)**2/3
Let s(d) = 4*d**4 + 4*d + 2. Let b(c) = -17*c**4 - c**3 - c**2 - 17*c - 9. Let j(z) = 4*b(z) + 18*s(z). Factor j(n).
4*n*(n - 1)**2*(n + 1)
Factor 0*c - 4*c**2 - 5*c + 4*c + 5*c.
-4*c*(c - 1)
Let w(d) be the third derivative of 3*d**2 + 0 - 1/735*d**7 + 0*d - 1/84*d**4 + 0*d**3 + 1/210*d**5 + 1/420*d**6. Factor w(f).
-2*f*(f - 1)**2*(f + 1)/7
What is w in -42*w**2 - 7*w**5 + 25*w**2 - 15*w + 57*w**2 + 2 + 30*w**4 - 50*w**3 = 0?
2/7, 1
Let l(o) be the first derivative of -o**4/14 + 10*o**3/21 - 3*o**2/7 - 18*o/7 + 7. Factor l(c).
-2*(c - 3)**2*(c + 1)/7
Let r = 8 - 5. Let n be (-1 - 1 - -1) + r. Factor w**n + 3*w**2 - 3*w**2.
w**2
Let d(g) be the second derivative of -g**7/1260 + g**6/360 + g**4/12 - 3*g. Let n(x) be the third derivative of d(x). Factor n(w).
-2*w*(w - 1)
Let c(g) be the first derivative of -g**3/5 - 6*g**2/5 - 9*g/5 - 1. Factor c(x).
-3*(x + 1)*(x + 3)/5
What is k in -55*k - 66 - 10 + 0*k**2 + 5*k**2 + 16 = 0?
-1, 12
Let f(t) = 2*t**2 - 2*t - 2. Let b be f(2). Let n = 2 - b. Suppose 1 - 5 + 6*k - 2*k**2 + n = 0. What is k?
1, 2
Factor 0 - 1/9*l**2 - 1/3*l.
-l*(l + 3)/9
Let y(h) be the first derivative of 3 + 0*h**3 + h + h**4 - 3/2*h**2. Factor y(j).
(j + 1)*(2*j - 1)**2
Let m(l) be the first derivative of -l**4/8 + l**3/2 - l**2/2 + 4. Factor m(d).
-d*(d - 2)*(d - 1)/2
Let k(y) be the first derivative of 3*y**4/16 + 3*y**3/2 + 9*y**2/2 + 6*y - 18. Let k(q) = 0. What is q?
-2
Let i be (4/10)/1 - (-12)/20. Let b(q) be the first derivative of -2/7*q - i + 0*q**2 + 2/21*q**3. Factor b(m).
2*(m - 1)*(m + 1)/7
Let l(q) be the first derivative of -3 - 3/5*q + 1/5*q**2 + 1/15*q**3. Suppose l(d) = 0. What is d?
-3, 1
Suppose 0 = -4*w + 2*w - 4. Let j be w/(-2 + (-2 - -1)). Factor 2/3*f**4 - j*f**5 + 2/3*f**3 + 0 - 2/3*f**2 + 0*f.
-2*f**2*(f - 1)**2*(f + 1)/3
Let q(x) be the second derivative of x**7/14 - 3*x**6/50 - 3*x**5/50 + 7*x. Determine r so that q(r) = 0.
-2/5, 0, 1
Suppose -2*z + 4*z**2 - 2*z - 10*z**3 + 9*z**3 = 0. Calculate z.
0, 2
Let r(h) be the first derivative of -4/9*h - 5/18*h**4 - 5 - 2/3*h**3 - 2/45*h**5 - 7/9*h**2. Suppose r(u) = 0. What is u?
-2, -1
Find j, given that -233*j**3 + 57*j**4 + 293*j**4 - 53*j**2 - 120*j**5 + 163*j**2 + 15*j - 112*j**3 - 10 = 0.
-1/4, 1/2, 2/3, 1
Let l(u) = -9*u**3 - 29*u**2 - 13*u + 3. Let c(b) = -9*b**3 - 30*b**2 - 13*b + 4. Let n = -20 - -14. Let a(w) = n*l(w) + 5*c(w). Factor a(i).
(i + 2)*(3*i + 1)**2
Suppose 3*k + 5 = 14. Let z(t) = 3*t**3 - 2*t**2 - 2*t + 3. Let h be z(1). Factor 4/5 + 4*i + 23/5*i**h + 7/5*i**k.
(i + 1)*(i + 2)*(7*i + 2)/5
Factor -7*d**2 + 4*d + 14*d**2 - 4 + d + 2.
(d + 1)*(7*d - 2)
Let u(t) = -t. Let o(z) = -6*z**2 - 5*z. Let j(y) = -o(y) + 6*u(y). Let d(f) = -2*f + f + 8*f**2 - 3*f**2. Let a(r) = -7*d(r) + 6*j(r). Factor a(l).
l*(l + 1)
Let o(t) be the third derivative of 7*t**6/1440 + t**5/96 - t**4/48 - t**3/2 + t**2. Let w(b) be the first derivative of o(b). Suppose w(n) = 0. What is n?
-1, 2/7
Suppose 0 = 2*r - 5 + 1. Suppose 7*u - r*u = 60. Find y such that -4*y**3 - 22*y**4 - 3*y**2 + 3*y**2 + u*y**4 = 0.
-2/5, 0
Let u(l) be the third derivative of -l**5/240 + l**4/3 - 32*l**3/3 + 3*l**2 + 6. Factor u(a).
-(a - 16)**2/4
Suppose -3*d + 5*i - 70 = 0, 2*i + 0*i - 4 = 0. Let r be 5/(-18) + (-10)/d. Factor 0*x + 2/9*x**2 - r.
2*(x - 1)*(x + 1)/9
Suppose -2*k + 5*y + 18 = 0, 3*k - 2*k - 12 = 4*y. Let j be (-4)/10 + k/10. Let -1/3*r**2 + 2/3*r + j = 0. Calculate r.
0, 2
Let l(j) = -j**2 - 5*j - 1. Let u be l(-4). Factor 4*w + 3*w**2 + 5*w + 12 + u*w.
3*(w + 2)**2
Suppose 0 = 5*y - 5 - 5. Factor -y*x**4 - 2*x**3 + 6 - 6 + 2*x + 9*x**4 - 7*x**2.
x*(x - 1)*(x + 1)*(7*x - 2)
Let b(x) = 3*x**2 + 11*x + 5. Let c(h) = h + 1. Let v(a) = a**2 - 9*a - 5. Let w be v(10). Let z(l) = w*c(l) - b(l). Factor z(n).
-3*n*(n + 2)
Let c(u) be the first derivative of -u**6/3 + 4*u**5/5 + 3*u**4/2 - 8*u**3/3 - 4*u**2 + 16. Suppose c(l) = 0. What is l?
-1, 0, 2
Let -15*h**3 - 162*h**2 + 20*h + 0*h**4 + 142*h**2 + 10*h**4 + 5*h**5 = 0. What is h?
-2, 0, 1
Let b(x) be the third derivative of -3*x**8/896 - x**7/280 + x**6/120 + x**5/80 + x**4/192 + x**2. What is q in b(q) = 0?
-1, -1/3, 0, 1
Suppose 6 = 3*p - 3. Suppose -5*u = -12 - p. Solve -12*z**4 - 3*z**5 - 18*z**3 + 36*z**4 - 6*z**5 + u*z = 0 for z.
-1/3, 0, 1
Suppose -3*n = 4*b - 7, -4*b + b + 2*n + 18 = 0. Let d = 6 - b. Suppose 0*r**3 + r**d + r**3 + r + r**2 = 0. What is r?
-1, 0
Suppose -4*k = 3*q, 28 = -0*q + 4*q - 4*k. Let b be 0 + 4 - (-2)/(-2). Find t such that -2/7*t**2 + 0*t + 4/7*t**b + 0 - 2/7*t**q = 0.
0, 1
Let w(f) be the third derivative of 2/9*f**3 + 0*f + 2*f**2 + 1/180*f**5 + 0 + 1/18*f**4. Let w(d) = 0. What is d?
-2
Let y(x) = -x - 5. Let u be y(-6). Let z = 6 - u. Find o such that z*o - 4*o - 5*o - 2*o**2 = 0.
-2, 0
Let k(p) be the first derivative of -p**6/8 - 3*p**5/20 + 3*p**4/8 - 60. Factor k(o).
-3*o**3*(o - 1)*(o + 2)/4
Factor -2*f**2 + 0 + 0*f**3 + 4/3*f + 2/