 1
Let s(z) = z**3 - 3*z**2 + 4*z - 2. Let j be s(2). Let r(a) be the second derivative of 7/3*a**4 - 49/20*a**5 + 0*a**j - 2/3*a**3 - a + 0. Factor r(k).
-k*(7*k - 2)**2
Let x(g) be the second derivative of g**7/3 + 3*g**6/5 - g**5/2 - 3*g**4/2 - 2*g**3/3 - 9*g. Solve x(p) = 0 for p.
-1, -2/7, 0, 1
Let n(q) be the third derivative of -q**9/5040 - q**8/2240 - 7*q**4/24 - 9*q**2. Let j(m) be the second derivative of n(m). Solve j(f) = 0 for f.
-1, 0
Let u(i) = 16*i**2. Let k be u(-1). Suppose 5*v - 3*j + 0 - 4 = 0, -4*v + k = 4*j. Find w, given that 1/2*w**4 - 1/2*w**v + 1/2*w**3 + 0 - 1/2*w**5 + 0*w = 0.
-1, 0, 1
Let t(g) = -g**4 + g**3 - g**2 + g - 1. Let k(q) = 64*q**4 - 54*q**3 - 38*q**2 + 10*q + 32. Let v(n) = 2*k(n) + 28*t(n). Factor v(x).
4*(x - 1)**2*(5*x + 3)**2
Let o(r) = -51*r**5 - 30*r**4 + 60*r**3 - 21*r**2 + 21*r - 21. Let z(f) = 5*f**5 + 3*f**4 - 6*f**3 + 2*f**2 - 2*f + 2. Let u(y) = 2*o(y) + 21*z(y). Factor u(j).
3*j**3*(j - 1)*(j + 2)
Let f(a) be the second derivative of -a**4/24 - 7*a**3/36 - a**2/6 - a. Solve f(q) = 0 for q.
-2, -1/3
Let f(y) = 5*y**4 - 9*y**3 + 4*y**2 + 2*y - 2. Let q(p) = 10*p**4 - 19*p**3 + 9*p**2 + 5*p - 5. Let h(k) = -15*f(k) + 6*q(k). Determine d, given that h(d) = 0.
0, 2/5, 1
Suppose -24 = -3*y + 3*s, 0 = 5*y + 2*s + 3*s - 40. Determine f, given that 5*f**2 - y - 4*f**2 + f**2 = 0.
-2, 2
Let d be (-6)/11*2/1098. Let x = d - -21920/671. Suppose -500/9*i**2 - 16/9 + 658/9*i**3 + 152/9*i - x*i**4 = 0. What is i?
2/7, 2/3, 1
Suppose 0*k + 1/3*k**2 - 1/3 = 0. Calculate k.
-1, 1
Let q(h) be the first derivative of h**7/147 - h**6/105 - h**5/70 + h**4/42 - h + 2. Let z(m) be the first derivative of q(m). Find t, given that z(t) = 0.
-1, 0, 1
Let a(r) be the first derivative of r**4/4 + 2*r**3/3 - r**2/2 - r + 4. Let w(g) = -g**2 + g + 1. Let m(x) = -a(x) - w(x). Factor m(q).
-q**2*(q + 1)
Let x be 6/(-9) - 24/(-9). Factor 4*v**2 - 4*v**x + 3*v**2 + 12 - 12*v.
3*(v - 2)**2
Let s be (-5)/(90/4) - 1700/(-2142). Find p such that 0 + 0*p + 2/7*p**5 - s*p**4 + 2/7*p**3 + 0*p**2 = 0.
0, 1
Let s(x) be the second derivative of 1/6*x**3 + 7*x - 1/12*x**4 - 1/6*x**2 + 1/60*x**5 + 0. Let s(o) = 0. What is o?
1
Let w(p) be the first derivative of p**4 + p**3/3 - 2*p**2 - p + 10. Find n such that w(n) = 0.
-1, -1/4, 1
Suppose 3*f - 117 = -0*f. Let s = f - 155/4. Factor 0*i**2 + 0*i**4 + s*i**3 + 0*i + 0 - 1/4*i**5.
-i**3*(i - 1)*(i + 1)/4
Let n be 0*((-9)/(-6) + -2). Suppose -1 = -d - n. Factor 4*l**2 - l**2 - 2*l + d - 2*l**2.
(l - 1)**2
Factor 1/5*x**3 + 0 - 1/5*x - 1/5*x**2 + 1/5*x**4.
x*(x - 1)*(x + 1)**2/5
Let y be (-16)/72 - (-37)/126. Let h(r) be the second derivative of -1/12*r**4 + 0*r**2 - r - 1/20*r**5 + 0 + 0*r**3 + 1/6*r**6 - y*r**7. Factor h(n).
-n**2*(n - 1)**2*(3*n + 1)
Determine p so that -p**4 - 3*p**3 - 4*p + 5*p**3 + 0 - 4 + 3*p**2 = 0.
-1, 2
Let m(v) = -56*v**3 + 98*v**2 - 264*v + 142. Let h be 1 + 1 - -11*6. Let u(c) = 5*c**3 - 9*c**2 + 24*c - 13. Let d(y) = h*u(y) + 6*m(y). Factor d(b).
4*(b - 2)**3
Suppose -3*m - r - 1 = 4*r, 2*r = 4*m - 16. Determine y so that -7*y**3 - 6*y**4 + 8*y**3 + y**m + 6*y**5 + 14*y**4 = 0.
-1, -1/3, 0
Suppose -4/7*r**4 + 12/7*r**5 - 4/7 - 24/7*r**3 + 8/7*r**2 + 12/7*r = 0. What is r?
-1, 1/3, 1
Let w = 3 + -1. Suppose 4*s = 2*h + 8, -w*s + 0*h + 12 = 3*h. Factor -2*q**5 - 4*q**4 + 8*q**2 + 0*q**3 - 2*q + 12*q**4 - 12*q**s.
-2*q*(q - 1)**4
Factor 2/7 + 1/7*v**2 - 3/7*v.
(v - 2)*(v - 1)/7
Let w(i) be the third derivative of i**6/120 + i**5/60 - 7*i**2. Factor w(g).
g**2*(g + 1)
Let b(j) = j**4 - j**3 - j + 1. Let x(l) = -l**5 + 7*l**4 - 4*l**3 - 2*l**2 - 7*l + 7. Let h(v) = 6*b(v) - x(v). Suppose h(w) = 0. Calculate w.
-1, 1
Let o(j) = j**2 + 3. Let h(g) be the second derivative of -g**4/3 - g**3/6 - 13*g**2/2 - g. Let a(y) = 4*h(y) + 18*o(y). Let a(q) = 0. Calculate q.
1
Let l = -149/60 - -56/15. Factor l*b - 3/4*b**2 - 1/2.
-(b - 1)*(3*b - 2)/4
Let o = -526/5 - -110. Factor o*y**2 + 2/5*y**4 + 16/5*y + 0 + 12/5*y**3.
2*y*(y + 2)**3/5
Let u(s) be the second derivative of s**6/1620 - s**5/540 - s**3/6 - s. Let i(d) be the second derivative of u(d). Determine p so that i(p) = 0.
0, 1
Let f(m) be the second derivative of -m**9/6048 - m**8/1680 - m**7/1680 - 2*m**3/3 - 4*m. Let y(x) be the second derivative of f(x). Factor y(d).
-d**3*(d + 1)**2/2
Let b(k) = -k**3 + 3*k**2 + 8*k - 3. Let a(w) = -w. Let h(y) = 14*a(y) + 2*b(y). Factor h(n).
-2*(n - 3)*(n - 1)*(n + 1)
Let u(s) be the second derivative of s**4/24 + s**3/12 - s**2/2 - 21*s. Let u(v) = 0. What is v?
-2, 1
Let j(o) = -o**3 + 3*o**2 + 3*o - 3. Let u be j(3). Let p(c) = 2*c - 7. Let z be p(u). Factor 0*w**3 + z*w**5 + 2*w**3 + w**5 + 8*w**4.
2*w**3*(w + 1)*(3*w + 1)
Factor -6/5 - 9/5*q**3 - 19/5*q - 1/5*q**4 - 21/5*q**2.
-(q + 1)**3*(q + 6)/5
Let n(k) be the second derivative of k**6/75 + k**5/50 - 2*k**4/15 - 4*k**3/15 + 44*k. Factor n(j).
2*j*(j - 2)*(j + 1)*(j + 2)/5
Let v(y) = -y. Let z be v(-3). Let a(r) = r**2 - 12*r + 32. Let m be a(4). What is h in 0*h**z + 0 + 2/5*h**2 - 2/5*h**4 + m*h = 0?
-1, 0, 1
Factor -2/11*o + 0*o**3 + 4/11*o**4 + 0 - 4/11*o**2 + 2/11*o**5.
2*o*(o - 1)*(o + 1)**3/11
Let q(b) = -2*b**3 - 9*b**2 + 3*b - 5. Let s(r) = r**3 + 5*r**2 - 2*r + 3. Let m(a) = -3*q(a) - 5*s(a). Find y, given that m(y) = 0.
-1, 0
Let r(a) be the second derivative of 2*a**6/75 + a**5/25 - a**4/60 - a**3/30 - 34*a. Let r(c) = 0. What is c?
-1, -1/2, 0, 1/2
Let s(j) be the first derivative of -j**4/2 + 6*j**3 - 27*j**2 + 54*j + 6. Factor s(b).
-2*(b - 3)**3
Determine n so that 12*n - 6 - 16*n + 7*n - 3*n**3 + 6*n**2 = 0.
-1, 1, 2
Let u(i) be the first derivative of -2/3*i**3 - i**2 + 4*i - 1. Factor u(r).
-2*(r - 1)*(r + 2)
Suppose -49*a = -39*a. Factor a*s + 0 + 4/7*s**2 + 0*s**3 - 4/7*s**4.
-4*s**2*(s - 1)*(s + 1)/7
Let n(z) be the first derivative of -4*z - 21/5*z**5 - 11/2*z**4 + 5*z**3 + 6*z**2 + 7. What is p in n(p) = 0?
-1, 2/7, 2/3
Let i(m) be the third derivative of -m**5/40 - m**4/8 - m**3/4 - 11*m**2. Factor i(w).
-3*(w + 1)**2/2
Let w(q) = 16*q**5 - 28*q**4 + 16*q**3 - 20*q**2 + 20*q - 20. Let s(g) = g**5 - g**4 + g**3 - g**2 + g - 1. Let f(k) = -20*s(k) + w(k). Solve f(r) = 0 for r.
-1, 0
Find m such that -1/3 + 2/3*m - 1/3*m**2 = 0.
1
Find a, given that 7*a**3 - 8*a + a**3 + 9*a**2 - 11*a**3 + 2*a = 0.
0, 1, 2
Factor 0 + 2/13*n**2 + 4/13*n.
2*n*(n + 2)/13
Factor 2/9*b**4 - 4/9*b**2 - 2/9*b**5 + 2/9 + 4/9*b**3 - 2/9*b.
-2*(b - 1)**3*(b + 1)**2/9
Let g = 10 - 4. Let z be 4/g - 4/24. Factor 1/2*k**5 - 1/2*k**4 + 0 + 1/2*k**2 + 0*k - z*k**3.
k**2*(k - 1)**2*(k + 1)/2
Let l(d) be the third derivative of -1/336*d**8 + 0 + 1/6*d**3 - 2*d**2 + 1/6*d**5 - 1/12*d**6 + 1/42*d**7 - 5/24*d**4 + 0*d. What is y in l(y) = 0?
1
Let p be ((-2)/(-14))/(-4 + (-152)/(-28)). Let g(q) be the first derivative of -6/5*q - p*q**4 - 7/5*q**2 + 3 - 2/3*q**3. Determine z so that g(z) = 0.
-3, -1
Let h(r) be the second derivative of r**4/12 + 6*r. Let v(n) = n**2 + n. Let t(d) = -2*h(d) + v(d). Factor t(q).
-q*(q - 1)
Let d be (-50)/6*((-154)/35)/11. Factor -2/3*q**3 - 8/3 - 16/3*q - d*q**2.
-2*(q + 1)*(q + 2)**2/3
Find p such that -3*p + 2*p - 41*p**2 + 21*p**2 + 21*p**2 = 0.
0, 1
Factor 163 - 77 - 78 - 12*u + 4*u**2 + 0*u**2.
4*(u - 2)*(u - 1)
Solve -96*u**3 + 485*u**4 - 236*u**4 - 267*u**4 - 100*u - 170*u**2 = 0.
-2, -5/3, 0
Let k(m) be the third derivative of -5*m**2 + 0*m**3 + 1/240*m**5 + 0 + 0*m**4 + 1/480*m**6 + 0*m. Let k(l) = 0. Calculate l.
-1, 0
Let n(i) = 2*i + 1. Let w be n(3). Let -54*x**2 - 21*x**4 + 19*x**2 + 39*x + 1 - w + 69*x**3 - 46*x**2 = 0. What is x?
2/7, 1
Let o(a) be the first derivative of -a**4/4 + 4*a**3/3 - a**2/2 - 6*a + 48. Let o(g) = 0. Calculate g.
-1, 2, 3
Let r be (4/56*-4)/(36/(-21)). Let l(n) be the first derivative of 1/2*n - r*n**3 + 0*n**2 - 3. What is w in l(w) = 0?
-1, 1
Factor 20*h**2 - 25/2*h - 3*h**3 - 1/2*h**5 + 0 - 4*h**4.
-h*(h - 1)**2*(h + 5)**2/2
Let k(f) be the third derivative of 5/24*f**4 + 5/6*f**3 - 7/60*f**5 + 2*f**2 + 0*f + 0. Let m(g) = 7*g**2 - 5*g - 4. Let x(l) = 4*k(l) + 6*m(l). Factor x(v).
2*(v - 1)*(7*v + 2)
Factor 27/2*t**2 - 3/2*t**3 + 30 - 36*t.
-3*(t - 5)*(t - 2)**2/2
Suppose j + 6 = 3*j. Suppose j*w - w = 6. Factor -r + w*r**2 - 5*r**2 + r - r - r**3.
-r*(r 