- 16*s**2. Factor h(f).
(f + 10)**2/4
Let q(t) be the first derivative of -t**6/12 + t**5/2 - 9*t**4/8 + 7*t**3/6 - t**2/2 - 16. Find y, given that q(y) = 0.
0, 1, 2
Let a(u) be the third derivative of -u**5/45 - 7*u**4/9 - 2*u**2 - 29*u. Factor a(k).
-4*k*(k + 14)/3
Let s be (-40)/(-7) - (-2)/7. Factor -s*q**2 - 3*q**4 - 3*q + 3*q**3 + 6*q**4 + q**2 + 2*q**2.
3*q*(q - 1)*(q + 1)**2
What is d in 2/13*d**5 + 0*d**2 + 0*d - 6/13*d**4 + 4/13*d**3 + 0 = 0?
0, 1, 2
Let a(c) = c**2 - c - 1. Let p be a(1). Let v = p + 4. Factor 2*f**2 + 3*f**3 - 3*f**v + 2*f**3 - 2*f - 2.
2*(f - 1)*(f + 1)**2
Let v(w) be the third derivative of -7/120*w**6 + 0 + 0*w - w**2 + 7/24*w**4 + 1/3*w**3 - 1/30*w**5. Suppose v(i) = 0. What is i?
-1, -2/7, 1
Let s be 572/(-2352) - 1/(-4). Let q(n) be the second derivative of 1/21*n**3 + 0 - 1/7*n**2 - 3*n + 1/21*n**4 - 1/35*n**5 - 1/105*n**6 + s*n**7. Factor q(y).
2*(y - 1)**3*(y + 1)**2/7
Let k(j) be the first derivative of -j**3/18 - j**2/4 - j/3 + 20. Factor k(a).
-(a + 1)*(a + 2)/6
Let s(a) = 24*a**3 - 24*a**2 - 4*a + 12. Let l(d) = -25*d**3 + 23*d**2 + 4*d - 12. Let t(v) = 4*l(v) + 5*s(v). Factor t(g).
4*(g - 1)**2*(5*g + 3)
Let s(d) be the first derivative of d**5/10 - d**4/6 - d**3/3 + d**2 - 3*d + 3. Let p(t) be the first derivative of s(t). Suppose p(w) = 0. Calculate w.
-1, 1
Let b(k) be the first derivative of 2*k**2 + 4 + k + 4/3*k**3. Factor b(h).
(2*h + 1)**2
Let q(c) = 11*c**4 + 23*c**3 - 8*c**2 - 48*c + 36. Let k(m) = 10*m**4 + 22*m**3 - 8*m**2 - 48*m + 36. Let x(w) = 7*k(w) - 6*q(w). Factor x(t).
4*(t - 1)**2*(t + 3)**2
Let q = 10/27 + -73/270. Let y(o) be the second derivative of 2*o + 1/10*o**2 + 1/20*o**4 + 0 - q*o**3 - 1/100*o**5. Factor y(c).
-(c - 1)**3/5
Let p be 12/2 + 0 + -3. Suppose -4*k - 8/3*k**p - 2/3 - 6*k**2 = 0. Calculate k.
-1, -1/4
Let j be (9/(-3) + 4)/(10/30). Suppose 1/3*a + 0 + 5*a**j - 3*a**4 - 7/3*a**2 = 0. What is a?
0, 1/3, 1
Let t(g) be the first derivative of g**4/2 - 4*g**3/3 - 13. Factor t(k).
2*k**2*(k - 2)
Suppose -q - 4*x - 46 = -4*q, 0 = -q - 2*x + 2. Let 4*t - 14*t**5 - 4*t**3 + 3*t**3 + q*t**3 + 18*t**4 + t**3 - 18*t**2 = 0. Calculate t.
-1, 0, 2/7, 1
Let s(q) be the first derivative of q**4/8 - 5*q**3/2 + 75*q**2/4 - 125*q/2 - 4. Suppose s(c) = 0. Calculate c.
5
Let u be 3 + 2/4*2. Let x(z) be the first derivative of 0*z - 6/35*z**5 + 3/14*z**u + 1/21*z**6 + 2 + 0*z**2 - 2/21*z**3. Find g, given that x(g) = 0.
0, 1
Let t(n) = 5*n**3 + 31*n**2 + 25*n - 1. Suppose -4 = 2*o - 4*o. Let c(p) = -p**3 - 6*p**2 - 5*p. Let k(d) = o*t(d) + 11*c(d). Factor k(m).
-(m + 1)**2*(m + 2)
Suppose -3*s - 17 = 7. Let u be s/12 + 16/6. Factor t**2 + 2*t + t**2 + t**u + 1 - 2*t**2.
(t + 1)**2
Let p(j) = -7*j**3 + 18*j**3 - 10*j**3 + 6 + 2*j - 2*j**2 - 2*j**3. Let f(w) = w**2 - w - 1. Let l(i) = -5*f(i) - p(i). Solve l(b) = 0.
1
Let y be 58/551 - (-142)/95. Suppose 8/5*x + 2/5 + 2/5*x**4 + 12/5*x**2 + y*x**3 = 0. What is x?
-1
Factor -22*l**3 + 6*l**4 - 3*l**5 + 32*l**3 - 13*l**3.
-3*l**3*(l - 1)**2
Suppose n = 5*u - 3*n - 19, -16 = -5*u + n. Suppose 15 = -u*h - h + 5*q, 5*q - 15 = 0. Factor h + 1/3*k**2 + 1/3*k.
k*(k + 1)/3
Suppose 5*k = 4*k + 6. Let r(t) be the third derivative of 0*t - 1/3*t**3 + 1/12*t**4 + t**2 - 1/60*t**k + 0 + 1/30*t**5. Factor r(j).
-2*(j - 1)**2*(j + 1)
Let b(d) = -13*d**3 - 6*d**2 + 12*d - 7. Let o(i) = 7*i**3 + 3*i**2 - 6*i + 4. Let g(j) = -4*b(j) - 7*o(j). Determine p so that g(p) = 0.
-2, 0, 1
Solve 0*x**3 + 0*x + 0 + 2/5*x**2 - 2/5*x**4 = 0.
-1, 0, 1
Let c be 0/((1/((-4)/8))/(-1)). What is b in 2/7*b**2 + c + 2/7*b = 0?
-1, 0
Let v = -22 + 24. Factor 134*f + 4*f**3 + 0*f**3 - 2*f**2 - v*f**4 - 134*f.
-2*f**2*(f - 1)**2
Let p be 8/2 + 117/(-22). Let v = 13/11 - p. Find t such that 4*t**2 + v*t**3 + 1/2*t**4 + 0 + 2*t = 0.
-2, -1, 0
Let y(l) = l**2 + 1. Let s(f) = -2*f**2 + 6*f + 6. Let k(n) = -n**3 - 9*n**2 - 7*n + 5. Let b be k(-8). Let m(q) = b*y(q) - s(q). Determine i so that m(i) = 0.
-3
Let w(m) be the second derivative of m**6/195 - 3*m**5/65 + 3*m**4/26 - 5*m. Determine t so that w(t) = 0.
0, 3
Let y(q) be the first derivative of 15*q**4/8 + 50*q**3/9 + 65*q**2/12 + 5*q/3 - 12. What is l in y(l) = 0?
-1, -2/9
Let i = 119 + -473/4. Factor -1/4*y + 1/2 - i*y**2.
-(y + 1)*(3*y - 2)/4
Let i(s) be the third derivative of s**5/50 + 7*s**4/30 + 8*s**3/15 - 23*s**2. What is h in i(h) = 0?
-4, -2/3
Let a be -3 + 822/180 - (-2)/(-12). Determine n so that -n**2 + a*n**3 + 0 - 2/5*n = 0.
-2/7, 0, 1
Let t(r) = -r - 1. Let l be (-14)/(0 + 2) - -2. Let n be t(l). Factor -3*m**3 + n*m**3 - m**2 + 2*m**2.
m**2*(m + 1)
Let l(k) be the third derivative of 0*k + 0 + 1/20*k**4 + 8*k**2 + 0*k**3 - 7/100*k**5. What is d in l(d) = 0?
0, 2/7
Suppose -10 = -2*s - 6. Solve 0*d**2 + s*d + d**3 + d**4 + 5*d**2 + 3*d**3 = 0.
-2, -1, 0
Let k be 3/(-8) - 255/(-360). Factor 1/3*y**4 - 5/3*y + k*y**3 - y**2 - 2/3.
(y - 2)*(y + 1)**3/3
Let l(c) = -c**3 - 6*c**2 + 5*c - 7. Let u be l(-7). Let 3 + u*m**2 - 1 - 6*m**2 + 3*m = 0. What is m?
-2, -1
Let r(y) be the third derivative of -y**6/450 - y**5/450 + y**4/90 + y**3/45 - 46*y**2. Let r(f) = 0. What is f?
-1, -1/2, 1
Let z(h) = -h**4 + 8*h**3 + 3. Let u(o) = -o**4 + 16*o**3 + 7. Let i(k) = -3*u(k) + 7*z(k). Factor i(b).
-4*b**3*(b - 2)
Let n be 88/22 + ((-99)/15 - -3). Find b such that 4/5*b**2 + 0 + n*b = 0.
-1/2, 0
Let p be ((-6)/(-3) - -1)/1. Factor 0*n - 15*n - 12*n**2 + p*n - 3*n**3.
-3*n*(n + 2)**2
Let g(y) be the second derivative of -y**5/50 + y**4/6 - 8*y**3/15 + 4*y**2/5 + 7*y. Suppose g(u) = 0. Calculate u.
1, 2
Suppose -3 = -m + 2*m - b, 3*b = -4*m - 12. Let o = 5 + m. Factor 0*n + 0 + 2*n**4 - o*n**3 - 2/3*n**5 + 2/3*n**2.
-2*n**2*(n - 1)**3/3
Suppose 1/4 + 1/4*f**3 + 3/4*f**2 + 3/4*f = 0. What is f?
-1
Let i(l) be the second derivative of -l**8/4200 - l**7/1050 - l**6/900 + l**3/3 - 3*l. Let w(a) be the second derivative of i(a). Solve w(z) = 0.
-1, 0
Let a(n) be the first derivative of 4/5*n**5 - 8/3*n**3 + 3*n**2 + 2 - 3*n**4 + 4*n + n**6. Let a(r) = 0. What is r?
-1, -2/3, 1
Let h(x) be the second derivative of x**4/4 + 5*x**3/6 - x**2 + 19*x. Factor h(y).
(y + 2)*(3*y - 1)
Let k(t) be the third derivative of 0*t**3 - 3*t**2 + 0*t - 1/150*t**5 - 1/150*t**6 + 0*t**4 - 1/525*t**7 + 0. Factor k(s).
-2*s**2*(s + 1)**2/5
Let x = 3 - 3. Suppose x = 2*i - i - 24. Let -28*p**3 - 132*p**2 + 156*p**3 + i*p + 36*p**2 - 2 = 0. Calculate p.
1/4
Let c(j) be the second derivative of -5*j**7/42 - 5*j**6/3 - 33*j**5/4 - 50*j**4/3 - 40*j**3/3 + 4*j. Factor c(g).
-5*g*(g + 1)**2*(g + 4)**2
Let c(b) = b**2 + b. Let d(m) = m**3 + 2*m**2 + m. Let a(k) = -2*c(k) + d(k). Determine u, given that a(u) = 0.
-1, 0, 1
Let k(c) be the first derivative of -2*c**5/5 - c**4 + 2*c**3 + 8*c**2 + 8*c - 8. Factor k(h).
-2*(h - 2)*(h + 1)**2*(h + 2)
Let w(m) be the first derivative of 1/10*m**2 + 4 - 1/15*m**3 + 2/5*m. Factor w(t).
-(t - 2)*(t + 1)/5
Suppose 12 = 2*d - d. Let m = -8 + d. Factor 8*u**3 - 9*u**3 + 3*u**m - 4*u**4 + u + u**2.
-u*(u - 1)*(u + 1)**2
Let r be 75/10*(-8)/(-10). Let q(m) be the first derivative of -1/4*m**4 - 1/2*m - 1/12*m**r + 3/10*m**5 - 1/3*m**3 + 3/4*m**2 - 3. Suppose q(a) = 0. What is a?
-1, 1
Let b(m) = 4*m**2 + 1. Let n be b(1). Determine i, given that -i**5 + 3*i**n + 2*i**4 - 4*i**4 = 0.
0, 1
Let q(k) be the first derivative of 9 + 10/3*k**3 + 3*k**5 + 0*k**2 - 2/3*k**6 - 5*k**4 - k. Factor q(s).
-(s - 1)**4*(4*s + 1)
Let u(a) be the second derivative of 0 + 3/8*a**3 + 1/16*a**4 + 3*a + 3/4*a**2. Factor u(l).
3*(l + 1)*(l + 2)/4
Let b = 8 - 2. Find t such that -6*t**4 + 13*t**4 + b - 4*t**4 + 27*t**2 - 21*t - 15*t**3 = 0.
1, 2
Let j = -21 - -23. Factor 0 + 14/9*n**j + 4/9*n.
2*n*(7*n + 2)/9
Suppose 2/11*b - 2/11*b**3 - 4/11 + 4/11*b**2 = 0. What is b?
-1, 1, 2
Suppose 6 + 20*m**4 + 20*m**3 - 3 - 20*m - 8 - 15*m**2 = 0. Calculate m.
-1, -1/2, 1
Suppose 0*t + 4/5*t**2 + 0 = 0. What is t?
0
Suppose 12*m = 25*m - 26. Factor 1/5*f + 2/5*f**m - 1/5*f**3 - 2/5.
-(f - 2)*(f - 1)*(f + 1)/5
Let v(g) be the third derivative of 0 + 6*g**2 + 1/12*g**4 + 1/60*g**5 + 0*g + 1/6*g**3. Determine q, given that v(q) = 0.
-1
Let y(q) be the third derivative of -q**9/30240 - q**8/13440 + q**7/5040 + q**6/1440 - q**4/8 + 5*q**2. Let w(m) be the sec