Factor the following polynomial 3y^2-13y+4

There is no GCF, so just factor it out: (3y−1)(y−4) OR you can have (y-4)(3y-1).

Okay multiply the coefficients of x² and the constant;
 
3×4=12 

How can we split -13 so that the numbers multiply to give 12?

-12×(-1)=12 and -12-1=-13 

Therefore, rewrite the equation; 

3y²-1y-12y+4
y(3y-1)-4(3y-1) <-- make sure everything inside the brackets remains the same
(y-4)(3y-1) 

Double check by expanding; 

(y-4)(3y-1)
3y²-1y-12²+4 
3y²-13y+4 <-- this is the same equation, meaning we were correct. 

Hope I helped :) 

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.